THE SEARCH FOR THE BROKEN WINDOWS TIPPING POINT: A DOSE - RESPONSE PROPENSITY SCORE ASSESSMENT OF THE RELATIONSHIP BETWEEN DISORDER AND VIOLENT CRIME B y Alaina De Biasi Podges A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Criminal Justice Doctor of Philosophy 2020 ABSTRACT THE SEARCH FOR THE BROKEN WINDOWS TIPPING POINT: A DOSE - RESPONSE PROPENSITY SCORE ASSESSMENT OF THE RELATIONSHIP BETWEEN DISORDER AND VIOLENT CRIME By Alaina De Biasi Podges Wilson and Kelling (1982) provide a simple instruction for the implementation of order - maintenance policing: direct limited police resources to the broken windows tipping point . In doing so , they imply a certain functional form of the relationship between disorder and violent crime f the tipping point suggests that the disorder - crime relationship is best captured as a threshold effect . If this is indeed the case, then a proper test of the validity of broken windows theory should accommodate nonlinearity. To this end, this study empir ically examined the functional form of the relationship between physical disorder and violent crime rate in Detroit, Michigan utilizing a dose - response propensity score methodology. To facilitate its analysis, this study utilize d block - group level data on physical disorder, violent crime, as well as socioeconomic and land use characteristics from the Detroit record management system, Motor City Mapping project, and Census . Despite its comprehensive analysis, th e functional form of the disorder - crime relationship remains unclear. That being said, the bulk of the evidence favors a nonlinear relationship, with point. Severa l directions for future research are identified in an effort to spur the cultivation of this undeveloped avenue of research. Copyright by ALAINA DE BIASI PODGES 2020 iv This dissertation would not have been possible without the support of James Podges , husband and editor extraordinaire. v TABLE OF CONTENT S LIST OF TABLES ................................ ................................ ................................ ........................ vii LIST OF FIGURES ................................ ................................ ................................ ....................... ix CHAPTER 1: INTRODUCTION ................................ ................................ ................................ ... 1 Statement of the Problem ................................ ................................ ................................ ............ 1 Research Aims ................................ ................................ ................................ ............................. 6 Study Outline ................................ ................................ ................................ ............................... 9 CHAPTER 2: LITERATURE REVIEW ................................ ................................ ...................... 11 Broken Windows Theory ................................ ................................ ................................ .......... 11 Theoretical Foundation of the Broken Windows Theory ................................ ....................... 11 Empirical Support for Broken Windows Theory: Implications for the Broken Windows Tipping Point ................................ ................................ ................................ ......................... 18 A Closer Look: Alternative Perspectives ................................ ................................ .................. 23 Policing Disorder & The Broken Windows Tipping Point ................................ ....................... 30 What is Order - Maintenance Policing? ................................ ................................ .................. 30 Empirical Support for the Effectiveness of Policing Disorder Strategies ............................. 37 Implications for the Broken Windows Tipping Point ................................ ............................ 40 Current Study ................................ ................................ ................................ ............................ 51 CHAPTER 3: STUDY DESIGN AND IMPLEMENTATION ................................ .................... 54 Measures and Data Sources ................................ ................................ ................................ ....... 54 Analytic al Strategy ................................ ................................ ................................ .................... 66 Step 1: Modeling the conditional distribution of the treatment given covariates ................. 67 Step 2: Estimating the conditional expectation of the outcome given the treatment and GPS ................................ ................................ ................................ ................................ ............... 70 Step 3: Estimating the dose - response function to discern treatment effects ......................... 71 Sensitivity Checks ................................ ................................ ................................ ..................... 72 CHAPTER 4: ANALYSIS & RESULTS ................................ ................................ ..................... 77 Pa rametric Method ................................ ................................ ................................ .................... 77 Step 1: Parametric Approach: Modeling the conditional distribution of the treatment given covariates ................................ ................................ ................................ ............................... 77 Step 2: Parametric Approach: Estimating the conditional expectation of the outcome given the treatment and GPS ................................ ................................ ................................ ........... 94 Step 3: Parametric Approach: Estimating the dose - response function to discern treatment effect ................................ ................................ ................................ ................................ ....... 96 Semiparametric Method ................................ ................................ ................................ .......... 100 Step 1: Semiparametric Approaches: Modeling the conditional distribution of the treatment given covariates ................................ ................................ ................................ ................... 100 vi Step 2 : Semiparametric Approaches : Estimating the conditional expectation of the outcome given the treatment and GPS ................................ ................................ ............................... 101 Step 3: Semiparametric Approaches: Estimating the dose - response function to discern treatment effects ................................ ................................ ................................ ................... 102 Summary of Findings ................................ ................................ ................................ .............. 108 CHAPTER 5: DISCUSSION & CONCLUSION ................................ ................................ ....... 111 An Overview: The Search for The Broken Windows Tipping Point ................................ ...... 111 Directions for Future Research ................................ ................................ ............................... 113 Measures of Disorder ................................ ................................ ................................ .......... 113 Neighborhood Context ................................ ................................ ................................ ......... 114 Confounding Factors ................................ ................................ ................................ ........... 115 Longitudinal Data Analysis ................................ ................................ ................................ . 118 Closing Remarks ................................ ................................ ................................ ..................... 119 REFERENCES ................................ ................................ ................................ ........................... 127 vii LIST OF TABLES Table 1. Key Research Question & Hypotheses. ................................ ................................ .......... 52 Table 2. Physical Disorder Summary Statistics. ................................ ................................ ........... 58 Table 3. Principal Component Factor Analysis. ................................ ................................ ........... 59 Table 4. Control/Matching Variables: Full Sample (N = 857). ................................ .................... 65 Table 5. Physical Disorder: Goodness of Fit Statistics. ................................ ................................ 78 Table 6. Conditional Distribution of Physical Disorder given Covariates. ................................ .. 80 Table 7. Common - support Sample (N = 760). ................................ ................................ ............. 83 Table 8. Group Means from Common - support Samp le (N = 760). ................................ .............. 85 Table 9. Off - support Sample (N = 97). ................................ ................................ ......................... 87 Table 10. Off - support and Common - support Mean Differences. ................................ ................. 89 Table 11. Adjustment for the GPS: Group 1. ................................ ................................ ................ 90 Table 12. Adjustment for the GPS: Group 2. ................................ ................................ ................ 91 Table 13. Adjustment for the GPS: Group 3. ................................ ................................ ................ 93 Table 14. Base. ................................ ................................ ................................ .............................. 95 Table 15. Quadratic. ................................ ................................ ................................ ...................... 95 Table 16. Cubic. ................................ ................................ ................................ ........................... 95 Table 17. Lik elihood Ratio Tests. ................................ ................................ ................................ . 96 Table 18. Penalized Spline Model. ................................ ................................ ............................. 102 Table 19. Radial Spline Model. ................................ ................................ ................................ .. 102 viii Table 20. Hypotheses & Support. ................................ ................................ ............................... 110 ix LIST OF FIGURES Figure 1. Theoretically - derived Interpretations of the Relationship between Disorder and Violent. ................................ ................................ ................................ ................................ ....................... 14 Figure 2. The Broken Windows Developmenta l Sequence. ................................ ......................... 18 Natural Hazard: Implications for Understanding the Relationship between Disorder and Fear of Environmental/Ecological Psychology , 18 (5), p. 631. ................................ ................................ ................................ ................................ ............ 28 Weisburd, J.C. Hinkle, A. Braga, and A. Wooditch, 2015, Journal of Research in Crim e and Delinquency , 52 (4), p. 594. ................................ ................................ ................................ ........... 30 Figure 5. Shorthand descriptions of some property - act Center for Problem - Oriented Policing, 11, p.10 ................................ ................................ ........... 33 Figure 6. Scout Car Areas within Precincts. ................................ ................................ ................. 36 Figure 7. The Broken Windows Tipping Point: Crime Prevention vs. Crime Reduct ion. ........... 44 Figure 8. Hypotheses H1, H2a, H2b, and H3. ................................ ................................ .............. 53 Figure 9. Selected Block - groups. ................................ ................................ ................................ .. 54 Figure 10. Physical Disorder. ................................ ................................ ................................ ........ 59 Figure 11. Physical Disorder: Kernel Density Estimate. ................................ .............................. 60 Figure 12. Violent Crime Rate (2015). ................................ ................................ ......................... 61 Figure 13. Violent Crime Rate (2015): Kernel Density Estimate. ................................ ................ 62 Figure 14. Variograph Model. ................................ ................................ ................................ ...... 64 Figure 15. Theoretical Densities. ................................ ................................ ................................ .. 78 x Figure 16. Common - support (gray) and Off - support (red) Block - groups ................................ .... 87 Figure 17. Interaction Models: Dose - response Functions across Model Specifications. ............. 97 Figure 18 . Noninteraction Models: Dose - response Functions across Model Specifications. ...... 98 Figure 19. Combined Display of Parametric Methods. ................................ ................................ 99 Figure 20. Semiparametric Methods. ................................ ................................ .......................... 103 Figure 21. Combined Display of Semiparametric Methods. ................................ ...................... 104 Figure 22. Spline Methods w ith Relevant Treatment Levels Highlighted. ................................ 106 Figure 23. Inverse Weighting Kernel Method with Relevant Treatment Levels Highlighted. ... 107 Figure 24. Parametric & Semiparametric Methods. ................................ ................................ ... 109 1 CHAPTER 1: INTRODUCTION Statement of the Problem In a seminal article published in The Atlantic Monthly , James Q. Wilson and George L. Kelling (1982) first describe d broken windows theory (BWT) as a developmental sequence of events in which unattended minor issues produce deleterious consequences for neighborhoods . These issues encompass physical conditions ( e.g., aba ndoned structures /lots , graffiti, trash, and overgrown vegetation ) and social nuisances ( e.g., panhandling, loitering, and public drinking ) that signify neighborhood decline and inspire fear within residents , hereon referred to collectively as disorder. Th e perpetuation of violent crime - a controversial topic of study in broken windows research is foremost among the consequences of unattended disorder . However, disorder has also been linked to high levels of fear ( e.g., Taylor & Shumaker, 1990; Covington & Taylor, 1991; LaGrange, Ferraro, & Supancic, 1992; Ross & Jang, 20 0 0 ; Markowitz et al. , 2001; Spelman, 2004 ), low levels of informal social control and collective efficacy ( e.g., Foster - Fishman et al., 2007; Kleinhans & Bolt, 201 4 ; Wickes & Hipp, 2018; Wickes, Broidy, & Hipp, 201 8 ), as well as poor mental and physical health ( e.g., Cutrona et al., 2000; Ross & Mirowsky, 2001; Hill, Ross, & Angel, 2005 ). In light of these consequences, e fforts to reduce disorder within neighborhoods are of great interest to residents, police, and policymakers, alike. That being said , simple solution to the problem of neighborhood disorder - stop small problems before they becom e much larger - has incited much debate, resulting in a voluminous and mixed body of research which questions the validity of BWT (e.g., Skogan, 1990; Sampson & Raudenbush, 1999; Kelling & Sousa, 2001; Braga et al., 2015; Weisburd et al., 2015 ). 2 While the mechanisms through which disorder affects violent crime are hotly debated, order - maintenance ( or broken windows ) policing is still a popular means of disrupt ing the broken windows cycle and restor ing order within neighborhoods . In keeping with Wi lson and original conceptualization, order - maintenance polic ing addresses threatening behaviors and physical aspects of the environment that are determined by negotiated rules for street - level order realized through police - community partnerships . In the most comprehensive evaluation to - date, Braga, Welsh , and Schnell (2015) utilize d meta - analytical techniques to evaluate 30 randomized experimental and quasi - experimental tests of policing strategies that address ed diso rder (i.e. , policing disorder strategies) . Overall, they found these strategies to have a significant , yet modest effect on crime reduction (Braga et al., 2015) . The programs that had the strongest impact were those that utilized community and problem - solving interventions , reflective of order - maintenance policing (Braga et al., 2015) . Drawing from a subset of studies from this review , Weisburd et al. (2015 , p. 591 ) later there is little evidence that the model proposed in broken windows policing is driving such crime reductions. Rather, they argue that the mechanisms underlying criminal opportunity theories may better help explain its crime control gains (Weisburd et al., 2015) . windows research has failed to heed a critical instruction provided by Wilson and Kelling (1982 , para . 47 ): to identify neighborhoods at the tipping point but not unreclaimable, where the streets are used frequently but by apprehensive people, where a window is likely to be broken at any time, and must quickly be fixed if all are not to be shattered. This failure is significant. E fforts to identify the broken windo ws tipping point hold important implications for how police resources should be directed and for evaluations of the 3 effectiveness of policing disorder initiatives . K nowledge of the location of the broken windows tipping point can also be used to inform eva luations that seek to validate the theoretical pathways of BWT. According to Wilson and Kelling (1982), the tipping point lies somewhere between two stable neighborhood equilibria existing at opposing extremes : low disorder , low crime neighborhoods , and high disorder , high crime neighborhoods . T he y recognize that some neighborhoods are so demoralized and crime - ridden that the best the police can do is react to calls for service (CFS) , while some neighborhoods are so stable and serene that order - maintenance polic ing is not need ed (Wilson & Kelling, 1982) . In other words , the implementation of order - maintenance policing initiatives at these extremes is a poor use of police resources. Rather, Wilson and Kelling (1982) argue that the best use of limited police resources is to stabilize neighborhoods located at the tipping point . Unfortunately, they provide limited detail on how to identify such neighborhoods (Wilson & Kelling, 1982) . A logical first step toward identif ying neighborhoods at the tipping point is to examine the functional form of the relationship between disorder and violent crime . A focus on functional form is necessary in order to generate a more holistic theoretical understanding of the disorder - crime relationship . Unfortunately, w ithin the social sciences, generally, and C riminology, specifically, very few theorists have specif ied the function al form of the causal relations hips explicated in their theories. In the absence of this information, many rese archers are quick to assume a linear relationship. To this point, description of neighborhood extremes leaves open the possibility of a linear relationship between disorder and violent crime . That is, for every unit increase in disorder , violent crime increases by a constant amount . In fact, the vast majority of broken windows research has assume d a linear relationship 4 ( e.g., Skogan, 1990; Sampson & Raudenbush , 1999 ; Harcourt, 2001; Eck & Maguire, 200 5 ; Steenbeek & Kreis, 2015 ; Wheeler, 2018 ; Konkel, Ratkowski, & Tapp, 2019 ). In one such study , Steenbeek and Kreis (2015) develop ed a method for identifying areas with ; areas that neither have too little , n or too much disorder. As a ge neral rule, t hey argue that it is reasonable to assume that tipping point rank near the middle of the range of values on the disorder scale (Steenbeek & Kreis, 2015 , p. 527 ) . windows tipping point. Overlooked by Steenbeek and Kreis (2015), however, is that Wilson and description of a tipping point - at which small incr eases in disorder have a large impact on violent crime - is suggestive of a nonlinear relationship between disorder and violent c rime . For this reason , Steenbeek and Kreis (2015) approach , if applied, may result in the misdirection of police resources , a consequence that hold s especially severe implications for police departments that have limited resources and high levels of violent crime. A n onlinear effect can be described in terms of a dose - response relationship, wherein the causal variable - represented as a level (or dose) - does not have a proportional effect on the outcome variable of interest across the range of its distribution ( see Galster, 2014 , 2018 ). Threshold effects are a spe cial kind of nonlinear effect in which the impact of the causal variable dramatically changes once some critical level is surpassed ( see Galster , 2014, 2018). Wilson and description of a tipping point suggests that disorder maintains a thr eshold effect on violent crime . To elaborate, their theory suggests that neighborhood disorder will not have a large impact on violent crime so long as it does not exceed too far beyond the lower equilibrium (Wilson & Kelling, 1982 ). In an ideal scenario, i nformal social control would work to decrease disorder and return the neighborhood back to a low disorder , low crime state. However, if 5 disorder were to go unaddressed for too long and reach too high a level, informal social control would become ineffective . Without intervention , the neighborhood would eventually be propelled into a high disorder , high crime state. In a c ompeting view , Crane ( 1991 ) suggests in his E pidemic T heory of U rban G hettos that the impact of disorder on violent crime should be the greatest in the worst quality neighborhoods : urban ghettos . Thus, Crane ( 1991 ) places the location of the tipping point not in the middle of the disorder distribution , but near its end. Ultimately, pol ic ing initiatives directed to disorder and/or crime hot spots that achieve significant crime control gains make alternative interpretation s of the broken windows tipping point more attractive ( see Braga et al., 1999; Braga & Bond, 2008; Braga, Hureau, & Papachristos, 2012 , 2014 ) . In the only study that considers a nonlinear relationship between disorder and violent crime , Geller (2007) use d a first - difference model to evaluate (1982) and interpretations of the tipping point . She found no support for either (Geller, 2007) . Instead, she identifie d increasing concave relationship, in which the disorder - crime relationship is strongest in lower - disorder neighborho ods Geller, 2007, p. 87). While supportive of a nonlinear effect, t his finding is in consistent with the traditional understanding of a tipping point as a threshold effect. In summary, evaluations of the theoretical foundation and effectiveness of order - maintenance policing initiatives cast doubt on whether BWT contributes a unique and valuable framework to the field of C riminology . That being said, broken windows research has failed to such initiatives : to identify neighborhoods at the tipping point . Their description of a tipping point suggests a threshold effect , whereby the impact of disorder on violent crim e dramatically increase s past a 6 critical level of disorder located somewhere in the middle of the disorder distribution (Wilson & Kelling, 1982) . However, in the only examination that models the relationship between disorder and violent crime as nonlinear, Geller (2007) failed to find support for either Wilson and or ( 1991 ) interpretation of the broken windows tipping point. Instead, she identifie d a nonlinear relationship that is not consistent with a threshold effect (Geller, 2007) . Ultimately , more research must be conducted on the disorder - crime relationship before any conclusions can be drawn regarding the broken windows tippi ng point . Importantly, this research must utilize methods that minimize c oncerns about selection bias and account for the possibility of nonlinearity. Research Aims T his study examine s the functional form of the relationship between disorder and violent crime in an effort to shed light on the broken windows tipping point. T his knowledge is especially beneficial for cities that have limited police resources to combat violent crime and contain neighborhoods in desperate need of revitalization. For this reason, this study focus es on the city of Detroit, Michigan . At an area of a pproximately 139 square - miles, Detroit contains a population of approximately 672,662 ( as of 2018 ) . It is a predominantly African American city characterized by high levels of poverty and violent crime. Detro it was once considered the affluent capital of the G reat L ake s region; a city with a vibrant culture, developed infrastructure , and strong auto - manufacturing economy. However, this label of affluence slowly began to disintegrate . R eliance on auto - manufacturing and competition with foreign adversaries proved to be a catastrophic combination, result ing in the eventual deindustrialization of Detroit and pervasive joblessness which reached its peak in 2009 during the Great R ecession (2007 2009) . Detro , however, was not unlike other rust belt 7 cities ( e.g., Cleveland, OH ; Gary , IN ; and Youngstown , OH ) which also relied heavily on auto - manufacturing. During this time , out - migration and financial insecurity resulted in an explosion in the number of abandoned structures , driving the creation of the Detroit Demolition Program which organize s their sale or demolition . 1 To this point, a report released in 2014 by the city of Detroit found that nearly a third of it s land parcels ( 84,641 ) had been abandoned by their owners. 2 The majority of these parcels contained structures in very poor condition , indicated by broken or boarded windows /doors , fire damage, and/or a collapsed porch/roof ( Blight Removal Task Force Plan , 2014 ). Given its deteriorated urban landscape and high level of violence, t he implications of the tipping point for police operations in Detroit has received much attention . When asked about adopting order - maintenance polic ing in Detroit neighborhoods, Kelling (as cited in Williams, 2012) that are at the tipping point and how much do you invest in the areas that have been largely Williams, 2012) statement underscores the importance of efforts to identify t he tipping point for police operations in Detroit and motivates this study . To this end , this study examine s the relationship between physical disorder, measured at , = 2014 on violent crime rate , measured at = 2015 , while also addressing the possibility that factors that are associated with different levels o f physical disorder are not proportional across levels . Importantly, this 1 Emerging from the Great Recession, Detroit experienced a 16.18% decrease in its population, Gary a 17.04% decrease, Cleveland a 10.10% decrease , and Youngstown a 9.83% decrease. 2 L and parcel is a term used in real - estate to define a plot of land that is owned (or intended to be owned) by a person or entity. 8 interest in efforts that address and mitigate the effects of blight physical indicators of neighborhood decline - in order to spur neighborhood revitalization . Furthermore, this study utilize s an extension of propensity score matching - the generalized d ose - response propensity score (GPS) approach - t o conduct its assessment . This approach is uniquely suited for the identification of tipping points because it explicitly model(s) the functional form of the level of a causal variable and a given outcome w hile also addressing selection effects, when possible, through covariate balancing across matched levels of the causal variable ( Mears et al., 201 3 , p . 460 ) . In particular, t his approach is superior to traditional regression which addresses selection effects through the addition of control variables - because covariate balance must be achieved across matched levels of the causal variable before they can be reliably compared . To facilitate this analysis, t h is study collect s census block - group level data on physical disorder, violent crime , as well as socioeconomic and land use characteristics from a variety of sources, including the , Motor City Mapping (MCM) project , and Census. In summary, this study seeks to advanc e knowledge on the functional form of the disorder - crime relationship . Evidence that supports a nonlinear relationship between disorder and violent crime rate - i nterpretation of the broken windows tipping point would suggest that a proper test of the validity of BWT must accommodate nonlinearity. I t would also support the idea that the impact of order - maintenance policing on violent crime may be more optimal in some neighborhoods than in others . T he peculiarities of the disorder - crime relationship would provide some indication of where to focus these initiatives in order to achieve the greatest crime control benefits . Alternatively , evidence that supports a linear relationship between disorder and violent crime 9 rate would also be of value. This finding would provide validation for research that has modeled the disorder - crime relationship as linear. It would also lessen concerns rega rding where to implement order - maintenance policing initiatives . Regardless of which functional form is supported , police - community relations and police resources are two factors that stand to mitigate the effectiveness of order - maintenance policing initia tives , and therefore deserve the utmost consideration . Study Outline Moving forward, consists of four sections. The first section summarizes BWT and its e mpirical support , as well as interprets the functional form of the disorder - (1982) description of the tipping point . It also highlights t he failure of broken windows r esearch to consider the tipping point and discusses the implications of this failure . With this foundation set, the second section reviews research that challe nges BWT , including alternative perspectives of the tipping point. Shifting gears, the discussion turns to order - maintenance policing. The third section - Broken Windows Tipping Point describes the central tenants of order - maint enance policing and strategies used to address disorder , with a particular focus on Detroit . It also r eview s the empirical evidence of policing disorder strategies before proceed ing to a discussion of the implications of the tipping point for police operations. The final section - presents this r esearch q uestion and h ypotheses , setting the stage for the following chapter. 3: Project Design and I mplementation consists of three sections. The first section easures and D ata S ources describes the measures used to evaluate this 10 hypotheses and their respective data sources . In particular, it highlights the strengths of th is caus al (i.e., physical disorder) and outcome (i.e., violent crime rate) measures . The second section describes the GPS approach and its merits as they relate to the ability to make c ausal inferences . The final section describes a series of additional precautions that were taken to inspire confidence in this These precautions include both parametric and nonparametric techniques of estimating the dose - response function. s of three sections. The first section Parametric Method describes the outcome of each step of the parametric GPS approach , with particular attention given to the estimation of the dose - response fun ction . The second section - describes the estimation of the dose - response function produced from three types of semiparametric methods: penalized spline, radial spline, and inverse weighting kernel function . The final section summar key research findings. s of three sections. The first section briefly summarizes the motivation behind this study, as well as its design, implementation, and results . The second section identifies and discusses four domains in which res earch can be developed to advance knowledge of the f unctional form of the disorder - crime relationship : 1) Measures of disorder; 2) Neighborhood context; 3) Confounding factors; and 4) Longitudinal data analysis . The final section discusses the ways in which this study contributes to th eory, practice , and policy. 11 CHAPTER 2: LITERATURE REVIEW Broken Windows Theory Theoretical Foundation of the Broken Windows Theory In their seventeen - page article in The Atlantic Monthly , Wilson and Kelling (1982) describe d a developmental sequence in which unattended disorder produce s deleterious consequences for communities , most outstanding among them the proliferation of violent crime . T hey offer ed the police a simple solution to prevent this sequence of events from unfo lding: address disorder before it escalate s (Wilson & Kelling, 1982) . This solution is based on the idea that minor issues will eventually lead to a breakdown of informal social control within neighborhoods . Informal social control reflects the ability of a neighborhood to exert control over the behavior of its residents and its capacity to socialize them conventionally (Bursik , 1988; Bursik & Grasmik, 1993; Sampson & Groves, 1989). When strong, informal social control help s thwart the proliferation of violent crime within neighborhoods (Sampson & Groves, 1989; Bursik & Grasmick, 1993; Wilson, 1996; Warner & Rountree, 1997; Sampson , Raudenbush , & Earls, 1997; Bursik , 1999; Morenoff et al., 2001 ; Kubrin & Weitzer , 2003 ) . Furthermore, W il son and Kelling (1982) reason that more severe problems can be avoided if disorder is quickly addressed . However, if disorder is left unchecked , the broken windows developmental sequence will unfold over time . According to Wilson and Kelling (1982), unat tended disorder lowers the benchmark for expected and acceptable behaviors within neighborhoods , signal ing a breakdown of informal social control. In doing so, it invites more disorder to occur. However, the presence of disorder alone is not enough to trigger the next step in the broken windows developmental sequence . Re sidents must perceive disorder to be a p roblem within their neighborhoods and interpret it as a 12 consequence of failing social control s . As a response to worsening neighborhood conditions , Wilson and Kelling (1982) contend that residents will eventually become fearful and withdraw from community life , and may leave the neighborhood altogether. This effect further undermines informal social control . As informal social con trol weaken s and disorder and minor crimes increase, criminals become embolden ed to commit more severe criminal acts , interpreting disorder as a cu e of neighborhood disinvestment . Accordingly, Wilson and Kelling (1982, p ara . 25 ) state , [i] f the neighborhood cannot keep a bothersome panhandler from annoying passersby, the thief may reason, it is even less likely to call t he police to identify a potential mugger or to Following this logic , neighborhoods with high levels of disorder are more likely to experience increases in crime than neighborhoods in which informal social con trol is effectively exercised to constrain and/or eliminate it . O nce rising crime rates are noticed by residents , their fear and isolation from community life deepens. This acknowledgement serves to further entrench the neighborhood in a cycle of disorder and decline . Unfortunately, t he time - frame in which th is process is expected to unfold is unclear and has yet to be fully explored . Missing from this overview of the broken windows developmental sequence is Wilson and Kelling (1982 ) description of the tipping point . In their article, they devote a a meager paragraph toward describing it : Some neighborhoods are so demoralized and crime - ridden as to make foot patrol useless; the best the police can do with limited resources is respond to the enormous number of calls for service. Other neighborhoods are so stable and serene as to make foot pa trol unnecessary. The key is to identify neighborhoods at the tipping point where the public order is deteriorating but not unreclaimable, where the streets are used frequently but by apprehensive people, where a window is likely to be broken at any time, and must quickly be fixed if all are not to be shattered . (Wilson & Kelling, 1982, para . 47) 13 From what little information they provide, it can be determined that the tipping point is located somewhere between two opposing neighborhood extremes: low disorder , low crime neighborhoods , and high disorder , high crime neighborhoods (Wilson & Kelling, 1982) . Notwithstanding its implications for polic ing , later discussed in detail , t he tipping point affects our understand ing of the relationshi p between disorder and violent crime in two important ways . First , suggests that the impact of disorder on violent crime is nonlinear. Specifically, it suggests that this relationship can be best captured as a threshold effect. As previously mentioned, threshold effects are a special kind of nonlinear effect in which the impact of the causal variable dramatically changes onc e some critical level is surpassed ( see Galster , 2014, 2018). A ccording to Wilson and Kelling (1982), this critical level the tipping point - is located somewhere between two neighborhood extremes: low disorder , low crime neighborhoods , and high disorder , high crime neighborhoods . For this reason , efforts that seek to shed light on the broken windows tipping point must accommodate nonlinearity. Second , vague description of the broken windows tipping point requires that we make several theoretically - informed assumptions regarding the exact functional specifications of the relationship between disorder and violent crime . To this point , two competing interpretations of th is relationship emerge f rom their description of the tipping point (Wilson & Kelling, 1982) . These interpretations are visually depicted in Figure 1 by the line segments and . Both line segments share the same origin ( at point ) and location of the broken windows tipping point ( at point ). Importantly, the simplest construction of each line segment was selected to reflect each hypothesized functional form. 14 Recall Wilson and Kelling (1982 , p ara . 47 ) argue stable and serene as to make foot patrol unnecessary This description suggests that efforts to address disorder in low disorder, low crime neighborhoods will not be a worthwhile investment of police resources. In other words, we can expect the strength of the relationship betwe en disorder and violent crime in these neighborhoods to be such that efforts to decrease disorder will not produce large enough crime reduction gains (i.e., the amount by which crime is reduced ) to warrant police efforts. This relationship is depicted by t he line segment Figure 1. Theoretically - derived Interpretations of the Relationship between Disorder and Violent . Beyond the tipping point, however, there are two viable interpretations of the relationship between disorder and violent crime. Recall Wilson and Kelling ( 1982 , p ara . 47 ) argue ome neighborhoods are so demoralized and crime - ridden as to make foot patrol the best the police can do with limited resourc es is respond to the enormous number of calls for service What motivates the following competing interpretations is how we come to understand the factors that render foot patrol useless. For example, w e can apply a similar interpretation as before to inf orm our understanding of the relationship between disorder and violent crime in high disorder , high crime neighborhoods : T he strength of the relationship between disorder and 15 violent crime in these neighborhoods is such that efforts to decrease disorder will not produce large enough crime reduction gains to warrant police efforts. This relationship is captured by the line segment and completes the line segment Alternatively, we can interpret Wilson to suggest that the dosage of police response needed to address disorder in high disorder , high crime neighborhoods is extraordinary, and beyond what police departments with limited resources are equipped to provide. Thus , the ineffectiveness of foot patrol in high disorder , high crime neighborhoods is now an issue of inadequate police response dosage . Therefore, i f police resources are plentiful or highly focused on small areas (i.e., hot spot s ), there is a potential to ac hieve significant crime reduction gains. This relationship is captured by the l ine segment and completes the line segment T hree sets of neighborhood characteristics emerge from this assessment. These characteristics are based upon a neighborhood location relative to the broken windows tipping point : 1) Before the tipping point; 2) At the tipping point; and 3) Beyond the tipping point . In neighborhoods that are located befo re the tipping point, disorder , fear of crime , and violent crime are low , and residents have the opportunity to build and exercise informal social control. If disorder do es not exceed too far beyond the lower equilibrium , in formal social control is expected to decrease disorder , helping return the neighborhood s back to a low disorder, low crime state (Wilson & Kelling, 1982) . In neighborhoods located at the tipping point, disorder is mounting and about to reach a level that will elicit a significan t fear response , resulting in social withdrawal followed by a breakdown of informal social control and an uptick in violent crime (Wilson & Kelling, 1982) . P ublic order is deteriorating and along with it the ability of informal social control to constrain 16 and/or eliminate disorder (Wilson & Kelling, 1982). 3 Wilson and Kelling (1982) advocate the use of formal mechanisms in neighborhoods located at the tipping point ; t hese neighborhoods are those that are at the greatest risk of being propelled into a high disorder , high crime state . To this point, they state that [t] hough citizens can do a great deal, the police are plainly the key to order - Wilson & Kelling, 1982, para. 46) . In neighborhoods located beyond the tipping point, disorder , fear of crime, and violent crime are high , and social isolation prevents residents from contributing to the development of informal social control . Without resident involvement, informal social control will disintegrate. T h is description paints a relatively bleak image of neighborhoods located beyond the tipping point . However, there is a path forward. P roblem - oriented policing initiatives directed to disorder and/or crime hot spots have been shown to be part icularly effective at reducing crime levels without significant displacement or damag e to police - community relations ( Braga & Bond, 2008; Braga et al., 1999; Braga et al., 2012 , 2014 ). Often a part of problem - oriented policing initiatives, n eighborhood revitalization efforts also have been shown to reduce crime levels in declining neighborhoods , although they may come at the cost of gentrification ( see MacDonald & Stokes, 2019 ) . Examples of these efforts include the demolition /rehabilitation of vacant housing ( e.g., Kondo et al., 201 6 ; Spader et al., 2016; Wheeler et al., 2018; Jay et al., 2019; Larson et al., 2019 ) and transformation of vacant lots ( e.g., Ga r vin et al., 2013; Kondo et al., 2018; Branas et al., 2018 ), as well as the creation o f defensible spaces ( e.g., Jeffery, 1971; 3 Outside of the broken windows perspective, there are a variety of factors that may undermine the effectiveness of informal social control, such as the strength , density, and type of social ties (Sampson & Groves, 1989; Bursik & Grasmick 1993; Bursik 1999; Sampson, 2012; Browning et al., 2017), as well as the level of neighborhood attachment (Kitts, 1999; Rohe & Stegman 1994; Silver & Miller, 2004; Xiao & McCrigh t, 2014), and shared local exposure (Jacobs, 1961; Small, 2009; Browning et al., 2017). 17 Newman, 1972 , 1996 ; Brown & Altman, 1983; Taylor, Gottfredson, & Brower, 1984; Ratcliffe, 2003 ; Eck & Guerette, 2012 ). Ultimately, it is possible for n eighborhoods that are located beyond the tipping point to experience reductions in both disorder and crime levels . However, t he question remains whether the efforts discussed can change neighborhoods enough to transition them from a high disorder , high crime state, to a low disorder, l ow crime state. In order to begin to address this question, it is first important to recognize that not all neighborhoods start off on equal footing. Group - based trajectory models (GBTMs) of crime suggest as much (Weisburd et al., 2004; Yang, 2010; Weisburd , Groff, & Yang, 201 2 ; Curman, Andresen, & Brantingham, 2014; Wheeler et al., 201 6 ; Andresen, Curman, & Linning, 201 7 ; Gill, Wooditch, & Weisburd, 201 7 ) . This modeling technique is able to capture the developmen tal patterns of crime as they unfold over time, revealing patterns of stability and change. N eighborhood structural features help shed light on the crime patterns revealed by GBTMs . D rawing from social disorganization theory , t hese features traditionally include physical disorder, poverty, residential instability , ethnic heterogeneity , and concentrated disadvantage . Furthermore , a large body of research has found neighborhood structural features to be positively associated with crime ( Shaw & McKay, 1942; Sampson et al. , 1997; Boggess & Hipp, 2010; Steenbeek & Hipp, 2011; Hipp, Kim, & Kane, 2019 ) , and, in particular, high crime trajectories (Weisbur d et al., 201 2 ; Gill et al., 2017 ; Krivo et al., 2018) . Of these features, physical disorder is arguabl y the easiest feature to alter. In light of these findings, the e ffort required to facilitate a transition from a high disorder , high crime state to a low disorder, low crime state is likely in fluenced by the degree of flexibility afforded by its 18 trajectory , as well as the systemic features that contribute to it. Thus, neighborhoods that are on a high and stable crime trajectory will likely be the most difficult to change. Empirical Support for Broken Windows Theory : Implications for the Broken Windows Tipping Point The broken windows developmental sequence, as described above, is depicted in Figure 2. As can be clearly seen, the path from disorder to violent crime comprises three core theoretical propositions. These propositions must be supported for BWT to be in a position to meaningfully contribute to the field of C riminology . First, unattended disorder must lead to an increase in fear of crime . Second, fear of crime must lead residents to withdraw from community life , resulting in a decrease in informal social control. Third, violent crime must increase in response to declining levels of info rmal social control. Figure 2 . The Broken Windows Developmental Sequence . T here is considerable evidence supporting these linkages. R esearch has largely identified a positive association between disorder - including both systematically observed and perceived levels - and fear of crime ( e.g., Taylor & Shumaker, 1990; Covington & Taylor, 1991; LaGrange, et al. , 1992; McGarrell , Giacomazzi, & Thurman, 1997, 199 9 ; Markowitz et al. , 2001; Spelman, 2004 ; Hinkle & Weisburd, 2008) . Furthermore , there has been a comparatively smaller body of research with a greater degree of mixed findings that examines the relationship between fear of crime and community withdrawal and informal social control , primarily captured as Disorder goes untreated Citizens become fearful and minimize their use of public space Informal social control decreases and/or is perceived to decrease by criminals As disorder is left untreated, crime proliferates, citizens remain fearful, and informal social control continues to disintegrate 19 collective efficacy . 4 That being said, this pathway still garners a fair amount of support ( e.g., Gar o falo, 1981; Markowitz et al., 2001; Crank, Giacomazzi, & Heck, 2003 ). Lastly , a rich line of criminological inquiry has tied reductions in collective efficacy to an increase in crim e ( e.g., Ka sa rada & Janowitz, 1974; Sampson, 1988 ; Sampson & Groves, 1989; Bursik & Grasmick, 1993 ; Wilson, 1996 ; Sampson et al., 1997 ; Warner & Rountree, 1997 ; Bursik, 1999 ; Morenoff et al., 2001 ; Browing, 2002; Kubrin & Weitzer, 2003 ; Lowenkamp, Cullen, & Pratt, 2003; Sabol, Coulton, & Korbin, 2004 ; Armstrong, Katz, & Schnebly, 2015 ) , securing the final link of the broken windows developmental sequence . Despite this large body of evidence , the majority of broken windows research lend s support to only one step of the broken windows developmental sequence and are challenged - to varying degrees - by competing findings. To this point, a recent meta - analysis of 96 studies on the effect of disorder on aggressive behavior s and fear of crime and Welsh (2019) failed to find consistent support for the relationships laid out in BWT. However, it is important to consider that BWT details a longitudinal process of neighborhood decline. Yet, most studies that seek to va lidate BWT utilize cross - sectional data and, therefore, are unable to capture the dynamics of the broken windows developmental sequence . In fact, all but six utilized cross - sectional data . Further more , ver y few studies evaluate the cyclic nature of BWT by accounting for reciprocal effects between crime and neighborhood conditions ( Sampson & Raudenbush , 1999 ; Markowitz et al. , 2001 ; Robinson et al. , 2003 ; Steenbeek & Hipp, 20 1 1 ; Boggess & Maskaly , 2014; & Sampson , 2015 ). In arguably the most complete examination of BWT to date, Steenbeek and 4 Traditionally defined, c ollective efficacy includes two key components: social cohesion and informal social control (Sampson et al.,1997). In general, collective effi cacy requires trust and solidarity amongst resident, as well as their willingness to intervene to maintain order within neighborhoods (Sampson et al., 1997). 20 Hipp (2011) examine d 10 years of neighborhood data in a series of sophisticated longitudinal cross - lagged models and conclude d : [T]he results suggest a cyclical model in which neighborhoods have relatively stable levels of disorder overtime, and the processes that lead to disorderly neighborhoods are difficult to turn around. Neighborhoods with high levels of disorder cause more people to move out, and higher residential instability leads to a lower percentage of people taking action to improve the livability and safety of the neighborhood. Neighborhood disorder thus has cumulative effects over and above the direct effect on residential instability by re inforcing itself via a weakening of community processes of social control . (p. 864) Overall , they found considerable support for the longitudinal process of neighborhood decline hypothesized by Wilson and Kelling (1982) (Steenbeek & Hipp, 2011) . I t should be clear that Wilson and Kelling (1982) argue that the primary pathway through which disorder affects violent crime is through fear and social withdrawal , leading to lower levels of informal social control within neighborhoods ( see also review in G ualt & Silver, 2008). Despite this argument, many researchers have interpreted BWT to suggest a direct relationship between disorder and violent crime (e.g., Skogan, 1990; Sampson & Raudenbush ,1999 ; Harcourt, 2001; Eck & Mc g uire, 200 5 ) . Indeed, the role of disorder as a cue which signals to offenders that no one cares , in turn inspiring them to commit crime, is consistent with this understanding . To this point , in a later article Wilson and Kelling (1989 , p. 47 ) imply a direct relationship between disorder and crime: A rash of burglaries may occur because drug users have found a back alley or an abandoned building in which to hang out. In their spare time, and in order to get money to buy drugs, they steal from their neighbors. If the back alleys are cleaned up and the abandoned buildings torn down, the drug users will go away . Skogan (1990) was the first to seriously consider the direct relationship between disorder and violent crime. In Disorder and Decline , he identifie d a significant positive re lationship between disorder and robbery , controlling for poverty, residential stability, and racial composition (Skogan, 1990) . Using the same data , Harcourt ( 2001 ) applied a corrected 21 approach that addresse d several serious 1990) consideration of missing values, construction of independent variable s , and narrow focus on only one crime outcome . A fter removing neighborhoods with strong disorder - crime ties, Harcourt (2001) fail ed to identify any significant relationship s between disorder and crime . However, Eck and Maguire (200 5 ) later argue 2001 ) study did not disprove support of the disorder - crime link . Rather, Harcourt ( 2001 ) discovered that the dat a were affected by outliers. Sampson and Raudenbush (1999) utilized data from the Project on Human Development in Chicago Neighborhoods (PHDCN) to investigate the disorder - crime link. Through weighted least squares regression and variable path analysis, they identified a positive direct link between disorder and violent crime (Sampson & Raudenbush, 1999). In all cases except for robbery, however, this link disappeared when collective efficacy was introduced into the model , defined ion and mutual trust with shared expectations for intervening in support - 613). The y also identified a reciprocal relationship between collective efficacy and crime, where collective effica cy negatively affected crime and crime negatively affected collective efficacy (Sampson & Raudenbush, 1999). Ultimately, Sampson and Raudenbush (1999 , p. 627 ) arg ue that their results . Later, Bratton and Kelling (2006) in an article published in the National Review : T hey [Sampson and Raudenbush (1999)] claimed that broken windows posit s a direct link between disorder and serious crime . From the first presentation of broken windows we have argued, to the contrary, that the link, while clear and strong, is indirect . Citi zen fear, created by disorder, leads to weakened social controls, thus creating the conditions in which crime can flourish. (para. 9) 22 Supporting Bratton and Kelling (200 6 ) argument , Xu, Fielder, and Flaming (2005) argue that 99) discovery of a reciprocal relationship between collective efficacy and crime in fact supports an indirect link between disorder and crime. Utilizing a different data source, they demonstrate d that disorder has strong direct, indirect, and total effects on crime even while controlling for collective efficacy (Xu et al., 2005) . Overall, studies that evaluat e the direct relationship between disorder and crime have done little to produce a clear er image of this relationship. At their worst, they fail to find a significant relationship ( e.g., Harcourt, 2001 ; Sampson & Raudenbush, 1999 ). While disorder ha s been found to have a strong direct effect on crime (e.g., Xu et al., 2005), it is more often the case that a modest effect is identified ( e.g., Boggess & Maskaly, 2014; Wheeler, 2018 ; Konkel et al. , 2019 ) . It is also common for this effect to vary by crime type and/or type of disorder ( e.g., Sampson & Raudenbush, 1999; Taylor, 1999 , 2001 ). T his review of empirical evidence of BWT clearly demonstrates its highly contentious standing within the field of C riminology and the need for more complete tests of the broken windows developmental sequence that draw upon longitudinal data and consider reciprocal effects between crime and neighborhood conditions , such as collective efficacy . The current study acknowledges the mixed body of findings revealed from its review that provide sufficient grounds on which to question the validi ty of BWT . However, it has no intention of directly addressing these findings . Rather, it seeks to advance broken windows research in another way : by exploring the functional form of the relationship between disorder and violent crime in an effort to shed light on the broken windows tipping point . Studied directly, evaluations of the disorder - crime link ignore the social - psychological underpinnings of BWT and are incomplete test s of the theory . However, a direct evaluation is an 23 appropriate starting place for efforts that seek to evaluate the function form of the disorder - crime relationship given of the tipping point as located somewhere between low disorder, low crime neighborhoods and high disorder , h igh crime neighborhood s . If this study finds evidence in support of a nonlinear relationship, then it would suggest that future evaluations of the validity of BWT must accommodate the possibility of nonlinearity, and that past evaluations which failed to d o so my have over - or under - stated the effect of disorder on violent crime based upon t he nuances of this relationship. A Closer Look: Alternative Perspectives Unfortunately, t here is a surprising dearth of studies on the broken widows tipping point . T he vast majority of studies do not explicitly evaluate the broken windows tipping point , n or do they consider how the tipping point may impact their findings. As previously discussed , Wilson interpretation of the tipping point suggests a threshold effect of disorder on violent crime. Nonetheless , most studies that examine a direct relationship between disorder and violent crime assume a linear trend in disorde r. I f the disorder - crime relationship has been misspecified, however, regression estimates and assumptions of statistical tests which assume linearity will produce misleading findings . Quite obviously, evaluations that misspecify the relationship between disorder an d violent crime are unable to advance our understanding of the disorder - crime relationship or the broken windows tipping point , for that matter . Without having conducted formal evaluation s , a small number of studies suggest th at the relationship between disorder and violent crime may in fact be nonlinear ( Taylor & Shumaker, 1990; Gau & Pratt, 2010 ; Yang, 2010 ) . For example, Gau and Pratt (2010) utilized an ordinary least squares regression model to evaluate the interaction effect bet ween perceptions of disorder and a disorder - crime difference score . This score was constructed by taking the absolute value of 24 the difference between scores obtained from scale s that measured perceptions of neighborhood crime and disorder problems . Thus, h igher disorder - crime scores represent a larger disparity between perceptions of disorder and crime problems . Furthermore, Gau and Pratt (2010) divided their sample of respondents into two. One sample consisted of respondents who perceived low levels of dis order, and the other those who perceived high levels of disorder . Running a regression analysis for each sample , Gau and Pratt (2010) found that respondents who lived in orderly neighborhoods could not distinguish disorder from crime, but respondents who lived in disorderly neighborhoods could make this distinction . They argue that their finding s suggest a nonlinear trend in disorder (Gau & Pratt, 2010) . Beyond some critical threshold of disorder, respondents are better able to differentiat e between disorder and crime. In another study, Yang (2010) utilized group - based trajectory and joint trajectory analyses to evaluate the longitudinal relationship between disorder and crime. She found that while the absence of disorder ensure d that a pl ace would be free of violence, high levels of disorder only predict ed violence problems 30% of the time (Yang, 2010) . Furthermore, Yang (2010 , p. 158 ) suggest s violence only occurs in plac es where disorder has passed the tipping point . instructs that focus on examining the possible existence of a threshold which must be 158). n onlinear effects have been found to drive a number of other neighborhood - level processes (see review in Galster , 2018) . In one such process pertinent to our understanding of the broken windows tipping point, Crane (1991) propose s a contagion model to understand the spread of social problem s within communities. As implied, the model assumes that social problems are 25 contagious . If they are kept below a critical threshold, the ir frequency and prevalence will eventually return to low levels . B eyond this threshold, however, social problems will spread like an epidemic , as increasing numbers of individuals engage in problematic behaviors. Crane (1991) identifie d t wo factors that d etermine the susceptibility of a community to an epidemic : 1) R ; and 2) overall risk of developing social problems. Ultimately , he hypothesize d that [t] he relationships between neighborhood quality and the incidence of particular social problems should be nonlinear. Social problems should increase as neighborhood quality declines, but not at a constant rate. Somewhere near the bottom of the distribution of neighborhood quality, t here should be a jump in the rate of increas Crane, 1991, p. 1228). To explore h is hypothesis, C rane (1991) examine d the effect of neighborhood quality on high school dropout rates and teenage childbearing . In particular, he capture d neighborhood qual ity as the percentage of individuals in a neighborhood that held either a managerial or professional job (Crane, 1991) . Neighborhoods that were on the low range of this measure were considered to be of low quality, while neighborhoods on the high range wer e considered to be of high quality. Crane (1991) found t he effects of neighborhood quality were the largest in the lowest - quality neighborhoods, otherwise referred to as urban ghettos (Crane, 1991) . Insofar as disorder is an indicator of neighborhood quali ty and crime a social problem , Crane (1991) contagion model of fers an alternative perspective to interpretation of the broken windows tipping point . In particular, his perspective suggests that the impact of disorder on violent crime will be the most severe in urban ghettos (Crane, 1991) . In other words , Crane (1991) contagion model moves the tipping point from the middle of the disorder distribution to wards its end. 26 Furthermore, findings from a Detroit study conducted by Raleigh and Galster (201 5 ) which explore s the relationship between neighborhood disinvestment and violent crime rate . T hey utilized several attributes of Detroit neighborhood s to simulate five stages of neighborhood disinvestment , with the fifth stage representing the greatest level of disinvestment (i.e., highest levels of vacant land, vacant housing units, and renters; the lowest median incomes, employment rates, and populati on density) (Raleigh & Galster, 2015) . Raleigh and Galster (201 5 ) found the transition from one stage of disinvestment to the next to have a disproportional effect on violent crime rate. While violent crime rate increase d at each transition, the final tran sition (from stage 4 to stage 5) experienced the largest increase in the growth rate. measure , Raleigh and Galster 5 ) measure of neighborhood quality (i.e., neighborhood disinvestment) capture d indicators of physical disorder ( v acant land and vacant housing units ) . For this reason, their findings are especially compelling in support of a nonlinear relationship between disorder and violent crime, with a tipping point located at the high end of the disorder distribution (Raleigh & Galster , 201 5 ) . Adding to these findings, in areas with high levels of social problems consistent with urban ghettos, efforts to address disorder have been largely successful at reducing crime ( Braga & Bond, 2008; Braga et al., 1999; Braga et al. , 2012 , 2014 ) . In fairness, however, policing strategies that target disorder in hot spots are often embedded within problem - oriented and situational crime prevention strategies which draw from competing theoretical mechanisms to explain crime reduction , an issue that will be discussed later . For this reason, it is difficult to disentangle the effects of these complementary strategies. Nonetheless, these studies open the possibility of th e broken windows tipping point being located toward the end of the disorder distribution. T hey also lend support to the interpretation of the relationship between disorder and 27 violent crime depicted by the line segment in Figure 1. Given sufficient police resources or a high spatial dosage of these resources, t his relationship supports significant crime reduction gains in high disorder , high crime neighborho ods . (1982) description of a tipping point, (2007) evaluation is the only study that explores the functional form of the disorder - crime relationship . To elaborate , she use d a first - difference model to capture the relationship between physical disorder and violent crime rate (Geller, 2007) . The inclusion of a squared - term of physical disorder provide d the model some flexibility , impos ing a global structure on the relationship between physical disorder and violent crime rate . Geller (2007) identifie d a concave relationship in which the disorder - crime link was the strongest in low disorder neighborhoods (Geller, 2007) . Setting aside for now issues regarding how nonlinearity was captured , her finding do es garner support . To this point, Taylor and Shumaker (1990) argue in favor of the idea of inoculation, whereby the severity of previous experiences of an adverse phenomenon are lessened over - time as individuals adapt to their surroundings. They apply this idea to the relationship between fear er in locales where the level of disorder is higher, because residents in the higher threat contexts are experiencing a Supporting inoculation , Taylor and Shumaker (1990) identified a concave relationship between disorder and fear , where the slope flattens then declines at high levels of disorder (see Figure 3 ). Furthermore, t he idea of inoculation has been adapted to explain disparities in perceptions of disorder among res idents living in the same neighborhood ( see Sampson & Raudenbush, 2004; Franzini et al., 2008; Hipp, 2010; Sampson, 2012). In particular, Sampson and Raudenbush (2004) suggest that 28 the greater past exposure residents have to disorder , the greater the amoun t of disorder they will need to be exposed to for them to perceive it to be a problem within their neighborhood . a Natural Hazard: Implications for Understanding the Rel ationship between Disorder Environmental/Ecological Psychology , 18 (5), p. 631. F ear is a crucial response to disorder that is needed for the broken windows developmental sequence to unfold. A s suggested by Taylor and Shumaker (1990) , this sequence will be affected if residents become desensitized to disorder at high levels . There are three likely ways in which inoculation stands to affect the broken windows developmental sequence at high levels of disorder . First , the relationship between disorder and violent crime a t high levels of disorder may flatten as residents adapt to disorder. In other words, an increase in disorder will n ot result in a proportionate (or greater) fear response which is needed to drive neighborhood decline . With levels of fear at (or nearly at) a constant, increases in disorder will no longer positively contribute to the perpetuation of violent crime within neighborhoods . Second, the relationship between disorder and violent crime at high levels of disorder may be negative . This 29 relationship indicate s a reversal of the broken windows developmental sequence . In this case, adaptation to disorder will re sult in a decrease in levels of fear . Less fearful, residents will be more l ikely to reclaim public space and seiz e opportunities to develop and exercise informal social control , resulting in a decrease in violent crime within neighborhoods . Third, a combi nation of these two outcomes is also possible. As disorder rises, levels of fear will plateau and eventually decline, resulting in a decrease in violent crime within neighborhoods through the previously described mechanisms. In summary, the mechanisms through which disorder affects crime are hotly debated and generate an understandable amount of skepticism regarding the value of BWT to the field of C riminology. That being said, research on BWT has failed considerably - with few exceptions - on two fronts: 1 ) I t has failed to investigate whether disorder has a nonlinear effect on violent crime ; and 2 ) More specifically, i t has failed to consider how the tipping point if it exists - may impact study findings . To - date, only one stu dy investigates the nonlinear relationship between disorder and violent crime . evaluation revealed a concave relationship which suggest s that the disorder - crime link is the st rongest in low disorder , low crime neighborhoods , a finding that interpretations . However , this single study is far from conclusive . A topic that remains to be discussed is the impact of these failures for police operations . T he following section provides a n overview of order - maintenance policing with a particular focus on Detroit , f ollowed by a focused discussion on the significance of the broken windows tipping point for policing strategies that address disorder . 30 Policing Disorder & Th e Broken Windows Tipping Point What is Order - Maintenance Policing ? Originating from BWT, o rder - maintenance polic ing is a community - driven approach that seeks to reduce violent crime by address ing physical aspects of an environment and threatening behaviors within the public domain that inspire fear and upset community lif e . The primary goal of order - maintenance policing is to reinforce informal social control associated with these physical and social phenomena . The logic being that w ith disorder no longer driving the broken windows cycle, residents will be less fearful and more inclined to use public space , in turn providing them mor e opportunities to engage in behaviors that fortify informal social control (see Figure 4) . Thus, a clear gauge of whether order - maintenance policing is operating through the pathways laid out in BWT is whether it of fear. Figur by D. Weisburd, J.C. Hinkle, A. Braga, and A. Wooditch, 2015, Journal of Research in Crime and Delinquency , 52 (4), p. 594. In its intended form , order - maintenance policing is shaped by negotiated rules for street - level order realized through police - community partnership s (Wilson & Kelling, 1982) . In this way, it is compatible with a procedural justice framework since the manner in which the police exercise their legal authority is shaped by the community and presumed fair. However, this is not to say that order - maintenance policing cannot go awry . I t is often uncl ear whether individuals who violate community - specific standards for public conduct are violating the law. For example, Police reduce physical and social disorder Residents' fear is reduced Neighborhood informal social control is increased Crime rates decline 31 many social disorder violations are termed soft crimes and classified into ambiguous legal categories , such as disturbing the peace, l oitering , and vagrancy. Due to the legal ambiguity of disorder violations, officers are not prompted to resolve such violations with arrests (Kelling & Coles, 1996) . R ather , they are encouraged to use discretion to resolve issues (Kelling & Coles, 1996) . T o this point , n on - arrest solutions are able to address issue s before they escalate , and also serve to protect community and police relationships by discouraging aggressive enforcement ( Bittner, 1967 ; Brown, 1981; Kelling & Coles, 1996 ; Gau & Brunson, 20 10 ; Todak & James, 2018 ) . It is worth emphasizing that a ggressive enforcement of mino r offenses is a characteristic of zero - tolerance policing . Unlike order - maintenance policing, zero - tolerance policing damages police - community relations and is inherently in opposition with procedural justice, as epitomized by research which exposes it as a racially biased tactic ( Harris, 1993 ; Gelman et al., 2007; Ridgeway, 2007; Gau & Brunson, 2010; Hanink, 201 3 ; Gau, 2014; Rengifo & Fratello, 2015 ; Rengifo & Folwer, 2016 ). T he rigidity of zero - tolerance policing also denies officers from using discretion in enforcing minor offenses . A staple of order - maintenance policing, this crucial tool is needed to safeguard police - community relations (Kelling & Coles, 1996 ). Kelling and Coles (199 6 , p. 9) make these distinctions clear and attack zero - tolera nce policing as an unsustainable Furthermore, o rder - maintenance policing seeks to reduce the physical and psychological distance between the police and residents in an effort to mount an appropriate and leveled response to address disorder and secure the cooperation and compliance of residents (Pate et al. , 198 5 ) . Align ed with this objective, - 32 maintenance policing was strongly focused on the implementation of foot patrol. This policing strategy is well known for its ability to increase perceptions of safety , as well as de crease fear of crime, and, to a lesser degree, crime (Kelling, 1981; Trojanowicz & Branas , 198 5 ; Esbensen & Taylor, 1984; Cordner, 1986; Bowers & Hirsch, 1987; Skogan & Frydl, 2004; Ratcliffe, Taniguchi, Groff, & Wood, 2011; H ara, 2014 ; Groff et a l., 2015 ; Andresen & Hodgkinson, 2018 ). As compared to car patrol officers, f oot patrol officers are more likely to address disorder incidents, engage in public service activities and information gathering, and initiate pedestrian stops (Trojanowicz, 198 6 ; Groff et al., 2012) . In addition , one - to - one contact with police officers has the potential to improve police - community relations by providing opportunities for residents and off icers to become more familiar with one another and establish trust ( Trojanowicz, 198 6 ; Groff et al., 2015 ; Cowell & Kringen, 2016 ) . To this point , the Newark F oot Patrol Experiment and the Flint Neighborhood Foot Patrol Program early seminal studies - both identified foot patrol to have a positive effect Kelling , 1981; Trojanowicz & Baldwin, 1982 ). Complementing this finding, m ore recent studies have garnered support for the ability of foot patrol to increase perceptions of the police as approachable, friendly, fair, accountable, and respectful ( Cowell & Kringen, 2016; Simpson, 2017). These per ceptions have been shown to encourage resident involvement in police efforts and strengthen existing police - community partnerships ( Hinds, 2007; Reisig, 2007; Tyler & Fagan, 2008 ; Leroux & McShane, 2017) . Outside of foot patrol, a nother tactic to address disorder is through prob lem - oriented policing . In fact, order - maintenance policing can be understood to be a branch of problem - oriented policing which focuses on a particular type of problem: disorder. To this point, o rder - maintenance policing often involves strategic partnerships with local community groups, 33 businesses, social services , and city agencies in order to develop solutions to address disorder ( e.g., Weisburd & Green, 1995 ; McGarrell et al., 1997, 1999; Baker & Wolfer, 2003; Skogan, 2006; Braga, 20 10; Braga, Hureau, & Papachristos, 2011; Taylor, Koper, & Woods, 2011; Weisburd et al., 2012) . These solutions may or may not directly involve the police. For example, civil remedies have become a popular means through which to address disorder and are oft en used in conjunction with criminal penalties (see Figure 5 ) . In particular, c ode enforcement and nuisance abatement are the most common ly used civil remedies . Unlike traditional order - maintenance policing, t hese tactics address both public and private di splays of disorder. Figure 5. Shorthand descriptions of some property - Mazerolle, 201 3 , Center for Problem - Oriented Policing, 11, p.10 . a violation of one or more municipal health and safety code s Smith & Mazerolle, 2013, p.10). Nuisance abatement is considered to be a broader, more formalized ver sion of code enforcement. As a municipal ordinance, nuisance abatement allows legal action to be taken in situations which a person is being deprived of his or her right to quiet enjoyment by some existing condition, or by actions being carried out b y another person, group, or business (Worrall & Wheeler, 2019 , p. 14 ). As such, nuisance abatement ordinance s can take many forms . 34 P roperty - owners are motivated to comply to the standards established by a code or ordinance through a civil injunction . Con sequences for noncompliance range in severity and may include a fine, jail - time, eviction, or forced closure or sale of the property ( see Smith & Mazerolle, 2013) . Property - owners may also be held civilly liable for illegal activities that occur on their p roperties ( see Smith & Mazerolle, 2013). Outside of the police, enforcement rel ies on a broad range of actors ( e.g., building, health, electrical, plumbing, and fire inspectors ) that encompass a variety of agencies ( see Smith & Mazerolle, 2013) . The police may collaborate with these agencies by bringing problem properties to their attention, assisting on inspect ions, issuing notices of violations (e.g., excessive alcohol consumption, over - crowding, litter, overgrown foliage, unkempt properties, an d aband oned/derelict buildings ) , and/or enforcing the consequences of noncompliance . Around the time - frame of interest to this study (2014 - 2015) , the DPD engaged in several efforts t hat align ed with the central tenants of o rder - maintenance policing . In 2012, the city of Detroit, on the verge of bankruptcy, enlisted the assistance of the Manhattan Institute and Bratton G roup to facilitate the DPD adoption of policing tactics inspired by BWT . This collaboration resulted in a community polici ng pilot program which launched in Grandmont - Rosedale neighborhood . The pilot program consisted of three main components: A f ocus on individuals who commit home invasions; a n increase in what is known as the ; l everaging the community as the eyes and ears to report suspicious/criminal activity. (Detroit Public Safety Foundation, 2013) United by a shared purpos e of creating a safer community, t he DPD forged partnerships with residents and business - owners within Grandmont - Rosedale, as well as the criminal courts, Wayne County Sheriff Department, Michigan Department of Corrections, Greater Detroit Centers for Work ing Families, and Detroit Public Safety Foundation (Detroit Public Safety Foundation, 2013) . 35 During the year - long pilot program , the DPD made over 1,200 proactive contacts with residents and conducted home visits with individual s who were previously arre sted for serious crimes (Detroit Public Safety Foundation, 2013) . Due to its low density, foot patrol was not implemented in Grandmont - Rosedale. 5 A t the completion of the pilot program in June 2013 , the DPD announced a 26% reduction in home invasion s (Detroit Public Safety Foundation, 2013) . Kelling - a senior fellow at the Manhattan I nstitute - you increase the felt presence of police and conduct proactive outreach, the police and community together can pre , p.1 ). Following the success of the pilot program, the city hired a new police chief : Chief James R. Craig. Soon after his arrival to Detroit, Chief Craig launched the Neighborhood Police Officers progr am , a comprehensive strategy aimed at improving communication and collaboration between the police, residents, and local businesses in an effort to create safer neighborhoods (City of Detroit, 2020) . This program is currently on - going. For each precinct, t hree to five officers are designated to serve in the long - term position of neighborhood police officer (NPO ) (City of Detroit, 2020) . On average, an NPO is responsible for two scout car area s (SCA s ) , consis ting of an area of approximately 2.09 square - miles. Together, the long - term nature of the position and responsib ility for a smaller , more manageable geographic area enable s NPOs to become more familiar with the community dynamics of the SCA s to which they are a ssigned (see Figure 6 ) . 5 Grandmont - 36 Figure 6 . Scout Car Areas within Precincts . Furthermore, NPOs play a non - adversarial role within their assigned SCAs , primarily addressing non - emergency and quality of life issue s . Aligned with this role, NPOs receive additional training aimed at promoting positive interactions between the police and the community . Importantly , t he program seeks to increase one - to - one contact with NPOs in settings outside crime in an effort to deve lop two - way relationships of trust with the community . To this end , NPOs are provided personal cellphones to communicate directly with residents and business - owners , and are encouraged to engage in playful interactions with youth and attend community event s. Residents and business - owners are also provided the opportunity to meet NPOs at monthly Community Relations Council meetings in which they can raise issues for discussion . Thus, w hile NPOs still rely on their patrol vehicles to get from place - to - place, it does not hinder them from directly interacting with individuals within their assigned SCAs. The initiation of the NPO program coincided with service request program , which had ceased operations on June 30 th , 2012. Almost two years later, the 37 This program is currently on - going. T he development of a mobile application (app) and online reporting system provide alternative ways to report non - emergency issues related to th e physical environment ( e.g., abandoned vehicle s , potholes, and illegal dumping). T hese upgrades provide easier, more streamlined alternatives to report and track issues. By downloading the mobile application onto thei r cellphones, NPOs can easily report i ssues as they come to their attention on assignment . Currently , NPOs are amongst the most active users of the Improve Detroit app. Meanwhile downtown was also undergoing several changes of its own . I n an effort to improve its appearance and safety , the city invested in the installation of more and better street lighting, beautification efforts (e.g., planting trees, plants , and flowers), and property development. In addition , the Downtown Detroit Partnership (DDP) combine d the efforts of the DPD and more than 20 businesses to maintain orde r. In particular, the DPD focused its efforts on , and the perceptions and realizations of public order created by clean st reets and sidewalks, well - maintained landscaping, 2013). Empirical Support for the Effectiveness of Poli ci ng Disorder Strategies A host of studies have evaluate d the impact of policing disorder strategies on violent crime . Most controversial among them are those that sought to identify the contributions of order - maintenance policing to the crime drop in New York City during the 1990s. Controlling for a host of socio - demographic variables , Kelling and Sousa (2001) found a significant negative relationship between misdemeanor arrests a proxy for order - maintenance policing activities - and violent crime. They interpret ed these results as supporting order - maintenance policing and discrediti ng explanations that focu s However, in a re - 38 analysis of the evidence Harcourt and Ludwig (2006) failed to find an association between misdemeanor arrests in New York Ci ty and violent crime. Several evaluations conduct ed in other cities have also failed to find evidence of a crime reduction effect associated with policing disorder strategies ( e.g., Katz, Webb, & Schaefer, 2001; Pace, 2010; Weisburd , Hinkle, Famega, & Ready , 201 1 ). In a later study, Rosenfeld, Fornango and Rengifo (2007) address ed several limitations in account for the effects of spatial autocorrelation , and simultaneity b etween order - maintenance policing and serious crimes. Their re - analysis suggest s that order - maintenance policing contributed to small but significant decline s in homicide and robbery in New York City. However , unlike Kelling and Sousa (2001), they found se veral root causes of crime, such as low socio - economic status, racial composition , and immigrant concentration , to have a positive and significant effect on crime (Harcourt & Ludwig, 2006) . In another study, Messner et al. (2007) found misdemeanor arrests to be associated with significant reductions in homicide rates, with the greatest impact on gun homicide rates. Several evaluations conducted in other cities also lend support to the ability of policing disorder strategies to produce si gnificant crime reduction gains ( e.g., Braga et al. , 1999 ; McGarrell et al. , 1999; Braga & Bond , 2008; Berk & MacDonald , 2010) Ultimately, early and evaluations conducted elsewhere provide d no cl earer understanding of the effectiveness or significance of policing disorder strategies . In the wake of these mixed evaluation s , Braga et al. (2015) conducted a systematic review of published and unpublished empirical evidence on the effectiveness of policing disorder strategies . This review consisted of 30 randomized experimental and quasi - experimental evaluations (Braga et al., 2015) . U sing meta - anal ytical 39 techniques , Braga et al. (2015) found that policing disorder strategies had a significant modest effect on crime reduction . T he strategies that had the greatest impact were those that utilize d community and problem - solving interventions consistent with the central tenants of order - maintenance policing, while a ggressive strategies had no significant effect (Braga et al., 2015) . While Braga (2015) review sheds light on the effectivenes s of policing disorder strategies , it tells us nothing about the validity of BWT. More specifically, it tells us nothing about whether the crime control gains associated with policing disorder strategies are achieved by disrupting the cycle of disorder and decline described by Wilson and Kelling (1982). T he observed crime control gains may be partially or wholly achieved by competing theoretical mechanisms . To the extent that this is true, BWT would fail to provide a unique and valuable framework to the field of C riminology. In a fol low up review , Weisburd et al. (2015) address ed this issue , casting doubt on Braga (2015) findings. They argue that if policing disorder strategies indeed disrupt the broken windows process, then they should be associated with significant reductions in fear of crime (Weisburd et al., 2015). Using meta - analytical techniques, they evaluat e d six studies on the effect of policing disorder strategies on fear (Weisburd et al., 2015) . Overall, W eisburd et al . (2015) fail ed to find evidence to suggest that policing disorder strategies yield significa nt reductions in fear, and one evaluation on its effect on collective efficacy also found no significant impact. T hey conclud e policing mechanisms are behind the crime control gains of disorder polic ing programs observed Instead, Weisburd et al. (2015) argue that the mechanisms underlying criminal opportunity theories may help to better explain the crime control gains observed in policing disord er evaluations . 40 Implications for the Broken Windows Tipping Point Four separate but related questions emerge from the review provided on the broken windows tipping point and policing disorder strategies . First, how may the t i pping point impact the effectiveness of policing disorder strategies ? Second , what, if anything, do evaluations of the effectiveness of policing disorder strategies tell us about the location of the broken windows tipping point ? Third, what implications does the tipping poi nt have for the allocation of police resources? Fourth , w hat does it mean for efforts to identify the tipping point if policing disorder strategies are not found to disrupt the broken windows cycle? Q 1 : H ow may the broken windows tipping point impact the effectiveness of policing disorder strategies ? As previously mentioned , evaluations of the effectiveness of polic ing disorder strategie s fail to to identify neighborhoods at the tipping point . The implication s of this failure are multifaceted . Broadly speaking, t he nature of the relationship between disorder and violent crime encourages certain expectations regarding the potential crime control gains of policing disorder strategies . Without this kn owledge, we are unable to accurately judge the effectiveness of policing disorder strategies . W e are also un able to know how best to direct police resources . For these reasons, it is very likely that policing disorder strategies have been directed to the w rong locations, and have, as a result , not realized their full potential . W instruction to police - stop small problems before they become much larger is not so simple after all. 41 Q 2 : What, if anything, do evaluations of the effectiveness of policing disorder strategies tell us about the location of the broken windows tipping point ? Ultimately, it is unclear what the empirical findings from evaluation s of the effectiveness of poli cing disorder strategies tell us about the tipping point . To start , evaluations t hat find no effect on crime do not suggest that policing disorder strategies were implemented in the wrong neighborhoods (i.e., neighborhoods that were not located at the tipp ing point ) . As will later be discussed, there are several issues associated with evaluations of policing disorder strategies that may lead researchers to incorrectly conclude that they have no effect on crime . In addition to these issues , research has show n that neighborhood context plays a critical role in the effectiveness of policing strategies (Kelling & Coles, 199 6 ; Kane & Cronin, 2009). R ecall a goal of order - maintenance policing is to aid residents in re gaining control over their communities . S trategic police - community partnerships are instrumental to achieving this goal ; they require that residents trust in the police and are commi tted to police efforts to improve their neighborhood . However, certain neighborhood condition s may un dercut the effectiveness of these partnerships or prevent them from occurring altogether. For example, deeply embedded negative attitudes toward the police may prove to be an insurmountable obstacle toward est ablishing police - community partnerships . In fac t, research has shown that individuals who harbor negative attitudes toward the police are less willing to utilize formal mechanisms of social control ( Scaglion & Condon, 1980; Dunham & Alpert, 1988; Silver & Miller, 2004). R esearch has also shown that resid en ts neighborhood attachment s predict their willingness to collectively engage in informal social control , as well as partner with the police (Silver & Miller, 2004; Long & Perkins, 2007 ). Thus, in neighborhoods in which neighborhood attachments are low, such as in highly transient neighborhoods, the potential of order - maintenance policing to drive positive neighborhood change may not be fully realized . 42 Furthermore, empirical findings which indicate that policing disorder strategies do reduce crime also provide no insight on whether they were implemented in neighborhoods at the tipping point. This is because Wilson and Kelling (1982) never argue that to have an effect on crime policing disorder strategies must be implemented in such neighborhoods. In stead, they argue that the best use of limited police resources is to target neighborhoods at the tipping point (Wilson and Kelling, 1982). That being said, how we interpret the tipping point (and the nature of the relationship between disorder and violent crime it suggests) set s up certain expectations for the effectiveness of order - maintenance policing initiatives . the broken windows tipping point depicted by the line segments and in Figure 1 and replicated in Figure 7 . In neighborhoods at or leading up to the tippi ng point , efforts to decrease disorder should not produce very large crime reduction gains (see Zone 1 depicted in Figure 7 ) . W hat distinguishes these neighborhoods are their (1) ability to address disorder via informal social control and (2) risk of infla ming the broken windows developmental sequence . In neighborhoods located at the tipping point , informal social control is faltering . Without intervention, it is unable to return the neighborhood s back to a low disorder, low crime state . Given their position, these neighborhoods are at great risk of being propelled into a high disorder , high crime state . P olicing disorder strategies implemented in neighborhoods at the tipping point are oriented towards preventing disorder from extending beyond tipping point levels , resulting in an uptick in violent crime . Police intervention should be minimal , just enough to supplement and restore informal social control within neighbor hood s . If possible, however, c itizen action should 43 be the primary mec hanism through which disorder is addressed (Wilson & Kelling, 1982 ; Kelling & Coles, 1996 ). To this point, Wilson and Kelling (1982 , para. 44 ) argue that [e] ven in areas that are in jeopardy from disorderly elements, citizen action without substantial police T hey provide some examples of what citizen action may entail : Meetings between teenagers who like to hang out on a particul ar corner and adults who want to use that corner might well lead to an amicable agreement on a set of rules about how many people can be allowed to congregate, where, and when . Where no understanding is possible or if possible, not observed citizen patrols may be a sufficient response. (Wilson & Kelling, 1982, para. 44 - 45) Beyond the tipping point, however, the primary purpose of policing disorder strategies is geared to wards return ing disorder to pre - tipping point levels (see Z one 2 depicted in Figure 7 ) . In other words, policing disorder strategies are oriented toward achieving significant crime reduction gains . However, our expectations regarding whether we think this goal can be easily achieved depend s , in part, on which interpretation of the nature of the relationship between disorder and violent crime we place stock in . Wilson and Kelling (1982) description of the broken windows tipping point can be understood as a statement regarding the appropriate dosage of police response needed to address disorder in neighborhoods located beyond the tipping point . According to their description, w e should not expect policing disorder strategies to elicit significant crime reduction gains if they are implemented with lim ited police resources (Wilson & Kelling, 1982) . In such a scenario, Wilson and Kelling (1982) argue that the best police can do is to respond to calls for service. That being said, there is an other option that Wilson and Kelling (1982) fail ed to consider: police resources can be directed to small geographic areas that contain heighten ed levels of disorder and/or crime (i.e., hot spots). In this scenario, a high spatial dosage of policing disorder activities can be achieved with limited police resources ( Trojanowicz, 1986 ; Ratcliffe et al., 2011) . 44 Therefore, a ssuming the proper dosage of police response was utilized, we should expect policing disorder strategies directed to neighborhoods that fall along the or line segments depicted in Figure 7 t o return significant crime reduction gains given the strong relationship between disorder and violent crime in such places. Alternatively, description of the tipping point can be understood as an assessment of the strength of th e relationship between disorder and violent crime in high disorder , high crime neighborhoods . In such neighborhoods, t he relationship between disorder and violent crime is modest . For this reason, b eyond point efforts to address disorder will not return significant crime reduction gains. Upholding this competing interpretation , we should not expect significant crime reduction gains for neighborhoods that fall along the line segment depicted in Figure 7 . Regardless of which interpretation we place st ock in, the strength of police - community partnerships, as well as the degree of flexibility afforded by trajectory and the systemic features that contribute to it are additional factors that reasonably affect the effort required to facilitate a high disorder , high crime state to low disorder, low crime state . Figure 7. The Broken Windows Tipping Point: Crime Prevention vs. Crime Reduction . 45 There are several reason s to question t he expectations described here . To start, policing disorder strategies that have been effective at reducing crime in hot spots may indicate that the tipping point is located further down the disorder ( Braga & Bond, 2008; Bra ga et al., 1999; Braga et al., 2012 , 2014 ). Further complicating matters, Geller (2007) finding of a concave relationship in which the effect of disorder on violent crime is the strongest at low levels of disorder suggests that the broken windows tipping point may not resemble a threshold effect as suggested by Wilson and Kelling (1982) . While much more research needs to be conducted on this phenomenon, this small handful of studies provide reason to critically re - consider Q 3 : What implications does the broken windows tipping point have for the allocation of police resources? A prime metric by which to assess the success of a policing strategy is the effect it has on crime . e may have encouraged [the police] to suppose, however, on the basis of our oft - repeated concerns about serious, violent crime, that they will be ju dged exclusively on their capacity as crime - fighters. With this metric in mind , i f the police want to have a large observable impact on crime, research suggests that it focus its efforts on crime hot spots (see Braga et al., 2019 ) . However, BWT requires that this metric of success be reconsidered . In actuality, BWT suggests that policing disorder strategies should be directed to neighborhoods that are at the brink of decline : neighborhoods at the broken windows tipping point . As co mpared to neighborhoods located beyond the tipping point , these strategies are expected to achieve much smaller crime reduction gains given the nature of the disorder - crime relationship suggested by Wilson and Kelling (1982) . Adding a layer of complexity, the identification of a valid treatment effect will be much 46 harder in neighborhoods located at the tipping point than neighborhoods located beyond it given l ow er base rates of disorder and crime ( see Hinkle et al ., 2013). Fu rthermore, policing disorder strategies focused on neighborhoods located at the tipping point are oriented toward preventing future increase s in violent crime . This increase is anticipated by virtue of being at the tipping point. The logic being that f utur e expenditures of police resources, as well as the consequences of violence for neighborhoods and their residents, can be avoided by providing a minimal police presence in neighborhoods located at the tipping point until neighborhood informal social contro l is able to re - establish and sustain public order unaided . Thus, t he benefits of police efforts oriented toward crime prevention , defined as actions taken to prevent future crime emergence , are overlooked by gauging success primarily in terms of crime reduction gains , defined as the amount by which crime is reduced. In an ideal scenario, the police should work to reduce overall crime incidents in neighborhoods, as well as prevent future cri me emergence. Police efforts geared towards the former objective are relatively easy to assess . For example, a simple comparison of crime levels before and after a police intervention can be used to identify a treatment effect. However, it is exceedingly m ore difficult to identify a treatment effect for efforts geared toward the latter objective, as their aim is to avoid a future potentiality : crime that has not yet occurred . Thus, evaluation s of these efforts require knowledge of what would have likely happened in the neighborhood had the police never intervened . According to Wilson and Kelling (1982), the best use of limited police resources is to direct them to neighborhoods at the tipping point. However, the proven effectiveness of hot spot policing provides reason to question this approach. Therefore , a better approach is to conduct a comprehensive assessment of the costs and benefits associated with how resources should be 47 allocated, dif ferentiating policing strategies aimed at crime reduction from those aimed at crime prevention . To this point, Wilson and Kelling (1982) seemingly support such an assessment: But the most important requirement is to think that to maintain order in precario us situations is a vital job. The police know this is one of their functions, and they also believe, correctly, that it cannot be done to the exclusion of criminal investigation and responding to calls. (para. 51) Factors worthy of consideration in such c ost - benefit assessments might include t he ability of the police strategy to of life , reduce fear of crime, strengthen police - community relations , and avoid the financial and social costs that would likely accompany future violence. Of course, this short list of factors is far from complete. The identification of the tipping point will surely advance this list by facilitating the identification of appropriate performance outcomes associated with police efforts geared toward crime prevention at the tipping point. Ultimately, even with limited police resources one strategy need not be completely abandoned to support the other. Rather, resources should be differentially allocated. In such a scenario, neighborhoods that stand to experience the largest net benefit from a polic ing disorder strateg y should be prioritized. Q 4 : What does it mean for efforts to identify the broken windows tipping point if policing disorder strategies are not found to disrupt the broken windows cycle? What remains to be discussed are the implications of efforts to identify the broken windows tipping point in the event that policing disorder strategies are not found to disrupt the broken windows cycle . As previously mentioned, Weisburd et al. (2015) r eview suggest s that the mechanisms underlying criminal opportunity theories may better help explain the crime reduction gains observed in policing disorder evaluations . Importantly, this suggestion is motivated by their failure to find these strategies to have a significant effect on fear of crime and, in one case, collective efficacy (Weisburd et al., 2015) . While our theoreti cal understanding of 48 the mechanisms underlying the tipping point would no longer hold merit , the idea still hold s rel evance for efforts to address disorder . To elaborate, even in the extreme case in which policing disorder strategies have no roots in BWT it is still reasonable to direct limited police resources to neighborhoods located at the tipping point in an effort t o avoid future crime emergence . While we may anticipate significant crime reduction gains if policing disorder strategies are implemented in high disorder , high crime neighborhoods , the dosage of police resources that would be needed to return them to a lo w disorder, low crime state in which residents are able to exercise informal social control would likely come at too high a cost . At the opposing extreme , policing disorder strategies would be inappropriate in low disorder, low crime neighborhoods for the simple reason that disorder and crime are not issues in these areas . For these reason s , the allocation of limited police resources to neighborhoods at the tipping point emerges as a completely defensible approach in order to avoid the future potentiality of increased violence. N evertheless , this approach should be weighed in light of the ben efits associated with policing efforts geared toward crime reduction . Four critical issues of broken windows research impair evaluations of policing disorder strategies and may lead researchers to incorrectly conclude that they do not disrupt the broken windows cycle . First , the time - frame in which the broken windows developmental sequence is expected to unfold is unknown . Consequently, it is unclear how quickly the effects of order - maintenance policing are expected to impact fear of crime, eventually leading to a reduction in crime. That being said , it is reasonable to suspect that policing disorder activities should have a relatively i mmediate effect on potential offenders through deterrence - based processes. An increase in police activities should send a clear signal to potential offenders that criminal acts 49 will likely be detected , which should in turn heighten their risk of apprehensi on and deter offending. Second , i t has been suggested that some policing disorder strategies may increase ( Rosenbaum , 2006; Hinkle & Weisburd, 2008 ) . In particular, the implementation of heightened police activities may signal to residents that disorder and/or crime has risen , triggering public levels of fear to rise. Thus, any reduction in fear of crime that had been achieved by addressing disorder will be diminished by increases in fe ar associated with the strategy itself . As a result, researchers may incorrectly conclud e that policing disorder strategies have no effect on fear of crime. However, m ore recent research has questioned this phenomenon ( see Weisburd et al. , 2011 ; Ratcliffe et al., 2015 ). Ultimately, m uch more research needs to be conduct ed that explore s this phenomenon across various target populations and crime levels, as well as types of hot spots and policing strategies. 6 Third , th e appropriate dosage of polic ing needed to effectively address the issue of disorder is unknown (Wilson & Kelling, 1982) . This issue is not unique to order - maintenance policing and has been explored in applications of other policing strategies, such as hot spot policing , that are anchored in a deterrence - based understanding of crime ( Kelling, 1974; Koper, 1995; Telep et al., 2014; Groff et al. , 2015 ; Santos & Santos, 2015 ). As previously discussed, heightened policing disorder activities may be beneficial in terms of leveraging cri me reduction gains through deterrence - based pathways . However, it has been suggested that these activities may inspire fear within residents, which in turn may prevent the crime control gains associated with disrupting the broken windows cycle from being f ully realized . Thus, a key issue is whether 6 As previously mentioned, aggressive tactics to addre ss disorder, such as those employed in zero - tolerance, violate the central tenants of order - maintenance policing as described by Wilson and Kelling (1982) . For this reason, the implication s of these tactics on fear of crime were excluded from this discussion . 50 there exists an appropriate dosage of order - maintenance policing activities that is able to jointly harness deterrence - based and broken windows processes to produce maximum crime control benefits . Last , another reason to consider why policing disorder strategies may have little effect on fear of crime is that such strategies may be implemented in places in which the disorder - fear connection is weak or non - existent . To elaborate , research suggests that the disorder - fear connection may be weak or non - existent in neighborhoods in which disorder is either low or high ( Taylor, Shumaker, & Gottfredson, 1985 ; Taylor & Shumaker, 1990; Innes, 2004; Millie, 2008 ; Sampson & Raudenbush, 2004) . In low disorder neighbor hoods, residents are unlikely to perceive disorder as a problem. In high disorder neighborhoods, residents may become inoculated to its presence. The explanation for why the disorder - fear connection may be weak or non - existent in both neighborhood types is the same: if residents are unaware or unbothered by the presence of disorder, then it will likely not result in a fear response and the process of neighborhood decline - as hypothesized by Wilson and Kelling (1982) will not be spurred . For this reason, in such neighborhoods it would be unreasonable to expect policing disorder strategies to reduce neighborhood levels of fear by addressing disorder. In summary , evaluation s of policing disorder strategies are unable to provide us with a clear understandin g of the location of the broken windows tipping point, or the extent to which the crime control benefits associated with these strategies are driven by broken windows or alternative processes. The lack of attention that has been given to the tipping point is extremely surprising given its potential impact on the effectiveness of policing disorder strategies. Importantly , r esearch that seeks to identify the location of the tipping point not only has 51 significant implications for the effectiveness of police operations that address disorder, but also for evaluations that examine the theoretical mechanisms underlying such strate gies. Moving forward, i t is the purpose of this study to empirically examine the relationship between disorder and violent crime rate as a first step toward identifying the broken windows tipping point. R esearch that seeks to identify the tipping point should not implicitly assume that disorder maintains a linear relationship with violent crime, nor should it take Wilson and - value. To this point, the present study makes great strides to advance re search on the tipping point by adopting a methodological approach that allows for flexibility in modeling decisions . Current Study T his study empirically assess es the validity of four hypothesized functional forms of the relationship between physical disorder and violent crime rate that emerged from its literature review . In the absence of detail provided by Wilson and Kelling (1982), disorder has been hypothesized to have a positive linear effect on violent crime (H1) . However, Wilson and crime. Importantly, t heir description gives rise to two competing interpretations of this relationship (Wilson & Kelling, 1982) . F irst, disorder maintains a threshold effect on violent crime s uch that small variations in disorder exert a modest positive effect on violent crime at low levels of disorder , and a dramatic positive effect past a critical level located somewhere between low and high levels (H2a) . Second, d isorder maintains a threshold effect on violent crime s uch that small variations in disorder exert a modest positive effect on violent crime at low and high levels of disorder , and a dramatic po sitive effect past a critical level located somewhere between these extremes (H2b) . supported by 52 Raleigh and Galster (201 5 ) - pushes the tipping point toward the end of the disorder distribution. In particular, it suggests that small variations in disorder exert a modest positive effect on violent crime at low and mid - range levels of disorder, and a dramatic positive effect past a critical level located somewhere at high levels of disorder (H3) . As seen in Figure 8 , hypotheses H1, H2a, H2b, and H3 are captured by the , , , and line segments, respectively. Furthermore , there is also reason to believe that disorder may not exhibit a threshold effect on viol ent crime, but rather a nonlinear effect that may take one of many forms, such as the concave relationship between disorder and violent crime rate identified by Geller (2007 ) ( H4) . These f physical disorder on violent crime rate , and are explicitly stated in Table 1 . Table 1. Key Research Question & Hypotheses . Research Question: What is the functional form of the relationship between physical disorder and violent crime rate ? H1: Physical d isorder maintains a positive linear effect on violent crime rate. H2a: Physical d isorder maintains a threshold effect on violent crime rate s uch that small variations exert a modest positive effect on violent crime rate at low levels , and a dramatic positive effect past a critical level located somewhere between low and high levels. H2b: Physical d isorder maintains a threshold effect on violen t crime rate such that small variations exert a modest positive effect on violent crime rate at low and high levels , and a dramatic positive effect past a critical level located somewhere between these two extremes. H3: Physical d isorder maintains a threshold effect on violent crime rate such that small variations exert a modest positive effect on violent crime rate at low and mid - range levels, and a dramatic positive effect past a critical level located somewhere at high levels . H4: Physical d isorder maintains a nonlinear effect on violent crime rate. 53 To assess these hypotheses, t his study utilize s a dose - response propensity score method, an appropriate and rigorous evaluation design that minimizes concerns about selection bias and allows for causal inferences . This approach estimates the average treatment effect of various levels of physical disorder, measured at = 2014, on violent crime rate , measured at = 2015, explicitly models the functional form of these variables, and allows for covariate balancing across matched levels of physical disorder. Importantly, this method is well - suited for the identification of tipping points because it allows for nonlinear threshold effects to be estimated. To facilitate its analysis, this study utilize s block - group level data on physical disorder , violent crime, as well as socioeconomic and land use charac teristics from the system, MCM project, and Census. These sources provide the data necessary to create theoretically relevant variables of key interest to this study . Figure 8 . Hypotheses H1, H2a, H2b, and H3 . 54 CHAPTER 3: STUDY DESIGN AND IMPLEMENTATION Measures and Data Sources Th is study collect ed data on physical disorder, violent crime, as well as socioeconomic Census . These data were aggregated to the block - group level, a common unit of analysis in research on the relationship between disorder and crime (see Sampson & Raudenbush, 1999, ; Wheeler, 2018 ). Reflecting its focu s on neighborhoods , this study exclud e d block - groups that fell area, contain ed no population, and/or did not contain properties zoned for residential use. This selection procedure exclude d 22 block - groups, resulting in a total sample size of 8 57 (see Figure 8) . Figure 9 . Selected Block - groups . Physical Disorder . A traditional method to capture disorder in neighborhoods is through physical audits of the environment, referred to as systematic social observation (SSO). SSO is an 55 appealing approach to measuring disorder because it relies on independent and structured observations of the environment by trained surveyors. As a result, it avoids many measurement issues common to alternative approaches, such as community surveys and 311 service requests. To elaborate, community survey measures of disorder may be compromis inability to distinguish between disorder and crime (Gau & Pratt, 2008 , 2010 ), and have been found to be affected by individual - and neighborhood - level characteristics (Taylor, Shumaker, & Gottfredson, 1985; Sampson, 2009, 2012; Sampson & Raudenbush, 2004; Wickes, et al., 2013) As self - repo rted data, 311 service requests are affected by both under - and over - reporting (S herman, Gartin, & Buerger, 1989; Klinger & Bridges, 1997). These data may also be biased if , & Sampson, 2015; ; White & Tru mp, 2016 ). The use of SSO to measu re disorder is not without its limitations. To start, it is an extremely timely and costly approach . For these reasons alone , SSO may be out of reach for economically - strained communities . Virtual audits of the environment - made possible by geospatial technologies like Google Street View - are a less - costly alternative to SSO. However, much more research is needed to assess the reliability and validity of this method for capturing disorder (e.g., Clarke et al., 2010; Rundle et al., 2011; Odgers et al., 2012; Mooney et al., 201 6 ). Furthermore, it is well known that SSO is likely to vary depending on weather conditions, time of day, and day of the week, and is also dependent on unity in inter - rater reliability ( see Skogan, 2012, 2015). Perhaps the greatest limitation of SSO involves the argument that disorder is a social construct , rather than an objective condition that is similarly perceived across individuals (Harcout, 2001; Sampson & Raudenbush, 2004 ; Hinkle & Yang, 2014). Indeed, research 56 suggests that what residents perceive as disorder may not align with how disorder is captured by outsiders, such as those conducting SSOs ( e.g., Perkins et al., 1993; Franzini et al., 2008 ; Hinkle & Yang, 2014 ). Perceptions of disorder play a critical role in the broken windows development al sequence. If residents do not perceive disorder to be a problem in their neighborhoods , then this sequence will not unfold. From a purely theoretical s tandpoint, perceived disorder is the most appropriate measure to assess the validity of BWT. That being said, research finds considerable consistency between observed and perceived measures of physical disorder , the focus of this study ( Perkins, Meeks , & T aylor 199 2; Sampson & Raudenbush, 2004; Hinkle & Yang, 2014; Yang & Pao, 2015; Ren, Zhao, & He, 2017). Together, these findings suggest that physical disorder is more uniformly interpreted by residents as signaling neighborhood decline, resulting in higher levels of perceived disorder and fear. For this reason, SSO emerges as an appropriate approach to capture physical disorder. - in partnership with Michigan Nonprofit Association, Data Driven Detroit, and Lov eland T echnologies - developed a survey to capture the physical condition of every land parcel within Detroit. The motivation behind the city collaborative termed the Motor City Mapping (MCM) project - was to create a comprehensive, crowd - sourced database in an effort to id entify problem properties and track them over time. S urveyors were recruited from within the city to facilitate this initiative . As a result of this recruitment strategy, the surveyors possessed detailed knowledge on Detroit neighborhoods and the city as a whole. Once recruited, they received extensive training to ensure a comprehensive understanding of survey items and definitions. Additionally, the surveyors received training on how to use a mobile app conditions and was downloaded on Nexus 7 tablets which were provided to each surveyor . Over a 10 - week period, 57 teams of surveyors were assigned to micro - hoods 0.25 square - mile areas - to conduct physical audits of the entire city utilizing the Blexting ap p. For each property, the surveyors took photographs and responded to a series of survey items. Furthermore, a mission control center was established where staff performed quality checks of the data submitted by the surveyors in real - time. Data collection was completed in the winter of 2014. The parcel - level data was later aggregated to the block - group level and made items are particularly well - suited for the c urrent study. A description of each item - taken from the MCM project codebook - is provided below (see Motor City Mapping, 2020) . S ummary statistics are provided in Table 2 . Percent Poor Condition Number of p arcels with structures that are in poor condition divided by the number of parcels surveyed with structures. Structures that are in poor condition n eed major repairs . Their w indows and doors may be broken or boarded . They may also have l ight fire damage that can be repaired. Other indicators of structures in poor condition include damaged, n on - load - bearing elements like awnings, or porches collapsed , and damaged roof . Percent Suggested Demolition Number of parcels with structures that are suggested for demolition divided by the number of parce ls surveyed with structures. Structures that are suggested for demolition include structures that are no longer shaped like a building. They are d amaged beyond practical repair or renovation , and are uninhabitable . Percent Structure Unoccupied Number o f parcels with structures that are perceived to be unoccupied divided by the number of parcels surveyed with residential structures . Common characteristics of unoccupied structures include neglected facades, eviction notices, empty interiors, substantial p hysical or structural damages, extensive security measures, uncut or tall grass, weeds, scrub trees, trash or debris accumulated over time, or accumulated flyers on the porch or door. Percent Structure Need Boarding Number of parcels with structures tha t are in need of boarding divided by the number of parcels surveyed with structures . A structure is in need of boarding if it has missing windows, doors or is otherwise open and accessible to scrappers, squatters, or vandals. Percent Structure Fire Damage d Number of parcels with structures that are fire - damaged divided by the number of parcels surveyed with structures . A structure is 58 classified as having fire damage if it has visible indicators of fire damage in or around it , from as small as melted sidi ng to structures that have burned down to the ground. Percent Total Parcels Dumping Number of parcels, with or without structures, that have dumping divided by the number of parcels surveyed. A building or vacant lot is considered to have dumping when d ebris has been purposely left or placed on the property. This does not include litter or debris from a recent fire or ongoing demolition Percent Lots Unmaintained Number of parcels without structures that are unmaintained divided by the number of parcels without structures surveyed. Characteristics of an unmaintained lot include tall grass, overgrown trees or bushes, weeds in the cracks of pavement, and so on. A principal component factor analysis revealed that all items loaded strongly onto a single factor (see Table 3 ). For this reason, a single composite measure representing physical disorder was generated from a regression - weighted scale of constituent characteristics and adjusted so that all values were positive ( = 1.37, SD = 1.00, Min = 0, Max = 4.76). Figure 9 vis ually captures this measure by block - group, with classifications based upon natural - breaks. As can be seen, low levels of physical disorder (indicated by blue tones) are predominantly concentrated in north - west Detroit, while high levels (indicated by red tones) are concentrated in Table 2 . Physical Disorder Summary Statistics . Variable Mean Std. Dev. Min Max Percent Poor Condition 3.57 4.00 0 17.89 Percent Suggested Demolition 1.86 2.64 0 17.52 Percent Structure Unoccupied 19.32 12.50 0 59.33 Percent Structure Need Boarding 11.34 9.58 0 50.00 Percent Structure Fire Damage 2.79 2.99 0 20.18 Percent Total Parcels Dumping 2.38 2.67 0 24.84 Percent Lots Unmaintained 46.65 23.76 0 100.00 59 several areas, most notably in west, central, and north - east Detroit. Furthermore, Figure 10 displays the distribution of physical disorder captured as a density. The data reveal a moderate right skew. Table 3. Principal Component Factor Analysis . Figure 10. Physical Disorder . Physical Disorder Factor Loading Percent Poor Condition 0.86 Percent Suggested Demolition 0.82 Percent Structure Unoccupied 0.91 Percent Structure Need Boarding 0.93 Percent Structure Fire Damage 0.87 Percent Total Parcels Dumping 0.73 Percent Lots Unmaintained 0.75 Note: = 0.78. For factor analysis, N = 857 . A principal component factor estimation was used with no rotation. 60 Figure 1 1 . Physical Disorder: Kernel Density Estimate . Violent Crime Rate . Broken windows research customarily uses either incident or CFS data as a measure of violent crime (see Braga et al., 2015). However, CFS may contain perceptions of crime levels (see Hinkle & Weisburd, 2008). To this point, it can be argued that BWT does not place perceptions of violence, but rather substantiated incidents thereof. Furthermore, CFS tend to be a less accurate record of crime types (Klinger & Bridg es, 1997). For these reasons, this study collects violent crime incidents (homicide, rape, robbery, and aggravated assaults) that occurred in 2015 from the construct its dependent variable. Importantly, t on violent crime is not only consistent with BWT, but also help ed ensure that it s dependent variable is conceptually distinct from disorder (Weisburd et al., 2015). These data were geocoded in ArcMap (version 10.8) , aggregated to the block - group level, and recorded as a rat e (per 1,000 people) using five - year population estimates obtained from the American Community Survey (ACS) ( = 22.18 , SD = 19.09 , Min = 1.71 , Max = 277.37 ). 61 Figure 1 1 visually captures violent crime rate by block - group, with classifications based upon natural - breaks . As can be seen, high levels of violent crime rate ( indicated by red tones ) are predominantly concentrated in central and north - east Detroit, while low lev els ( indicated by blue tones ) are concentrated in several areas, most notably in north - east and south Detroit . Furthermore, Figure 1 2 displays the distribution of violent crime rate captured as a density. An extreme right - skew is evident . Figure 1 2 . Viole nt Crime Rate (2015) . 62 Figure 1 3 . Violent Crime Rate (2015) : Kernel Density Estimate . Control/Matching Variables. This study construct ed land use and socioeconomic variables from data sources compiled in 2014 (see Table 4 ). The identification of these variables was informed by the previous review of broken windows and related research . Given their presumed correlation with physical disorder, the omission of these var iables from this analysis would result in omitted variable bias. This consequence has severe implications for the ability of the GPS approach to draw causal inferences, a point of late r discussion. D ata on land use characteristics were obtained f rom the MCM project and constructed as a proportion of all parcels. The measures constructed include percent garden/park, percent commercial, percent residential, percent industrial, and percent mixed. Furthermore, socioeconomic variables were constructed using five - year estimates obtained from the ACS and population density (measured per square - mile) , percent male between the ages of 15 and 24, percent population under the age of 18 , percent unemployed, percent receiving public assistance, percent female - 63 headed households, percent owner - occupied home s, percent same residence (for at least one year), percent African American, percent Hispanic/Latino o rigin , percent white, percent foreign - born , and violent crime rate. 7 A measure of population growth was constructed using population estimates from the 2000 Census. Block - group boundaries in 2014 do not perfectly match those used over ten years ago. For this reason, areal interpolation was necessary in order to re - aggregate the data to the block - group boundaries used in 2014 . 8 available in ArcMap . The process first begins with the construction of a valid variograph mod el from which population estimates are calculated . According to the ESRI (2020) user - guide , 90% of the empirical covariances (blue cross) should fall within the (red) confidence intervals (see Figure 1 3 ) . Furthermore, the root - mean - square standardized value should also be close to one (RMSE = 1.1 0 ) . The constructed model met both of these criteria . The re - aggregated population estimates were then used to calculate a measure of population growth, defined as 7 A measure of concentrated disadvantage, consisting of percent unemployed, percent receiving public assistance, percent female - headed household, percent African American, and percent population under 18, could not be const ructed due to low correlation between its constituent characteristics ( = 0.39). 8 areal unit system based on that of another, spatiall (Qiu, Zhang, & Zhou, 2012, p. 645). 64 Figure 1 4 . Variograph Model . In addition, a spatially lagged variable was created to quantify the spatial relationship among block - groups on physical disorder. This relationship is suggested in BWT and has garnered much support (see Keizer, Lindenberg, & Steg, 2008; Cerd et al., 200 9; Boggess & Maskaly, 2014; Steenbeek & Kreis, 2015; Wheeler, 2018) . physical disorder exhibits spatial structure, characterized as significant clustering ( = 0.52, z - score = 33.57 ). 9 Consequently, a n inverse dist ance decay function was utilized to quantify this relationship. This function assumes that block - groups that are closer to the focal block - group are more influential than those that are further away. In particular, all block - groups within two miles of a fo cal block - group were considered to be influential and used in the calculation of the spatial lag. A distance of two miles was selected to reflect prior research which suggests that most offenders commit crime in nearby areas (Wright & Decker, 1997; Wiles & Costello, 2000; Wright, Brookman, & Bennett, 2006; Bernasco & Block, 2009) . 10 9 matrix and 999 permutations. This test was conducted in R using the sp package. 10 Additional spatial lag variables were constructed utilizing an inverse distance decay function with a cap of five - miles, as well as a queens contiguity matrix which defines neighbors as block - groups that share eith er a common boundary or point with the focal block - group. The resulting lag variables were highly correlated ( r < 0.90) with the lag variable used in this study and produc ed essentially identical results. 65 Table 4 . Control/Matching Variables: Full Sample (N = 857) . Variable Mean Std. Dev. Min Max Population Density (square - miles) 6442.03 3565. 60 369.95 23569.58 Percent Population Under 18 27.04 5.88 0 45.90 Population Growth - 12.50 46.93 - 92.24 393.55 Percent Male (15 - 24) 8.0 2 5.6 2 0 41.14 Percent Unemployed 28.36 14.52 0 88.06 Percent Receiving Public Assistance 8.32 7.71 0 69.81 Percent Female - headed Famil y Household 30. 70 14.24 0 78.76 Percent Owner - Occupied Homes 53.62 20.50 0 100 P ercent S ame Residence (a t l east o ne y ear ) 84.42 11.68 29.07 100 Percent African American 83.8 5 25.28 0 100 Percent Hispanic/Latino Origin 5.59 16.93 0 92.29 Percent White 10.86 18.17 0 100 Percent Foreign - born 4.08 9.36 0 61.09 Violent Crime Rate (per 1000) 23.12 21.92 0.72 350.37 Percent Garden/Park 1.90 6.00 0 100 Percent Commercial 4.91 6.16 0 71.43 Percent Residential 91.92 11.40 5.39 100 Percent Industrial 0.76 3.87 0 77.78 Percent Mixed 0.42 1.05 0 9.38 66 Table 4 Physical Disorder Lag 1.38 0.60 0 3.04 Note: If needed, these variables will be modified to facilitate matching. Analytical Strategy L evels of physical disorder are not randomly assigned and therefore a robust quasi - experiential design that takes into account selection effects is needed in order to evaluate the relationship between physical disorder and violent crime rate . In the absence of a n exogenous i nstrument needed to perform instrumental variable techniques, t his study utilize d the generalized dose - response propensity score (GPS) method to estimate the average treatment effect of various levels of physical disorder, measured at 201 4 , on violent crime rate , measured at 201 5 . This examination was performed using the program gpscore 2 available in STATA (version 16.0 ) statistical software ( Guardabascio & Ventura, 2013 ) . Dose - response models offer several advantages over traditional approaches. In particular, they are superior to regression approaches that address selection effects through the addition of control variables because they create matched groups that must achie ve balance on covariates in order for credible comparisons to be made. If balance is unable to be achieved, it means that are not possible. Furthermore, unlike traditional propensity score matching which is restricted to a di chotomous causal variable, dose - response models allow covariate balancing across levels of a causal variable. S imilar to traditional propensity score matching , the dose - response approach eliminates, where possible, bias associated with covariate imbalance s (Hirano & Imbens, 2004). A nother advantage of dose - response models is that they explicitly model the functional form across each level of the causal variable in such a way as to create balance among covariates. 67 Notwithstanding these advantages, it is important to acknowledge that both regression and propensity score matching approaches uphold the weak unconfoundedness assumption (or selection on observables assumption) (Heckman & Robb, 1985). Under this assumptio n, bias associated with the selection into treatment and treatment - specific outcomes is removed by controlling or conditioning on observable unit characteristics. I f there are hidden biases , however, then we lose confidence in this assumption and, conseque ntly, in our ability to draw causal inferences . For this reason, Loughran et al. (2015 , p. 636 despite the many practical advantages of propensity score matching over linear regression, there is nothing magical about propensity score matching that makes it immune to hidden biases that plague regression based causal inferences As it pertains to the current study, the GPS method is an appropriate approach for three important reasons. First, it allows for threshold effects to be estimated . Second, it addresses selection effects through covariate balancing across matched levels of physical disorder . Third, it requires that the treatment variable occurs before the outcome variable. This requirement complements BWT whi ch supports a delayed effect of disorder on violent crime (Wilson & Kelling, 1982; Kelling & Coles, 1996 ). The GPS method is conducted in three basic steps. Step 1: Modeling the conditional distribution of the treatment given covariate s The gpscore 2 package allows the condition al distribution of the treatment to be estimated using general linear models , accommodating a variety of distribution s with more flexible assumptions ( see Guardabascio & Ventura, 2014) . Using estimates from this model , the GPS defined as the conditional distribution of the treatment given covariates - is computed for each level of the treatment . The general formula for estimating the GPS for each observation using a general linear model is provided as , 68 , (eq. 1) where the parameters ( , ) are associated with distributions of the exponential family. Hirano and Imbens (2004) utilize a bl ocking approach to assess how well adjustment for the GPS improves balance among covariates. To begin , the sample is divided into three equal - sized groups, cutting at the 3 3 th and 66 th percentiles of the treatment distribution. Within each treatment group, the GPS is evaluated at the median for all treatment units . Thus, all treatment units have three sets of GPSs. Next, the treatment units are divided into five blocks for each calculation of the GPS, creating three sets of five blocks. For each block withi n a set , a mean - difference for every covariate is calculated between treatment units that belong to the corresponding treatment group used to calculate the GPS and those that belong to a different treatment group . Finally, t he resulting five mean - differences produced for every covariate are combined and calculated as a weighted average , and used to produce t - value s of differences - in - means. In an i deal scenario, t reatment units at each level of the treatment should not be significantly different from one another after adjustment for the GPS . A t - value that is below 1.96 indicates that the covariate means of treatment units belonging to a particular treatment group are no different than the covariate mean s of treatment units that belong to another treatment group but have similar GPS s . If significant differences are still detected, it should be demonstrated that the adjustment for the GPS greatly redu ced mean - differences, despite not reaching statistical significance. important to assess overlap among groups in regards to unit characteristics , known as common support . It is well known that adjustment for covariates will perform poorly if there is not sufficient overlap in their distribution s across treatment levels. In the case in which the treatment 69 is binary, common support is traditionally assessed by evalu ating the distribution of the estimated propensity score s for the treatment and comparison group s . U nits are often restricted to those that fall within the region of common support (i.e., the region in which the distributions overlap ) . If included, t reatment units that fall outside of the common support region not only may prevent balance from being achiev ed , but also may result in misleading predictions. I n the case in which the treatment is continuous, there tment groups and generalized propensity scores to compare matters l ess straightforward (Flores et al., 2012, p 161). Flores et al. (201 2 ) offer one approach which serves as a gauge of the degree of overlap across different levels of a treatment . Like before, the sample is divided into three equal - sized groups and t he GPS is evaluated at the group median , resulting in three sets of GPSs for each treatment unit . Next, t he distribution of the GPS for treatment units belonging to each treatment group is compared to the distribution of the GPS for treatment units outside of the evaluated treatment group . Finally , the sample is restricted to those treatment units that are simultaneously co mparable across all three treatment groups . In other words, treatment units are dropped that have a GPS that is not among the common support region. It is worth emphasizing, however, that in regions in which the data are sparse, there is less assurance in the accuracy of predictions. To a strong amount of support data at each level of the pr relationship will necessarily be based on strong and ultimately untestable functional form assumptions (in particular, where the functional form is off support of the data). es to the current study, predictions will be less reliable at high levels of disorder, signified by wider confidence intervals. 70 Step 2: Estimating the conditional expectation of the outcome given the treatment and GPS The functionality of the GPS requ ires that we assume that after controlling for unit characteristics, any remaining differences in treatment intensity, T , are independent of potential outcomes Y(t) . Importantly, this assumption only requires that pairwise conditional independence of the treatment with potential outcomes is assumed , known as weak unconfoundedness . Previously introduced, t his assumption requires that selection into a treatment level is random conditional on the observed covariate s (Hirano & Imbens, 2004) . O mitted variable bias poses a threat to weak unconfoundedness. For this reason, selection bias might still exist in a estimators if it does not account for all relevant variables . However, given this study use of an extensive set of covariates, it is argued that any bias that remains is likely not large enough to influence its findings in a meaningful way. Furthermore, t he balancing property of the GPS can shed light on the assumption of weak unconfoundedness . I t implies that treatment assignment is weakly unconfounded given the GPS (Hirano & Imbens, 2004 ). This quality indirectly addresses the assumption of weak unconfoundedness because t reatment units that have similar GP Ss also have similar covariates . To this point, Hirano and Imbens (2004) show that if treatment assignment is unconfounded given the covariates, then it is also the case that it is weakly unconfounded given the GPS. As a result, the GPS can be used to remove bias associated with differences in c ovariates in two steps, the first of which is estimating the conditional expectation of the outcome given the treatment and GPS. The conditional expectation of the outcome, , is estimated given the treatment, , and GPS , , given as E[ | . This function is estimated as a flexible linear function of the covariates . A basic model includes the treatment , GPS, and an interaction of these variables . 71 Quadratic and cubic transformations of the treatment variable are c ommonly included , providing even greater flexibility. Unfortunately , gpscore2 only supports dichotomous, ordinal, and continuous regression models . For this reason, violent crime rate is logged transformed. An example of a model containing a cubic approximation and interaction term is provided as, E | )} = ) ( eq. 2) = + + + + + , where ) relates to the conditional expectation . Importantly, the coefficients in this model are not directly interpretable (Hirano & Imbens, 2004) . That being said, Kluve et al. (2012, p. 19) note that whether all the estimated coefficients associated with the [ GPS ] terms are equal to zero can indicate whether the covariates introduce any bias. statistically significant GPS - related parameters suggest that the covariates introduce bias and that the propensity score matching approach is releva nt in that it helps tease out the causal relationship between the treatment and outcome . Step 3: Estimating the dose - response function to discern treatment effects The second way in which the GPS can be used to remove bias associated with differences in covariates is by estimating the dose - response function at each level of the treatment. In particular, t he parameters estimated in the previous step are used to estima te the average potential outcome associated with each treatment level over the GPS . This function is provided as, E = (eq. 3) Furthermore , Rosenbaum (2002) suggests conducting a sensitivity analysis to determine the magnitude of hidden bias that would need to be present to alter study findings. For this reason, a n estimate of uncertainty was conducted by bootstrapping standard errors , an option available in 72 gpscore2 (Rosenbaum, 200 2 ). When selected , this option incorporates the estimation of the GPS along with the estimation of the other predicting parameters. Each replication helps provi de a better understanding of the uncertainty associated with these estimates, which is captured by upper and lower confidence intervals. Sensitivity Checks Sullivan and Loughran (2014) identif y assumptions of the GPS approach that may hamper the identification of the true functional form of the relationship between the treatment and outcome . To start, the approach requires that the treatment be a linear function of the covariates , an assumption of parametric regression. As previously discussed, t he conditional expectation function is produced from a linear model and traditionally includes the treatment, GPS, and an interaction of these variables. Thus, the GPS approach assumes that the conditiona l expectation function is governed by a specific parametric form ( Sullivan & Loughran, 2014 ). Sullivan and Loughran (2014 , p. 714 ) state that [t]here are no theoretical reasons apparent as to why this particular functional form is optimal, nor is it clear why this is the best means of That being said, they suggest that the ( Sullivan & Loughran, 2014 , p. 714). As part of its sensitivity checks, the current study explores how slight alterations to the specification of the conditional expectation function , such as the inclusion of polynomial terms and the exclusion/ inclusion of an interact ion term , affect the estimation of the dose - response function . Furthermore , the GPS approach has been adjusted to incorporate nonparametric techniques , and for good reason ( see Flores et al., 2012; Kluve et al., 2012 ; Kreif, Grieve, Diaz, & Harrison, 2014; Fong, Hazlett, & Imai, 2018 ). These techniques relax many of the strong 73 assumptions made by traditional regression and are thought to allow the functional form of the relationship between the treatment and outcome to more naturally emerge f rom the data . Extending the parametric GPS approach, Bia et al. (2014) developed a set of Stata programs drf to estimate the dose - response function using semiparametric estimators that draw from penalized spline techniques, and a kernel estimator devel oped by Flores et al. (2012). T h ese approach es may capture nonlinear patterns that parametric regression models overlook. For example , polynomial regression as shown in step two of the GPS approach - includes polynomial terms ( , , etc.) for predictors in a linear regression model . The inclusion of polynomial terms provides regression models more flexibility to capture nonlinear relationships . However, polynomial terms impose a global structure o n the relationship between the predictor and outcome. For example, the use of a cubic polynomial term means that the relationship between the predictor and outcome is cubic over the entire range of the predictor. It is clear that imposing a global structure is limiting. Perhaps the relationship between the predictor and the outcome is only cubic at low ranges of the predictor. If so, then polynomial regression will fail to capture the true functional form of the relationship. Splines are a n onparametric technique that offer an alternative approach to estimating relationships of unknown functional form and are commonly used in semiparametric regression models . These models some of the covariates [to] enter the model in a parametric fash ion, while other variables enter as nonparametric terms Keele, 2008, p. 109 ) . Splines are customarily formed as the summation of locally defined polynomials referred to as basis functions - which meet at knots that span across th e entire range of the predictor. A s the number of knots increase, so too does the flexibility of the smooth function. However, using a large number of knots run s the risk of overfitting the data . Conversely, using a 74 small number of knots run s the risk of underfit ting the data. P enalized spline s attempt to strike a balance between overfitting and underfitting the data by impos ing weights on each smooth function ( Perperoglou et al., 2019 ) . In particular, t hese weights a re used to penalize overfitting the data while still offering enough flexib ility to fit the data wel l. In this way, the approach reduce s concerns regarding the appropriate number of knot s. In fact, many studies have found knot specification to be of minor concern for penalized splines (e.g, Eilers & Marx , 1996 ; French , Kammann, & Wand , 2001; Ruppert, 2002; Ruppert , Wand, & Carroll, 2003 ) . In particular, Ruppert et al. (2003) found the selection method K = min( , 35 ), where n is the number of unique , to work well . This method is the default for drf . 11 In addition, penalized splines have been found to avoid linearity constraints at boundary knots (Fox, 2000, p. 67). As it relates to the GPS approach , penalized spline regression is conducted for the second stage of the estimation of the dose - respon se function . This approach utilize s different basis functions to accommodate the nonlinear structure of the data and perform penalized spline smoothing. The simplest penalized spline approach performs smoothing in an additive fashion for the treatment and GPS using bivariate basis function s (see Bia et al., 2014) , aptly named for its consideration of two continuous variables (see Bia et al., 2014 ; Ruppert et al., 2003 ). This model is provided as, E[ | = + + + + , (eq. 4) where and are knots for the treatment and GPS, respectively , and and are the related knot coefficients ( see Ruppert et al., 2003 ; Bia et al, 2014 ) . 12 Furthermore, t he r adial 11 Ruppert (2002) provides empirical justification s for this knot specification method. 12 Ruppert et al. (2003) demonstrate that in the case of a simple additive model the penalization of and is incurred by treating them as random effects. 75 basis function approach add s complexity to this basic structure by relying on distance calculations between every data point and knots to inform penalized spline smoothing (see Wand, 2003; Ruppert et al., 2003 ; Bia et al., 2014 ) . This model is provided as , E[ | = + + + (eq. 5) where C is the covariance function based on knots for the treatment and GPS . For both applications, mixed models are used to represent the penalized splines using the xtmixed subcommand and are estimated using restricted maximum likelihood (REML) . Mixed models perform smoothing by including coefficients that are not associated with knots as fixed effects , while c oefficients that are associated with knots are included as random effects (Wand, 2003). Thus, the simple penalized spline approach includes two random effect s parameters (indicated in bold in equation 4 ) , while the radial basis function approach includes only one random effect parameter (indicated in bold in equation 5 ) . Ultimately, a model which includes both fixed and random effect s offers the greatest amount of flexibility in capturing the true functional form of the relationship between the treatment and outcome ( see Ruppert et al., 2003 ). In a similar manner as before , the parameters estimated from these models which are not directly interpretable - are subsequently used to calculate the average potential outcome at each treatment level by averaging over the GPS , the final step of the GPS approach . Another approach available in drf utilizes a nonparametric kernel estimator to estimate the final stage of the GPS approach . In particular, this appro ach estimates the dose - response function using local polynomial regression and an inverse weighting estimator that is based on kernel methods , where the weights are constructed from the GPS and adjust for covariate differences (Flores et al., 2012) . T he gl obal bandwidth of the kernel is selected using Fan and drf . In order to estimate the unknown 76 parameters of the optimal global bandwidth, t his procedure u ses global polynomials of the GPS of order p +3, where p is the order of the fitted local polynomial (Bia et al., 2014). The inverse weighted estimator of the average dose - response function is provided as, , ( eq. 6 ) where and , with the weighted kernel function indicated as (Flores et al., 2012) . This local estimator is preferred due to its ability to avoid bias near data boundaries (Flores et al., 2012). In summary, this study estimate d the dose - response function utilizing both parametr ic and nonparametric techniques. The parametric approach includes an assessment of the sensitivity of the dose - response function to slight alterations to the specification of the conditional expectation function. The best fitting model is identified and di scussed. Following this assessment, three different types of semiparametric methods are explored: penalized spline, radial spline, and inverse weighting kernel function . 77 CHAPTER 4: ANALYSIS & RESULTS Parametric Method The estimation of the dose - response function was first conducted using the parametric GPS approach and followed three key steps: 1) Modeling the conditional distribution of the treatment given covariates ; 2) Estimating the conditional expectation of the outcome given the treatment and GPS ; and 3) Estimating the dose - response function to discern treatment effects . Step 1 : Parametric Approach : Modeling the conditional distribution of the treatment given covariate s To begin, the conditional distribution of physical disorde r given covariates was estimated. The prediction model was developed using control variables identified from broken windows and related research . As the treatment variable is continuous and right - skewed, log - normal and gamma distribution s were evaluated to identify the most appropriate distributional fit . To this end, a n evaluation of theoretical densities and goodness - of - fit criteria was conducted using the Anderson - Darling and Kolmogorov - Smirnov statistic s, and Bayesian Information Criterion (BIC) (see Figure 1 4 & Table 5 ) . In particular , the Anderson - Darling and Kolmogorov - Smirnov statistic s compare the observed cumulative distribution function to the expected cumulative distribution function, which in this case is either a log - normal or gamma distribution. One key difference between these statistics is that the Anderson - Darling statistic gives more c onsideration to the tails of a distribution. In either case, a smaller test statistic indicat es better fit. Based on the likelihood function , the BIC is a well - known criterion for model selection that includes a larger penalty term - determined by the number of parameters in the model - than the closely related Akaike Information Criterion . A smaller BIC indicates better model fit. Considering these goodness - of - fit criteria, there was c onsiderable support in favor of a gamma distribu tion . For this reason, a gamma distribution was used to model physical disorder. 78 Figure 1 5 . Theoretical Densities . Table 5. Physical Disorder: Goodness of Fit Statistics . I ndividual effects are p resented in Table 6 from the estimation of the conditional distribution of physical disorder given covariates . Importantly, these findings are of interest insofar as they produce a GPS that achieves balance amongst covariates (Hirano & Imbens, 2004) . Following Hirano and Imbens ( 2004 ) suggest ion, two types of transformations were utilized in an effort to achieve balance : square - root and natural log. 13 As a consequence , the interpretation of the effects presented in Table 6 is not straightforward. Proceeding with caution , t he results presented in Table 6 largely reflect findings from prior studies . Although not relevant to the advancement of the GPS approach, a few of these findings are worthy of discussion . 13 Like the natural log transformation, the square - root transformation is used to minimize right skewness , although it has a weaker effect . Unlike the natural log transformation, however, it can be applied to zero values. Herein lies the key advantage of the square - root transformation over the natural log transformation. Goodness of Fit Tests Gamma Log - n ormal Anderson - Darling S tatistic 2.81 9.99 Ba y esian Information Criterio n 2176.10 2301.6 1 Kolmogorov - Smirnov S tatistic 0.0 5 0.0 8 79 Residential stability is captured by percent owner - occupied homes and percent same residence . Stability within neighborhoods encourages trust, and shared values and norms amongst residents (Shaw & McKay, 1942; Coleman , 1988 , 1990; Sampson , 2012; Markowitz et al. 2001 ; Ingoldsby & Shaw , 2002 ) . These social processes provide fertile grounds for the development of informal social control within neighborhoods which help protect against the spread of disorder . As anticipated, percent home - owners maintains a statistically significant ( p - value 0.0 0 1 ), negative r elationship with physical disorder, suggesting that home - ownership positively contributes to the social processes that occur within neighborhoods that help protect them against disorder. Contrary to what was expected , however, p ercent same residence maintains a marginally significant ( p - value 0. 09 ) , positive relationship with physical disorder. That being said, one year may not be long enough t o capture a protective effect . To this point, remaining in the same residence for at least five years is a more common metric by which to capture residential stability using Census data (e.g., Warner & Rountree, 1997 ; Sam pson et. al., 19 9 7 ; Boggess & Hipp, 2010) . However, this measure could not be constructed at the block - group level using five - year estimates provided by the ACS . Furthermore , population density maintain s a statistically significant ( p - value 0.0 01 ) , negative relationship with physical disorder , indicat ing that the most disor d erly neighborhoods are those that are the least densely populated . Since 2000 , Detroit has experienced a massive loss in population . abandoned and neglected properties increased . Consequently , neighborhoods that experienced the greatest loss es in population also experienced the largest increases in physical disorder . This effect is reflect ed by the statistically significant ( p - value 0. 0 01 ) , negative relationship observed between population growth and physical disorder . 80 In addition, percent garden/park maintain s a statistically significant ( p - value 0.0 5 ), negative relationship with physical disorder. Community g ardens and , to a lesser extent, parks and promote collective efficacy by providing opportunities for residents to informally interact with one another, establishing shared norms, trust, and solidarity ( Cohen , Inagami, & Finch, 2008; Teig et al., 2009; Clayton, 2007; Kearney, 2009; Alaimo et al., 2010 ). For these reasons , percent garden/park can be considered to be a reasonable (but imperfect) proxy of collective efficacy , helping explain its negative relationship with physical disorder . In fact, other studies have relied on similar indicators to serve as proxies in the absence of traditional measures of collective efficacy (e.g., Wheeler, 2018 , 2019 ). Table 6 . Conditional D istribution of P hysical D isorder given C ovariates . Variable ln( Population Density ) (square - miles) - 0 . 47 *** (0.0 6 ) Population Growth - 0. 003 *** (0.0 01 ) sqrt( Percent Population Under 18 ) 0.29 *** (0.0 5 ) sqrt( Percent Male (15 - 24) ) 0.01 (0.0 2 ) sqrt( Percent Unemployed ) 0 .0 8 *** (0.0 2 ) sqrt( Percent Receiving Public Assistance ) 0.0 4 ** (0.0 1 ) Percent Female - headed Famil y Household 0 .0 0 1 (0.002) Percent Owner - Occupied Homes - 0 .0 1 *** (0.001) 81 Table 6 Percent Same Residence 0.003 + (0.002) Percent African American 0.00 04 (0.00 3 ) sqrt( Percent Hispanic/Latino Origin ) 0.0 2 (0.02) Percent White - 0.00 5 (0.00 3 ) sqrt( Percent Foreign - born ) 0.0 0 7 (0 .0 2 ) ln( Violent Crime Rate ) (per 1000) 0. 04 * (0.0 2 ) sqrt( Percent Garden/Park ) - 0.0 5 * (0.0 3 ) sqrt( Percent Commercial ) 0.0 9 ** (0.0 3 ) sqrt( Percent Residential ) 0. 24 * ** (0.0 7 ) sqrt( Percent Industrial ) 0.0 01 (0.0 1 ) sqrt( Percent Mixed ) 0. 25 * ** (0.0 6 ) Physical Disorder Lag 0. 06 *** (0.0 1 ) Constant - 0.47 (0.98) + p - value * p - value .05; ** p - value . 82 Using estimates from this model, the GPS was computed for each level of the treatment , and common support and balance assessed. To begin, three equal - sized groups were created by dividing the distribution of physical disorder at the 33th and 66 th percentiles. (2011) approach was subsequently applied to identify the region of common support . Block - groups that fell outside of this region (i.e., off support block - groups) were removed, resulting in a n 11.52 % reduction of this (N = 760) . Table 7 displays the characteristics of the block - groups that fell within the common support region . For a more grounded understanding of these characteristics, they are presented without the transformations utilized to generate the GPS. A co mparison of means between the common support (N = 760) and full sample (N = 857) was conducted : A b onferroni - adjusted p - value was utilized - = 0.002 2 - to account for the increased probability of type 1 error associated with multiple comparisons . None of the identified differences reached statistical significance as determined by this conservative standard. Relaxing this standard, however, two statistically significant mean - differences were detected. T he mean levels of physical disorder ( p - value = 0.0 4 ) and physical disorder lag ( p - value = 0.0 7 ) are lower in the common support sample than in the full sample . While still positively skewed, the distribution of physical disorder now contains fewer block - groups with high levels of physical disorder. As a result, sparse data at these levels will reduce the reliability of predictions . For ease of comparison, T abl e 8 displays mean characteristics for each group within the common support region without transformations . Utilizing a one - way analysis of variance (ANOVA) , statistically significant mean group differences were identified for 1 5 out of the 2 2 83 variables used in this study : 14 These variables include physical disorder ( p - value violent crime rate (2015) ( p - value 0.001) , violent crime rate (2014) ( p - value , population density ( p - value , population under 18 ( p - value , population growth ( p - value , percent unemployed ( p - value , percent receiving public assistance ( p - value , perc ent female - headed households ( p - value = 0.09), percent owner - occupied home ( p - value , percent African American ( p - value = 0.07), percent white ( p - value = 0.03) , percent foreign - born ( p - value = 0.06), percent garden/park ( p - value and phys ical disorder lag ( p - value . Together, t hese findings support the relevance of the GPS approach, as there are substantial imbalances across covariates examined by group without utilizing transformations or adjusting for the GPS . The ability of the GPS approach to create balance where it is needed will soon be presented . Table 7 . Common - support Sample ( N = 760 ) . Variable Mean Std. Dev. Min Max Independent Variable (2014) Physical Disorder 1. 27 0. 91 0.02 4.76 Dependent Variable (2015) Violent Crime Rate (per 1000) 21.25 16.38 2.41 277.37 Control Variables (2014) Population Density ) (square - miles) 6681.73 3448.05 658.02 23569.58 Percent Population Under 18 27.22 5.78 9 0 .00 45.90 14 A one - way ANOVA simultaneously compares all group means. As a result, it is able to maintain the type 1 error probability at a user - designated level. Thus, this method of comparison as a single test - is not affected by the multiple comparison problem. 84 Table 7 Population Growth - 11 .24 45.96 - 92.24 3 93.55 Percent Male (15 - 24) 8.03 5.48 0.00 41.14 Percent Unemployed 27.87 13.9 4 0.00 87.24 Percent Receiving Public Assistance 8.07 7.15 0.00 43.33 Percent Female - headed Famil y Household 30.58 14.03 0.00 78.76 Percent Owner - Occupied Homes 54.28 19.92 0.00 100 .00 Percent Same Residence (at least one year) 84.71 11.39 36.93 100 .00 Percent African American 83.41 25.94 0.00 100 .00 Percent Hispanic/Latino Origin 6.03 17.76 0.00 92.28 Percent White 11.13 18.45 0.00 93.25 Percent Foreign Born 4.35 9.76 0.00 61.08 Violent Crime Rate (per 1000) 22.17 19. 46 1.20 350.36 Percent Garden/Park 1.47 3.91 0.00 40.00 Percent Commercial 4.79 6. 26 0.00 71.42 Percent Residential 92.28 11. 24 5.39 100 .00 Percent Industrial 0 .61 2.83 0.00 40.00 Percent Mixed 0 .22 0.56 0.00 5.60 Physical Disorder Lag 1.33 0. 56 0.00 3.04 85 Table 8 . Group Means from Common - s upport Sample (N = 760) . Variable Group 1 Mean (N = 260) Group 2 Mean (N = 276) Group 3 Mean (N = 224) Independent Variable (2014) Physical Disorder 0 .3 8 1. 05 2. 34 Dependent Variable (2015) Violent Crime Rate (per 1000) 17. 61 22. 51 23. 55 Control Variables (2014) Population Density (square - miles) 7 533.65 7332.87 5219.4 Population Growth 1.10 - 9.62 - 24.82 Percent Male (15 - 24) 7.89 7.7 1 8. 46 Percent Unemployed 23.69 28.33 31.51 Percent Receiving Public Assistance 6.70 8.42 9.07 Percent Female - headed Famil y Household 29.01 31.57 31.15 Percent Owner - Occupied Homes 58.92 53.68 50.34 Percent Same House (at least one year) 84.69 83.83 85.60 Percent African American 82.38 81.37 86.41 Percent Hispanic/Latino Origin 5.7 1 7.75 4.69 Percent White 12.62 12.21 8.64 Percent Foreign - born 4.38 5.37 3.33 86 Table 8 Violent Crime Rate (per 1000) 17.33 23.41 25.66 Percent Garden/Park 3.11 1.17 1.14 Percent Commercial 5.00 4.54 4.82 Percent Residential 91.68 93.17 91.99 Percent Industrial 0 .3 7 0 .7 2 0 .75 Percent Mixed 0 .24 0 .20 0 .22 Physical Disorder Lag 1.02 1.3 2 1.6 4 In addition, F igure 1 5 displays a map of the block - groups from the common support sample indicated in gray . Off - support block - groups are indicated in red. As can be seen, off support block - groups appear to be more highly concentrated in central and north - east Detroit. Characteristics of these block - groups are provided in T able 9 and shown without transformations . Out of the 22 examinations conducted, 6 statistically significant mean - differences were identified between the off support (N = 97) and common support (N = 760) samples : Statistical significance was determined utilizing the previously calculated b onferroni - adjusted p - value ( p - value 0.002 2) . In particular, m ean levels of physical disorder, physical disorder lag, violent crime rate (2015), violent crime rate (2014), and percent unemployed are significantly higher in the off support sample, while population density is significantly lower. Relaxing this conserva tive standard for statistical significance, 1 1 other difference s emerge d and are presented in T able 10 . With few exceptions , these findings suggest that the excluded block - groups include those with the most severe social problems , indicated by elevated levels of physical disorder, violence, and indicators of disadvantage ( p - value 87 Figure 1 6 . Common - support (gray) and Off - support (red) Block - groups . Table 9 . Off - s upport Sample (N = 97 ) . Variable Mean Std. Dev. Min Max Independent Variable (2014) Physical Disorder 2.15 1.27 0.02 4.48 Dependent Variable (2015) Violent Crime Rate (per 1000) 29.52 32.64 1.70 276.3 2 Control Variables (2014) Population Density) (square - miles) 4563.95 3916.52 369.95 17261.04 Percent Population Under 18 25.6 1 6.40 5.54 39.62 Population Growth - 22.38 53.16 - 90.18 268.62 88 Table 9 ( Percent Male (15 - 24) 7.96 6.64 0.00 30.26 Percent Unemployed 27.87 13.94 0.00 87.24 Percent Receiving Public Assistance 10.21 11.00 0.00 69.81 Percent Female - headed Famil y Household 32.13 15.46 0.00 77.35 Percent Owner - Occupied Homes 48.88 23.7 1 29.0 7 100.00 Percent Same Residence (at least one year) 82.12 13.58 29.0 7 100.00 Percent African American 88.7 1 15.80 22.51 100.00 Percent Hispanic/Latino Origin 1.99 6.8 6 0.00 46.32 Percent White 7.27 11.83 0.00 67.96 Percent Foreign - born 1.84 4.57 0.00 24.69 Violent Crime Rate (per 1000) 30.54 35.05 0 .72 302.63 Percent Garden/Park 1.47 3.91 0.00 40.00 Percent Commercial 5.91 5.29 0.00 25.14 Percent Residential 89.88 9.40 56 .00 100.00 Percent Industrial 1.05 2.95 0.00 16.6 7 Percent Mixed 0 .26 0. 37 0.00 1.57 Physical Disorder Lag 1.79 0.74 0. 31 2.86 89 Table 10 . Off - support and Common - support Mean Differences . Variable Mean - d ifference P - value Percent Population Under 18 - 1.61 0.0 1 Population Growth - 11.14 0.0 3 Percent Receiving Public Assistance 2.1 4 0.0 1 Percent Owner - Occupied Homes - 5.40 0.01 Percent Same Residence (at least one year) - 2.59 0.0 4 Percent African American 5.2 9 0.05 Percent Hispanic/Latino Origin - 4.04 0.0 3 Percent White - 3.85 0.0 5 Percent Foreign - born - 2.5 1 0.01 Percent Commercial 1.12 0.09 Percent Residential - 2.39 0.0 5 90 Following this assessment, the balancing property was evaluated on the common support sample using the previously created groups and transformations identified in T able 6 . C ovariate means for each group were compared against the remaining groups to assess how balance was affected by adjustment for the GPS, resulting in 60 mean group comparisons (see Tables 1 1 , 1 2 , & 1 3 ). Without adjusting for the GPS, 23 mean - differences were identified to be statistically significant, indicated by a t - value greater than or equal to 1.96. Thus, pre - adjustment comparisons indicate substantial imbalances across groups. To inspire confidence in the GPS approach, adjustment for the GPS should eliminate or substantially reduce these imbalances. After adjustment, the mean - difference for population density remained statistically significa nt for treatment group 3. That being said , the GPS adjustment resulted in a considerable improvement, reducing the mean - difference by 61.29% . Overall, the GPS adjustment reduced mean - difference s by an average of 5 5 . 18 %. Table 1 1 . Adjustment for the GPS: Group 1 . Treatment Group 1 [0.02, 0.68 ] Covariates Pre - GPS Post - GPS Diff. t - value Diff. t - value Percent Diff. Population Density (square - miles) 0.20 4.70 0.05 0.92 75.00 Percent Population Under 18 0.32 6.99 0.1 0 1 .67 68 . 75 Population Growth - 0.18 - 5.63 - 0.02 - 0.53 88.89 Percent Male (15 - 24) 0.02 0.18 0.01 0.15 50.00 Percent Unemployed 0.62 5.62 0.11 0.82 82.26 Percent Receiving Public Assistance - 0.40 - 3.59 - 0.06 - 0.44 85.00 Percent Female - headed Family Household 2.33 2.16 0.94 0.66 59.66 91 Table 11 Percent Owner - Occupied Homes - 6.93 - 4.57 - 0.86 - 0.44 87.59 Percent Same Residence (at least one year) 0.19 0.15 0.04 0.04 78.95 Percent African American 3.71 1.43 1.54 0.77 58.49 Percent Hispanic/Latino Origin - 0.21 - 0.99 - 0.01 - 0.10 95.24 Percent White - 2.61 - 1.47 - 2.22 - 0.16 14.94 Percent Foreign - born - 0.30 - 1.72 - 0.09 - 0.75 70.00 Violent Crime Rate (per 1000) 0.71 6.33 0.23 1.55 67.61 Percent Garden/Park - 0.28 - 3.21 - 0.12 - 1.13 57.14 Percent Commercial - 0.07 - 0.86 - 0.06 - 0.59 14.29 Percent Residential 0.08 1.54 0.07 1.19 12.50 Percent Industrial 0.36 1.66 0.19 0.69 47.22 Percent Mixed 0.10 2.54 0.01 0.28 90.00 Physical Disorder Lag 2.43 8.31 0.36 0.96 85.19 Table 1 2 . Adjustment for the GPS: Group 2 . Treatment Group 2 [0. 69 , 1.5 2 ] Covariates Pre - GPS Post - GPS Diff t - value Diff t - value Percent Diff. Population Density (square - miles) - 0.16 - 3.80 - 0.12 - 1.80 25.00 Percent Population Under 18 - 0.21 - 2.48 - 0.19 - 1.95 9.52 Population Growth - 0.02 - 0.72 - 0.01 - 0.27 50.00 Percent Male (15 - 24) 0.07 0.83 .04 0.52 42.86 92 Table 12 Percent Unemployed - 0.13 - 1.20 - 0.05 - 0.43 61.54 Percent Receiving Public Assistance - 0.19 - 1.75 - 0.12 - 1.03 36.84 Percent Female - headed Family Household - 1.52 - 1.32 - 1.47 - 1.36 3.29 Percent Owner - Occupied Homes 0.88 0.57 0.24 0.14 72.73 Percent Same House (at least one year) 1.31 1.50 0.94 1.00 28.24 Percent African American 3.05 1.52 2.56 1.22 16.07 Percent Hispanic/Latino Origin - 0.28 - 1.64 - 0.23 - 1.36 17.86 Percent White - 1.60 - 1.12 - 0.61 - 0.41 61.88 Percent Foreign - born - 0.22 - 1.68 - 0.20 - 1.43 9.09 Violent Crime Rate (per 1000) - 0.63 - 1.29 - 0.13 - 1.17 79.37 Percent Garden/Park 0.13 1.44 0.12 1.26 7.69 Percent Commercial 0.10 1.11 0.06 0.77 40.00 Percent Residential - 0.08 - 1.46 - 0.07 - 1.44 12.50 Percent Industrial - 0.17 - 0.74 - 0.15 - 0.72 11.76 Percent Mixed 0.04 1.13 0.03 0.91 25.00 Physical Disorder Lag - 0.39 - 1.30 - 0.21 - 0.65 46.15 93 Table 1 3 . Adjustment for the GPS: Group 3 . Treatment Group 3 [1. 53 , 4.76] Covariates Pre - GPS Post - GPS Diff t - value Diff t - value Percent Diff. Population Density (square - miles) - 0. 3 1 - 4.70 - 0.12 - 2.34 61.29 Percent Population Under 18 - 0.11 - 2.35 - 0.04 - 0.58 63.64 Population Growth - 0.11 6.02 - 0 .03 - 0.75 72.73 Percent Male (15 - 24) - 0.07 - 0.67 - .06 - 0.58 14.29 Percent Unemployed - 0.48 - 4.33 - 0.19 - 1.32 60.42 Percent Receiving Public Assistance - 0.20 - 1.80 - 0.01 - 0.07 95.00 Percent Female - headed Family Household - 0.85 - 0.79 0.33 0.23 138.82 Percent Owner - Occupied Homes 5.96 3.94 1.14 0.56 80.87 Percent Same House (at least one year) - 0.91 - 1.05 - 0.61 - 0.51 32.97 Percent African American - 4.53 - 2.28 - 1.75 - 0.64 61.37 Percent Hispanic/Latino Origin 0.29 1.74 0.17 0.77 41.38 Percent White 3.77 2.68 1.26 0.63 66.58 Percent Foreign - born 0.31 2.43 0.14 0.82 54.84 Violent Crime Rate (per 1000) - 0.57 - 5.04 - 0.04 - 0.28 92.98 Percent Garden/Park 0.15 1.74 - 1.2e - 05 - 9.2e - 05 100.01 Percent Commercial - 0.14 - 1.62 - 0.11 - 0.97 21.43 94 Table 13 Percent Residential - 0.02 - 0.27 - 0.004 - 0.08 80.00 Percent Industrial 0.20 0.92 0.02 0.09 90.00 Percent Mixed 0.09 1.70 0.04 1.13 55.56 Physical Disorder Lag - 2.79 - 9.76 - 0.45 - 1.56 83.87 Step 2 : Parametric Approach : Estimating the conditional expectation of the outcome given the treatment and GPS The second step of the GPS approach involve s estimating the conditional expectation of logged violent crime rate given physical disorder and the GPS using o rdinar y least squares regression. 15 In order to assess whether the functional form is robust to slight alterations in model specifications, models with and without interactions were separately conducted for base, quadr atic, and cubic transformations of physical disorder . This procedure resulted in the estimation of 6 models (see Ta bles 1 4 , 1 5 , & 1 6 ) : Model 1a Base, interaction Model 1b Base, no interaction Model 2a Quadratic, interaction Model 2b Quadratic, no interaction Model 3a Cubic, interaction Model 3b Cubic, no interaction T hese m odels were then compared using a series of likelihood ratio test s . Model 1b served as the reduced/ restricted model and was determined to have the best fit over all (see Table 1 7 ) . Across all models , the GPS term was statistically significant , lending support to the relevance of the GPS approach (Hirano & Imbens, 2004). 15 autocorrelation available in the sp package in R. In particular, this test was cond ucted using a row normalized inverse distance weighted matrix and 999 permutations. While statistically significant clustering was detected ( p - value = 0.02) , the level of spatial autocorrelation identified is unlikely to greatly affect model results. 95 Table 1 4 . Base . Model 1a Model 1b (Best) Beta SE Beta SE Physical Disorder 0.05 0.04 0.05 0.04 GPS - 0.28*** 0.08 - 0.28*** 0.08 Physical Disorder x GPS - 0.03 0. 37 - - Constant 2.93*** 0. 16 2.92*** 0.08 Adjusted R - Squared 0.0528 0.0540 BIC 1438.637 1432.012 +p - value * p - value p - value . Table 1 5 . Quadratic . Model 2a Model 2b Beta SE Beta SE Physical Disorder 0.07 0.1 3 0.06 0.1 3 Physical Disorder^2 - 0.003 0.0 3 - 0.002 0.03 GPS - 0. 28 * * 0. 11 - 0. 28 ** 0. 11 Physical Disorder x GPS - 0. 04 0. 39 - - Constant 2.92 *** 0. 22 2.91 *** 0.1 4 Adjusted R - Squared 0.0516 0.0528 BIC 1445.261 1438.64 + p - value * p - value p - value . Table 1 6 . Cubic . Model 3a Model 3b Beta SE Beta SE Physical Disorder - 0. 39 0 . 3 2 - 0 . 31 0 . 29 Physical Disorder^2 0 . 23 0 .1 6 0 . 19 0.1 4 Physical Disorder^3 - 0 . 0 4 0 .0 2 - 0 .0 2 0.02 GPS - 0 . 4 1 * * 0. 1 4 - 0 . 3 9 * * 0 . 1 4 Physical Disorder x GPS 0. 23 0. 42 - - Constant 3. 10 *** 0 . 2 2 3 .1 3 *** 0.2 1 Adjusted R - Squared 0.0532 0.0541 BIC 1449.603 1443.263 + p - value * p - value p - value . 96 Table 1 7 . Likelihood Ratio Tests . Model Comparisons D . F . Chi - square Statistic Probability Model 1b vs. Model 2b 1 0.01 0.93 Model 1b vs. Model 3b 2 2.02 0.36 Model 1b vs. Model 1a 1 0.01 0.93 Model 1b vs. Model 2a 2 0.0 2 0.99 Model 1b vs. Model 3a 3 2.31 0.51 Step 3 : Parametric Approach: Estimating the dose - response function to discern treatment effect Utilizing the coefficients calculated in the previous step, t he final step of the GPS approach involves estimating the dose - response function to discern treatment effects. Figure s 16 and 1 7 display the average predicted values of logged violent crime rate across each level of physical disorder . In particular, F igure 16 displays m odels with an interaction type ) , while Fi gure 1 7 displays models without an interaction model type ) . Both figures display the dose - response function with and without confidence intervals. For ease of comparison, F igure 1 8 jointly displays the dose - response function produced by each model . 97 Figure 17. Interaction Models: Dose - response Functions across Model Specifications . 98 Figure 1 8 . Noninteraction Models: Dose - response Functions across Model Specifications . 99 Figure 19. Combined Display of Parametric Methods . Across all models, the relationship between physical disorder and logged violent crime rate showcases linearity. With the exception of models 3a and 3b, physical disorder maintains a positive relationship with logged violent crime rate across all levels of physical disorder. This relationship is exhibited by a steep rise in logged violent crime rate at low levels of physical disorder, followed thereafter by a steady, approximately linear increase at a treatment level of 1.00 . Models 3a and 3b also showca se linearity at low and mid - range levels of physical disorder, as seen by a steady, positive increase in logged violent crime rate. The rate of increase, however, is slower than in models 1 a, 1b, 2 a , and 2 b . Furthermore, the relationship between physical d isorder and logged violent crime rate levels off at a treatment level of 3.00 , and then swiftly drops . This finding is suggestive of a potential inoculation effect, w hereby the severity of exposure to disorder is lessened over time as individuals adapt to their surroundings (Taylor & Shumaker, 1990; Sampson & Raudenbush, 2004). Other commonalities across models include tight confidence intervals at low and mid - range levels of physical disorder. This is where the majority of the data lies. T he widening of the 100 confidence intervals at high levels of physical disorder exposes values with limited data. Excluding the highest levels of physical disorder from consideration, a positive, linear trend is still apparent. Overall, the dose - response function is s omewhat robust to alterations in model specifications. Within model types 1, 2 and 3 , the inclusion of an interaction term did little to change the dose - response function. This finding may be due to the fact that in all cases the interaction term was insignificant. There is also substantial overlap between models 1a, 1b, 2a, and 2b (see Figure 1 8 ). Focusing on model 1b (i.e., the best fitting model), the relationship between physical disorder and logged violent crime rate does not resemble a threshold effect. Thus, no support is found for hypotheses 2a , 2b, or 3. While not entirely linear, physical disorder maintains a linear relationship with violent crime rate across a substantial portion of its distribution. For this reason, hyp othesis 1, which maintains that disorder has a positive, linear relationship with logged violent crime rate, garners more support than hypothesis 4, which supports nonlinearity. Semiparametric Method Following the parametric GPS approach , the dose - resp onse function was estimated using three types of semiparametric methods: penalized spline, radial spline, and inverse weighting kernel function . Step 1: Semiparametric Approaches: Modeling the conditional distribution of the treatment given covariates Step 1 of the GPS approach is the same for both parametric and semiparametric estimations of the dose - response function . 101 Step 2 : Semiparametric Approaches : Estimating the conditional expectation of the outcome given the treatment and GPS With the previo usly identified common support sample and estimated GPS, s tep 2 of the GPS approach was conducted utilizing penalized spline regression s that included additive spline bases and radial basis functions (see Bia et al., 2014) . For brevity , the former regression approach is referred to as the penalized spline model (or method ) , while the latter is referred to as the radial spline model (or method) . Estimates from the penalized spline and radial spline models are presented in Table s 1 8 and 1 9 , respective ly . Reviewing these tables, t here are several factors to consider. To start, both physical disorder ( p - value ) an d GPS ( p - value .001 ) are statistically significant in the penalized spline model. However, only the GPS ( p - value ) is statistically significant in the radial spline model . In addition , the likelihood ratio test is statistically significant for the penalized spline model ( Prob > Chi - square = 0.0062 ) , but only marginally so for the radial spline model ( Prob > Chi - square = 0.1056 ) . In the context of mixed effects models, the likelihood ratio test compares the fit of the evaluated mixed effect model to a standard regression model (i.e., the reduced model) that does not include random effects parameters . A statistical ly signif icant chi - square statistic suggests that the mixed effect model improves model fit over the reduced model. The likelihood ratio test s conducted for the penalized spline and radial spline models use the same reduced model for comparison . Therefore, these te sts can be compared to shed light on the superior approach: penalized spline or radial spline. A statistically significant chi - square statistic for the penalized spline model suggests that the inclusion of random effect parameters improves model fit . The chi - square 102 statistic for t he radial spline model is only marginally significant . Therefore, the penalized spline model emerges as superior. 16 Table 1 8 . Penalized Spline Model . Fixed Effec ts Beta SE Physical Disorder 0.13*** 0.03 GPS 0.71** 0.27 Constant 2.54*** 0.11 Random Effects 95% Confidence Interval Knot Physical Disorder 6.01e - 07 1.20e06 1.20e - 08 3 . 04 e - 05 Knot GPS 0.59 0.35 0 .18 1.91 Likelihood Ratio Test : Chi - square (2) = 10.18, Prob > Chi - square = 0.0062 +p - value - value - value Table 1 9 . Radial Spline Model . Fixed Effects Beta SE Physical Disorder 0.09 0.11 GPS - 0.19* 0.09 Constant 0.09 0.17 Random Effects Beta SE 95% Confidence Interval Knot s for Physical Disorder & GPS 0.06 0.04 0.01 0.22 Likelihood Ratio Test : Chi - square (2) = 1.56, Prob > Chi - square = 0.1056 + p - value - value - value - value Step 3 : Semiparametric Approaches: Estimating the dose - response function to discern treatment effects The coefficients calculated from the penalized spline and radial spline models were then used to estimate the dose - response function. The dose - response function was also estimated utilizing an inverse weighting kernel approach, with an optimal bandwidth ( bw = 0. 32 ) selected from Fan (see Flores et al., 2012). Recall Figure 1 9 display s the dose - response function estimated from each approach shown with and without 16 Shedding light on this finding, the standard error associated with the physical disorder coefficient of the radial spline model displayed in Table 19 is almost four times higher than the corresponding standard error of the penalized spline model displaye d in Table 18. 103 confidence intervals . For ease of comparison, F igure 20 jointly displays the dose - re sponse function produced from each method . Figure 20. Semiparametric Methods . 104 Figure 20 Figure 21. Combined Display of Semiparametric Methods . As indicated by more instances of nonlinearity, i t is immediately apparent that the semiparametric methods do indeed allow for greater flexibility in the estimation of the dose - response function than the previously presented parametric method . Therefore, there is clear support for hypothes is 4, indicating nonlinearity . Another clear distinction between these 105 methods is seen in their estimation of confidence intervals. The semiparametric methods generate much wider confidence intervals than the parametric method , especially at high levels of physical disorder . This finding is expected. The structure provided by parametric estimators allows extrapolation from regions in which data are abundant to regions in which data are scarce (Bia et al., 2014) . N onparametric methods are not afforded the sa me luxury . T herefore , estimates generated from limited support data are done so with a greater degree of uncertainty. R ecall t he penalized spline model fit the data better than the radial spline model . However, this method to generate the dose - response function does so with a much greater degree of uncertainty , indicated by wide confidence intervals across all levels of physical disorder . For this reason , estimates produced from the penalized spline method must be interpreted with more caution . Proceeding with caution , the penalized spline method identifies a positive relationship between physical disorder and logged violent crime rate at low levels of physical disorder . This relationship is shown by a modest rate of increase . In comp arison , the radial spline method does not identify physical disorder to have an effect on logged violent crime rate at very low levels . A relationship does not emerge until a treatment level of 0.6 0 , indicated by a n uptick in logged violent crim e rate. However, it is important to take heed of the wide confidence intervals at very low levels of physical disorder, suggest ing that the radial spline estimates produced at these levels must be interpreted with greater cautio n . After a treatment level of 1.4 0 , the penalized spline method indicates that physical disorder has no effect on log ged violent crime rate . L ogged violent crime rate remains relatively constant until a treatment level of 2.2 0 . Past this level, the penalized spline method shows logged violent crime rate steadily increas ing with physical disorder. In contrast, the radial spline 106 method shows logged violent crime rate increas ing with physical disorder after a treatment level of 1.4 0 , although at a much slower rate than before . Past a treatment level of 2.2 0 , the rate of increase substantially increases . Estimates produced beyond this level far exceed those produced by the penalized spline method . Figure 21 jointly displays the spline estimates and identifies the discussed treatment levels by vertical black lines. Figure 22. Spline Methods with Relevant Treatment Levels Highlighted . Focusing now on the inverse weighting kernel method , logged violent crime rate increases at low levels of physical disorder at a modest and steady rate . Similar to the penalized spline method, t he relationship between physical disorder and logged violent crime rate is relatively constant b etween the treatment levels of 1.0 0 and 1.8 0 . Past these level s , the inverse weighting kernel method shows logged violent crime rate steadily increas ing , picking up speed at a treatment level of 3. 00 . This change in rate occurs later than shown in either spline method. Reaching a precipice at a treatment level of 4.2 0 , the relationship between physical disorder and logged violent crime rate abruptly drops. This drop distinguishes the inverse 107 weighting kernel method from its spline counterparts , and is suggestive of a potential inoculation effect. However , it is again important to remember that estimates produced at high levels of physical disorder are done so with a greater degree of uncertainty. Figure 22 jointly displays the inverse weighting kernel estimates and identifies the discussed treatment levels by vertical black lines. Figure 2 3 . Inverse Weighting Kernel Method with Relevant Treatment Levels Highlighted . Overall, a relatively similar image of the dose - response function emerges across semiparametric approaches. To summarize, logged violent crime rate rises at a modest rate at low levels of physical disorder . Transitioning from low levels of physical disorde r, the strength of the positive relationship between physical disorder and logged violent crime rate is either greatly reduced or becomes nonexistent. Past some level located in the middle of the physical disorder distribution, the rate of increase picks u p. Excluding very high levels of physical disorder from consideration (i.e., those with the widest confidence intervals), this general pattern is still apparent. 108 T his description of the relationship between physical disorder and logged violent crime rate closely parallels the broken windows tipping point, with t wo caveats . First, there is not a dramatic break at mid - range levels of physical disorder. Although there is an increased change in rate , the transition is smoother than originally expected . In oth er words, there is an attenuated threshold effect . Second, a reduced effect at mid - range levels of physical disorder was also not expected . In spite of these differences, the semiparametric approaches lend support in favor of hypothesis 2a: the broken windows tipping point as a threshold effect. Summary of Findings To review, Figure 23 displays the dose - response function produced from the best fitting parametric method (i.e., model 1b), alongside those produced from semiparametric methods. Vertical black lines demarcate low, mid - range, and high levels of physical disorder, with less consideration given to very high levels due to wide confi dence intervals. Across methods, the relationship between physical disorder and logged violent crime rate is quite similar at low levels of physical disorder. Previously thought to be steep, the increase in logged violent crime rate observed in model 1b at low levels of physical disorder is quite modest, demonstrating the importance of scale in interpreting results. Furthermore, model 1b closely follows the radial spline method at mid - range levels of physical disorder, but diverges at high levels . To this p oint, clear divergences between methods can be seen at high levels of physical disorder, with the inverse weighting kernel method predicting the greatest amount of crime, followed by the radial spline method, model 1b, and the penalized spline method. 109 Figure 24 . Parametric & Semiparametric Methods . At each level of physical disorder, intersubjective agreement across methodological - response function was not consistently estimated across parametric and semiparametric meth ods. The method and the assumptions that underlie it influenced the estimation of the dose - response function. The inconsistencies that emerged demonstrate the importance of considering the potential sensitivities of each methodological approach and their i mpact on estimation . Complementing Figure 16, Table 20 re - t heir level of support. Strictly speaking, all of the identified relationships are nonlinear. However, labeling all of these relationships in this way masks intricacies that are revealed upon closer examination across the distribution of physical disorder. To this point, model 1b exposes a predominantly linear relationship between physical disorder and logged violent crime rate at mid - range and high levels of physical disorder, lending support to hypothesis 1. Furthermore, the semiparametric methods all identify an increased change in rate at mid - range levels of physical 110 disorder. The largest change is shown by the inverse weighting kernel method, followed by the radial spline and penalized spline methods. However, these changes are more gradual than expected to be considered true threshold effects. At the very least, however, these findings lend partial support in favor of hypothesis 2a. Table 20 . Hypotheses & Support . Hypotheses Support H1: Physical disorder maintains a positive linear effect on violent crime rate. Model 1b o Mid - range & high levels of physical disorder H2a: Physical disorder maintains a threshold effect on violent crime rate such that small variations exert a modest positive effect on violent crime rate at low levels , and a dramatic positive effect past a critical level located somewhere between low and high levels . Penalized Spline Method, Radial Spline Method, & Inverse Weighting Kernel Method o Increased change of rate at m id - range levels of physical disorder H2b: Physical disorder maintains a threshold effect on violent crime rate such that small variations exert a modest positive effect on violent crime rate at low and high levels , and a dramatic positive effect past a critical level located somewhere between these two extremes. No Support H3: Physical disorder maintains a threshold effect on violent crime rate such that small variations exert a modest positive effect on violent crime rate at low and mid - range levels, and a dramatic positive effect past a critical level located somewhere at high levels . No Support H4: Physical disorder maintains a nonlinear effect on violent crime rate. Model 1b, Penalized Spline Method, Radial Spline Method, & Inverse Weighting Kernel Method 111 CHAPTER 5: DISCUSSION & CONCLUSION An Overview : The Search for The Broken Windows Tipping Point Wilson and Kelling (1982) provide a simple instruction for the implementation of order - maintenance policing: direct limited police resources to the broken windows tipping point . In doing so , they imply a certain functional form of the relationship between disorder and violent crime . That is , the tipping point suggests that the disorder - crime relationship is best captured as a threshold effect : t he imp act of disorder on violent crime dramatically increases beyond some critical level of disorder located at mid - range levels . If this is indeed the case , then a proper test of the validity of BWT should accommodate nonlinearity. To this point, m isspecificati on of the functional form of the disorder - crime relationship obscures tests of validity and does not advance criminological theory. With few exceptions, broken windows research has ignored the tipping point , modeling the disorder - crime relationship as li near ( e.g., Skogan, 1990; Sampson & Raudenbush, 1999; Harcourt, 2001; Eck & Maguire, 2005; Steenbeek & Kreis, 2015; Wheeler, 2018; Konkel et al. , 2019). In an interesting twist , the few studies that evaluate this and similar phenomenon provide reason to do interpretation . For example, Crane (1991) and Raleigh and Galster (201 5 ) findings suggest that the tipping point may be located at high levels of disorder , while Geller (2007) finding suggests that the tipping point may not resemble a threshold effect at all . While mixed, this body of research does support a nonlinear relationship between disorder and violent crime, underscoring the importance of efforts to accommodate nonlinearity . Furthermore, t his finding has implications for policing disorder initiatives . A nonlinear relationship between disorder and violent crime suggest s that some neighborhoods may be more or less amenable to these initiatives than other s . If so, police resources should be 112 allocated in such a way as to have the most optimal effect on crime . To this point, Wilson and Kelling (1982) prioritize preventing future crime emergence by directing limited police resources to the tipping point . While this approach is contentious, their instruction suggests that a proper test of the effectiveness of policing disorder initiatives involves implement ing them at the tipping point . Beyond their ability to reduce violent crime, evaluations of the effect iveness of these initiatives should include nontraditional metrics , such as their ability to quality of life , reduce fear of crime, strengthen police - community relations , and avoid the financial and social costs associated with future vi olence . T his study empirically examine d the functional form of the relationship between physical disorder and violent crime rate as a first step toward identifying the broken windows tipping point . Great strid es were taken to accommodate nonlinearity by adopting a meth odological approach that allow s flexibility in modeling decisions , while also allowing for the identification of causal effects. In this regard, t he generalized dose - response propensity score (i.e., the GPS method) was perfec tly suited . T his approach explicitly models the functional form of the disorder - crime relationship at each level of physical disorder while addressing selection effects through covariate balancing and consists of three key steps: 1) Modeling the conditiona l distribution of the treatment given covariates ; 2) Estimating the conditional expectation of the outcome given the treatment and GPS ; and 3) Estimating the dose - response function to discern treatment effects . To facilitate its analysis, t h is study utilized block - group level data on physical disorder , violent crime, and socioeconomic and land use characteristics from the management system, MCM project, and Census. As part of its sensitivity checks, this study explore d how slight a lterations to the specification of the conditional expectation function and nonparametric techniques affected the estimation of the dose - response function . Despite its 113 comprehensive analysis , the functional form of the disorder - crime relationship remains u nclear. That being said, the bulk of the evidence favors a nonlinear relationship, with partial support for Directions for Future Research T his study found considerable support in favor of a nonlinear relationship between physical disorder and logged violent crime rate . However, this finding is far from definitive. Additional research is needed to establish whether the disorder - crime relations hip is truly nonlinear . There are four important domains in which research can be developed : 1) Measures of disorder; 2) Confounding factors ; 3) N eighborhood context; and 4) Longitudinal data analysis. Measures of Disorder R esearch suggests that disorder is social ly construct ed (Harcout, 2001; Sampson & Raudenbush, 2004; Hinkle & Yang, 2014). Turning to BWT for insight, a n emphasis is placed on perceptions of disorder , rather than objective measures thereof . Residents must perceive disorder to be a problem within their neighborhoods and respond fearfully for the broken windows development sequence to unfold . Unlike the case of social disorder, there is considerable overlap between objective and perceived measures of physical disorder, suggesting th at either is appropriate for examinations of the disorder - crime relationship ( Perkins et al., 1992; Sampson & Raudenbush, 2004; Hinkle & Yang, 2014; Yang & Pao, 2015; Ren et al. , 201 9 ) . Nonetheless , future research should prioritize perceived measures of disorder in examinations of the disorder - crime relationship, especially when social disorder is considered . Building upon this instruction, the allocation of police resources may be better informed by evaluations of the relationship between so cial disorder and violent crime. The reason being that the police often play a larger role in addressing social nuisances than the physical conditions of the environment. 114 That being said, variation in police responsibilities across departments is expected. In the case of Detroit, for example, the police play a substantial role in efforts to address physical disorder. perceptions that disorder is a problem. For example, Franzini et al. (2008) found that perceptions of disorder are more strongly influenced by severe, long - lasting indicators, such as abandoned properties, than by those that can be more easily rectified, such as trash and graffiti. For this reason , they arg ue that efforts to address disorder should focus on the former rather than the latter indicators in order to have the desired effect on crime (Franzini et al., 2008) . Complementing this finding , other studies have found the disorder - crime relationship to b e stronger for some classifications of disorder than for others ( e.g., Wheeler, 2018 ; Konkel et al., 2019 ). For these reasons, future research should give particular attention to the indicators that comprise d isorder and how they shape , as well as how disorder is classified and the unique contributions of these classifications to explaining crime. Neighborhood C ontext R esidents perceptions of disorder are shaped by observable cues of disorder , as well as neighborhood social structure . G enerally , individuals (of all races) perceive higher levels of disorder in predominately poor, minority neighborhoods (Sampson & Raudenbush, 2004; McCord et al., 2007; Hipp, 2010; Sampson, 2012; Wickes et al., 2013) . That being said , white individuals generally perceiv e more disorder than minorities living in the same neighborhood (Sampson & Raudenbush, 2004; Franzini et al., 2008 ; Hipp, 2010 ; Sampson, 2012 ) . Sampson and Raudenbush (2004) offer an explanation for this finding : if minority residents have a greater past exposure to disorder, th e n they may have a higher threshold for perceiv ing disorder to be a 115 problem. Together, these findings suggest th at the disorder - crime relationship may vary across neighborhood contexts , specifically across racial /ethnic lines . In predominately minority neighborhoods, greater levels of disorder may be needed than in predominantly white neighborhoods to elicit a fear response, inciting th e broken windows cycle. Relatedly, e valuating the average effect of disorder on violent crime across levels of disorder may mask differences that exist across neighborhood contexts that affect the functional form of the disorder - crime relationship . To be clear, BWT makes a global statement about the relationship between disorder and violent crime ; the process through which disorder influences violent crime is the same across all neighborhoods. T he consideration of average effects is aligned with this fr aming. In light of new knowledge since the advent of BWT , however, f uture studies should e xplore t he role of neighborhood context in shaping the disorder - crime relationship , perhaps creating neighborhood typologies based upon indicators correlated with dis order, such as concentrated disadvantage (Sampson & Raudenbush, 2004; Wilcox et al., 2004; Gau & Pratt, 2010). Furthermore , s uch evaluations may help flesh out the effect of disorder on violent crime at high levels of disorder, which this study estimated w ith much uncertainty . A ttention sh ould also be given to how neighborhood context affect s the development of informal social control, and the barriers within neighborhoods that serve to undermine police - community partnerships needed for the implementation of order - maintenance policing. Confounding Factors The GPS method estimates causal relationship s by controlling the effect of known confoun ding factors (i.e., factors that affect selection into treatment and treatment - specific outcomes). The exclusion of such factors results in omitted variable bias . Across regression approaches, o mitted variable bias impairs the identification of causal effe cts . In the case of the 116 GPS method, the omission of confounding factors effects the extent to which confidence can be placed in the estimation of the dose - response function . As it relates to BWT, collective efficacy has been shown to mitigate the relatio nship between disorder and violent crime across a variety of neighborhood contexts ( e.g., Sampson et al., 1997; Browning et al., 2004; Reisig & Cancino, 2004; Sampson, 2004; Wells et al., 2006; Warner, 2007; Mazerolle, Wickes, & McBroom, 2010; Maxwell, Gar ner, & Skogan, 2011; Swatt et al., 2013) . In other words, it is a known confounding factor. In the absence of formal measure s of collective efficacy, the current study utilized a proxy: percent gardens/parks . Within neighborhoods and crime research, collective efficacy has been traditionally defined as the willingness of residents to intervene to maintain order , coupled with trust and solidarity amongst resident s (Sampson et al. 1997; Browning et al., 2004; Maz erolle et al. , 2010 ; Sampson, 2013 ). Sampson (2013) has discusse d the merits and shortcomings of various measures of collective efficacy. He ultimately conclude d that collective efficacy is a theory of involving shared expectations about order and control, activated ties, and acts of informal control. How these concepts are measured and interrelate will vary depending on the research context (Sampson, 2013, p. 20). Community g ardens and, to a lesser extent, parks provide opportunities for the development of collective efficacy, and signify neighborhood investments ( Cohen et al., 2008; Teig et al., 2009; Clayton, 2007; Kearney, 2009; Alaimo et al., 2010 ) . However, they do not ca pture expectations of control and their ability to activate social ties to bring about neighborhood change , key components of collective efficacy . F uture evaluations of the functional form of the disorder - crime relationship should strive to incl ude formal measure s of 117 collective efficacy that capture all of its dimensions in order to bolster confidence in causal inferences . Another confounding factor to consider involves the way in which the police are deployed to neighborhoods . The relationship between disorder and violent crime will be impacted if the police are deployed based upon a level of disorder. For example, the attenuated threshold effect observed by this study may be an artifact of deployment strategy if it so happens tha t the police are disproportionally deployed to neighborhoods with mid - range levels of disorder, as compared to low or high levels . In the case of Detroit, however, routine police patrol primarily focuses on neighborhoods that have high population densities and violent crime rates . For this reason, this study included a measure of population density , as well as a temporal lag of violent crime rate to address the confounding factor of police deployment . Adding another layer of complexity, the leve l of police commitment to order - maintenance policing activities is a related confounding factor. Across Detroit, three to five NPOs are deployed to every SCA . As previously discussed, NPOs responsibilities are consistent with order - maintenance policing . Ho wever, the extent to which they engage in these activities is unknown. If NPOs or patrol officers, for that matter, are more likely to engage in order - maintenance policing activities in neighborhoods with mid - range levels of disorder, then the attenuated t hreshold effect observed by this study is suspect. Absent the eradication of the police, systematic differences in police deployment and order - maintenance policing activities across neighborhoods will pose issues for evaluations that seek to investigate th e causal relationship between disorder and violent crime. For this reason, f uture evaluations s hould s trive to account for these differences when possible . This effort is especially important for evaluations in which functional form is of interest . 118 Longitudinal D ata A nalysis Longitudinal data are best equipped to study the disorder - crime relationship g iven the process through which Wilson and Kelling (1982) argue disorder affects violent crime . Compared to cross - sectional data, longitudinal data ar e better - suited to tease out causal relationships and the processes that underlie them, such as how informal social control develop s and decline s over time , as well as the role of neighborhood context i n shaping this process . In , the advantages of longitudinal data are important insofar as they affect analyses of the functional form of the disorder - crime relationship. Quite obviously, if disorder does not cause violent crime, then explorations of the functional form of the disorder - crime relationship are meaningless. In the absence of longitudinal data, this study att empted to mitigate the issue of causality by adopting a methodological approach that addressed selection effects, when possible, through covariate balancing across matched levels of physical disorder. Setting aside the issue of causality , c ross - sectional data require that we assume a neighborhood s stage of progression in the broken windows cycle based upon its current level of disorder. Following the logic of BWT , the deeper entrenched a neighborhood is in this cycle , the higher its level of disorder , and therefore the higher its level of violent crime . Operating under this assumption , the functional form of the disorder - crime relationship can be dete r mined if cross - sectional evaluations include neighborhoods across all stages of decline . Comp ared to other levels, this study included the fewest neighborhoods with very high levels of physical disorder , presumedly those that are the deepest entrenched in the broken windows cycle . Therefore, the disorder - crime relationship was estimated with more uncertainty at these level s . Future research should strive to collect sufficient data across all levels of disorder in order to enhance confidence in the estimation of causal effects. 119 As previously discussed , there is reason to believe that average eff ects mask nuances that exist across neighborhood contexts which affect the functional form of the disorder - crime relationship . Methodological technique s that are able to capture developmental patterns as they unfold over time can help shed light on the extent to which neighborhood context shape s the disorder - crime relationship , as well as the dynamics that underlie it . One technique that shows promise is the dual GBTM . An extension of GBTM, the dual GBTM was designed to capture the relationship between two related but distinct development trajectories , such as disorder and violent crime, which evolve contemporaneously or over different time periods (Nagin & Trembla y, 2001). S everal renowned scholars within the field of Criminology have raised concerns regarding the existence of distinct developmental trajectories and the extent to which units within trajectories adhere to them (see Sampson & Laub, 2005; Raudenbush, 2005). In response to this critique, other approaches, such as growth mixture modeling (GMM) and nonparametric growth mixture modeling (NP - GMM) , have become popular. Unlike GBTM, GMM and NP - GMM include random effects in the estimation of trajectory models which allow for within - group variability (Nagin & Odgers, 2010). Future research should explore these (and other) modeling alternatives in an effort to establish intersubjective agreement. Closing Remarks Despite the need for future research , several implications for theory, practice, and policy can be tentatively drawn from this study . To start, this study suggests that broken windows research should accommodate nonlinearity in its exploration of the relationship between disorder and violent c rime . Misspecification of the functional form of this relationship might cause researchers to over - or under - state effects depending on the nature of this relationship across levels of disorder. Therefore, efforts to accommodate nonlinearity not only stand to improve 120 model fit , but also to provide a more accurate assessment of the disorder - crime relationship . Likewise, e fforts to gauge the effectiveness of policing disorder initiatives should be mindful of this relationship and manage their expectations for crime control accordingly . There are several possible options that researchers can pursue to accommodate nonlinearity . Known for their simplicity, polynomial transformations may be an entirely reasonable away to capture nonlinear effects. However, researchers must be aware of their shortcomings. Previously discussed, polynomial transformations assume that the relationship between X , the independent variable, an d Y , the dependent variable , do not vary across the distribution of X . In other words , they forc e researchers to assume a global fit. Another shortcoming of this approach is that the selection of polynomial transformation is often arbitrary. While some the ories may indicate a nonlinear effect, the actual power of the effect is often not clearly known and the incorrect selection may obfuscate results (see Keele, 2008) . In light of these shortcomings, researchers have turned to nonparametric techniques . The se techniques do not require a priori assumptions about functional form, but rather locally estimate it from the data. Given this feature , nonparametric techniques are well - suited for theory testing . T his study conducted local estimation using penalize d spline, radial spline, and inverse weighting kernel methods . However, t hese methods are by no means the only available to capture nonlinear effects . To this point, m achine learning systems, such as neural networks or tree - based models , are able t o implicitly detect complex nonlinear relationships through an automated process that learns from the (data) environment and applies changes to improve prediction s . However, they come at a cost. Known , the internal logic of machin e learning systems is often unclear ( see Ru d in & Carlson, 201 8 ) . Most concerning , it is not well understood how variables contribute to the model or how to interpre t model results ( see 121 Ru d in & Carlson, 201 8 ) . For these reasons, these computationally intensive methods are less aligned with theory testing which seeks to establish causality . In addition , this study found a interpretation of the broken windows tipping point , hypothes is 2a . Across semiparametric methods, an increased change in logged violent crime rate was identified at mid - range levels of physical disorder. However, this change is not nearly as severe as expected . Ultimately, a slower ascent provides reason to reconsi der mechanisms that underlie the tipping point , as well as their instruction for the implementation of order - maintenance policing . In neighborhoods located at the tipping point, recall Wilson and Kelling (1982) advocate the minimal use of formal mechanisms to address disorder in order to avoid its proliferation and precipitous rise of violent crime. While neighborhoods located at the tipping point may indeed have weakened levels of informal social control , their effect on violent crime may not be as significant as once thought . It may be the case that Wilson and Kelling (1982) overstated the effect of disorder on r esidents fe ar of crime . To this point, t here may be another tipping point at play tha t affects the disorder - crime relationship . As previously discussed, p ast exposure to disorder may increase the threshold for perceiving it to be a problem ( Taylor & Shumaker, 1990; Sampson & Raudenbush, 2004 ). On average, m inority residents are more likely to have been previously exposed to disorder and therefore will need to be exposed to greater levels before they perceive it to be a problem. In light of low income, African American neighborhoods , t his phenomenon may help explain the attenuated threshold effect identified by this study . I t may also help explain the negative effect of disorder on violent crime at very high 122 levels of disorder identified by the inverse kernel weighting method, and model s 3a and 3b. 17 If future research consistently uncovers similar relationship s between disorder and violent crime, then there is a strong basis for investigating its underlying causes. Furthermore, sources at neighborhoods at the tipping point was in part motivated by the practical limitations of allocating limited police resources to high disorder, high crime neighborhoods. In such neighborhoods, Wilson and Kelling (1982) argue that the demands to police resources would come at too great a cost . Consequently , the best (and only) option i s to focus police resources at neighborhoods at the tipping point; neighborhoods that are at the brink of decline . Contrary to what was expected, however , neighborhoods are not catapulted into a high disorder, high crime state past some level of disorder located in the middle of the disorder distribution . Rather, this study found an attenuated threshold effect. As a resul instruction loses significance . T here may be more opportunities for residents to strengthen and exercise informal social control without needing the assistance of the police, as the impact of fear of crime may not be as debil itating as previously thought. T here may also be more opportunities for the police to intervene beyond mid - range levels of disorder without great cost . Ultimately, there is less motivation without the looming threat of the tipping point. T he magnitude of the effect of disorder on violent crime is also worth consideration, especially past mid - range levels of disorder. Across parametric and semiparametric approaches, the magnitude of the ef fect of physical disorder on logged violent crime rate is diverse , with the inverse weighting kernel method predicting the largest effect and the penalized spline method 17 Minority individuals are the most likely to have extensive previous exposure to disorder, as well as to live in neighborhoods with very high levels of disorder (and violent crime) . 123 predicting the smallest . Although they do not accommodate the possibility of nonlinear ity, o ther studies have identified a modest effect of disorder on violent crime ( e.g., Sampson & Raudenbush, 1999; Taylor, 1999 , 2001; Boggess & Maskaly, 2014; Wheeler, 2018 ; Konkel et al., 2019 ). Nonetheless , efforts to address disorder may still be worth pursuing. Historically, they have played a key role in policies aimed at spurring neighborhood revitalization ( e.g., Newman, 1972; Brown & Perkins, 2001; Brown, Brown, & Perkins, 2004; Day et al., 2007; Dulin - Keita et al., 2015; Schuetz, Spader, & Cortes, 2016; Spader et al. , 2016; Prener, Braswell, & Monit, 2020; Rupp et al., 2020 ) . Outside of their effect on crime, efforts to address disorder may also improve quality of life and reduce fear of cri me ( Skogan, 1990; Perkins & Taylor, 1996; Day et al., 2007; Chappell, Monk - Turner, & Payne, 2010 ; Dulin - Dulin - Keita et al., 2015; Johnsen, Neal, & Gasteyer, 2015; Rupp et al., 2020 ) . While it is premature to cast aside BWT , this bolster a competing instruction for the allocation of police resources . I t has been repeatedly demonstrated that a small fraction of targets (e.g . , places, victims, and offenders) account for the vast majority of crime ( Wolfgang et al. , 1972; Forst et al. , 1978; Sherman et al. , 1989 ; Weisburd et al. , 2004; Eck et al. , 2007) . , Sherman ( 2007 ) argues that resources should be concentrated to targets that produce the greatest amount of harm in order to have the largest crime reduction effe ct. 18 Consistent with this finding, t his study suggests that the allocation of police resources to hot spots direct police resources to neighborhoods at the tipping point . Indeed, hot spot policing has been shown to achieve significant crime reduction gains (Braga et al., 1999; Braga & Bond, 2008; Braga et al., 2012, 2014) . That being said , Sherman (2007 , p. 308 ) warns that 18 Sherman (2017, p. 13) calls for the creation of a total 124 spots, are anyt - few may, in fact, be the hardest nuts to crack: the cases that are most difficult to solve because - . The issue of com orbidity presents a particular ly complex challenge to tackle. To this point, t he effect of hot spot policing on crime , however large, has yet to be shown to produce long - term crime reduction gains (see Telep & Weisburd , 2014) . One potential explanation concerns the extenuating role of e conomic disadvantage and collective efficacy , co - morbid features of places. These features have been found to contribute to the developmental patterns of disorder and crime (Weisburd et al., 2012 , 2013 ). In light of this finding , it has been argued that c rime prevention strategies which focus on initiating social change within hot spots are better equipped to produce long - term crime reduction gains , as compared to policing strategies driven by opportunity the ories (Weisburd et al., 2012 ; Weisburd, Davis, & Gill, 2015 ). In this regard, o rder - maintenance policing holds promise. Order - maintenance policing can be considered to be a future - oriented policing strategy. That is, it is geared toward preventing future crime emergence by targeting neighborhoods that are on the cusp of decline ; neighborhoods at the tipping point . In order to achieve this goal, p roponents of order - maintenance policing and, more generally , BWT have long advocated the role of the police in strengthening informal social control within neighborhoods , a key component of collective efficacy . According to Weisburd et al. (2015, p. 272 ), police effort s that seek to promote collective efficacy gencies) a shift from the myopic focus of crisis response to a bifurcated approach that allows space for community - To facilitate these efforts, the police must establish relationships of trust with residents . The recent mur der of George Floyd by a Minneapolis p olice officer has shed much needed light on 125 the growing chasm between the police and the communities which they serve . D eeply negative attitudes toward the police - amplified by widely publicized incidents of police brutality - feed this divide . Moving forward from this horrific event, procedural justice in police - resident interactions that are supported by community - oriented policing strategies , such as order - mainten ance policing, are paramount in order to restore trust in the police. 19 In an effort to secure long - term crime reduction gains , Weisburd et al. (2015 , p. 269 ) argue that these strategies should be implemented within hot spots and direct impact of everyday police intervention on informal social control and structuring a concrete approach for building community engagement and collective efficacy . They reason that such an a pproach will help empower residents to take responsibility for crime within their communities and self - regulate safety , ultimately decreasing reliance on the police (Weisburd et al., 2015). This approach aligns with the recent call to support alternative s olutions to address social problems within communities in an effort to minimize reliance on the police (see Chang & Wilson, 2020; Hawkins, Mettler, & Stein, 2020). In addition to th e challenge of comorbidity , evaluations of hot spot policing suffer from the same challenges of evaluations conducted elsewhere (see Sherman, 2007). One such challenge that is particularly relevant to this study regards determin ing the appropriate dosage of police response needed to ensure the identification of val id treatment effects . As previously mentioned, co - morbid features of hot spots pose significant challenges for police efforts to spur social change. Unfortunately, little is known about the dosage of police response necessary to 19 Broadly defined, community - oriented policing is a philosophy that promotes organizational strategies that support the systematic use o f partnerships and problem - solving techniques to proactively address the immediate conditions that give rise to public safety issues such as crime, social disorder, and fear of crime Oriented Police Services, 2020, p. 1). 126 achieve long - term crime red uction gains in hot spots , or elsewhere, for that matter. In particular, it is unknown whether long - term crime reduction gains can be achieved in hot spots with limited police resources . For this reason limited police resources to neighborhoods at the tipping point - in an effort to avoid the future potential of increased levels of violence - remain s a tenable alternative . dings, there are likely more places beyond mid - range levels of disorder in which order - maintenance policing could be implemented without great cost to police resources. Nonetheless, e fforts to elicit social change in these places will likely come much easi er than similar efforts implemented in hot spots , as the challenges posed by co - morbid features will likely not be as significant . That being said , i f short - term crime reduction gains are the priority , then the allocation of limited police resources to hot spot s emerges as the superior strategy . 20 Ultimately, a comprehensive assessment of the optimal allocation of police resources is necessary . 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