MODELING THE JOINT IMPACTS OF SOCIAL NETWORK AND BUILT ENVIRONMENT By Wei Liu A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Geography Doctor of Philosophy 20 21 ABSTRACT MODELING THE JOINT IMPACTS OF SOCIAL NETWORK AND BUILT ENVIRONMENT By Wei Liu This research stem s from the worldwide public health problem of childhood obesity and insufficient physical activity (PA) among adolescents. Studies have shown that both social networks and the built environment could affect PA, but how do they jointly exert influence? Under standing the scale and mechanism of this joint impact could shed light on developing an effective intervention to promote PA. The goal of this dissertation is to try to disentangle the joint influence of social network s and the built environment on changes in PA through social network analysis and test a novel intervention based on the findings from the social network models. This study use s two waves of Add Health data from two sample schools. Chapter Two investigate s how school - based friendship network s could influence Physical Education (PE) class enrollment. Chapter Three examin es the influence of home location, neighborhood characteristi cs, as well as the demographic characteristics and change in PA of peers who were nominated as friends in the Add Health social survey and PA dynamics between two academic years . Chapter Four presents a spatial age nt - based model that was derived from the social network model and integrate s a location - based mobile game similar to Pokémon Go as a PA - promoting intervention to test different intervention scenarios. enrollment status ha s a weak influence on the change of in two consecutive year s. Another total PA change can affect their PA behaviors . Contrarily, the built environment of the neighborhood did not prove to exert significant influence. Due to social influence, students participating in an intervention program may cause a change in PA of non - participants, i.e., we can observe a spillover effect of the intervention program. This d issertation enriches the field of health geography by integrating social network analysis and spatial thinking to jointly investigate the influence of environmental and social space s and to facilitate a more comprehensive understanding of the complex syste m of childhood obesity. It also extends existing models and provide s a spatial agent - based model as an intervention exploration tool that can be calibrated for research and education by other scholars. iv This dissertation is dedicated to my parents, Mr. Yinquan Liu and Mrs. Huanting Sun. v ACKNOWLEDGEMENTS I would like to express my gratitude to everyone who helped and encouraged me along the journey of pursuing my dream. This dissertation would not have been possible without the support from all of them. I would like to give special thanks to my advisor, Dr. Arika Ligmann - Zielinska. In the past eight years of my Ph.D. program, Arika has never gave up on me and has offered me tremendous help. I would also like to thank my other dissertation committee members, Dr. Igor Vojnovic, Dr. Sue Grady, and Dr. Kenneth Frank, who have provided me extremely valuable suggestions on m y research and helped me enhance my scientific thinking. I would like to thank all other faculty members in the Department of Geography, who helped me get through difficulties and made my years at Michigan State University unforgettable. I appreciate that Dr. Amber Pearson offered me the opportunity to work in the SHAC lab and she is also a great mentor who guides me become a more independent scholar. When I worked as course instructors, Dr. Ashton Shortridge always keeps his door open, and gave me many va luable advices on teaching pedagogy. When I was so frustrated and felt hopeless while debugging my model, I turned to Dr. Lifeng Luo for help. He selflessly devoted his valuable time to help me optimized the model by reducing the computation time from a th ousand year to a few minutes. I also thank my supervisors from OnGEO, who provided me the opportunity to gain skills in teaching online classes and course development. Many thanks go to the staff in our department, especially Ms. Claudia Brown, Ms. Sharon Ruggles, Ms. Ana O'Donnell, and Mr. vi Wilson Ndovie, who have helped me solved various questions and problems and made my life at MSU as an international student much easier. I want to thank all my friends from and outside of MSU. Special thanks to Dongyuan Wu, Jiang Chang, Peiling Zhou, Yingyue Liu, Rajiv Paudel, Kyle Rdican, Kayla Davis, Yue Dai, Jing Zhu, Xinru Zhao, Linjie Shi, and all my other friends who have provided me great mental support, the extra push I need, and a lot of joy to my life. Last bu t not least, I would like to thank my parents and my husband for their unconditional support and love. I have been away from my beloved ones and missed numerous birthdays, holidays, anniversaries, and all other important moments when I was supposed to be w ith them in the past 10 years, ever since I came to the US in 2011 for postgraduate degrees. I am grateful for their understanding and support all the way along . vii TABLE OF CONTENTS LIST OF TABLES ................................ ................................ ................................ ......................... ix LIST OF FIGURES ................................ ................................ ................................ ........................ x INTRODUCTION ................................ ................................ ................................ .......................... 1 Statement of the Problem ................................ ................................ ................................ ............ 1 Purpose of the Research ................................ ................................ ................................ .............. 4 Organizati on of the Research ................................ ................................ ................................ ...... 4 REFERENCES ................................ ................................ ................................ ............................... 6 PHYSICAL EDUCATION ENROLLMENT ................................ ................................ ................. 9 Abstract ................................ ................................ ................................ ................................ ....... 9 Introduction ................................ ................................ ................................ ............................... 10 Background ................................ ................................ ................................ ............................ 11 Research question ................................ ................................ ................................ .................. 13 Methods ................................ ................................ ................................ ................................ ..... 13 Data ................................ ................................ ................................ ................................ ........ 13 Data Preparation ................................ ................................ ................................ .................... 14 Social Influence Model ................................ ................................ ................................ .......... 15 Results ................................ ................................ ................................ ................................ ....... 16 Discussion ................................ ................................ ................................ ................................ . 21 PE enrollment from combined data ................................ ................................ ....................... 22 Conclusions from results ................................ ................................ ................................ ....... 23 Conclusion ................................ ................................ ................................ ................................ . 24 REFERENCES ................................ ................................ ................................ ............................. 26 ACTIVITY AND RESIDENTIAL LOCATIONS ................................ ................................ ....... 30 Abstract ................................ ................................ ................................ ................................ ..... 30 Introduction ................................ ................................ ................................ ............................... 31 Obesity, physical activity, environment, and social network ................................ ................ 31 SAB models of obesity and PA: a brief review ................................ ................................ ..... 32 Purpose of study ................................ ................................ ................................ .................... 34 Method ................................ ................................ ................................ ................................ ...... 35 Study population ................................ ................................ ................................ .................... 35 Measurements ................................ ................................ ................................ ........................ 36 Analytic plan ................................ ................................ ................................ .......................... 38 Results ................................ ................................ ................................ ................................ ....... 42 Descriptive statistics ................................ ................................ ................................ .............. 42 SAB friend selection model ................................ ................................ ................................ ... 44 SAB coevolution model ................................ ................................ ................................ ......... 47 viii Discussion ................................ ................................ ................................ ................................ . 53 Summary ................................ ................................ ................................ ................................ ... 56 APPENDICES ................................ ................................ ................................ .............................. 57 APPENDIX A : Distribution of Environment Variables ................................ ........................... 58 APPENDIX B : Specification of the SAB Model ................................ ................................ ...... 65 REFERENCES ................................ ................................ ................................ ............................. 70 CHAPTER 3: EFFECTS OF POKÉMON GO AS AN INTERVENTION TO PROMOTE - A SPATIAL STOCHASTIC AGENT - BASED MODEL SIMULATION ................................ ................................ ................................ .............. 75 Abstract ................................ ................................ ................................ ................................ ..... 75 Introduction ................................ ................................ ................................ ............................... 76 Methods ................................ ................................ ................................ ................................ ..... 79 Baseline Model and Empirical Data Analysis ................................ ................................ ....... 79 Baseline model validation ................................ ................................ ................................ ..... 82 Extended baseline model with PG intervention the PGABM ................................ ............ 83 Intervention scenarios ................................ ................................ ................................ ............ 88 Simulation and data analyses platforms ................................ ................................ ................ 89 Results ................................ ................................ ................................ ................................ ....... 89 Baseline model ................................ ................................ ................................ ...................... 89 Scenario results ................................ ................................ ................................ ...................... 92 Discussion ................................ ................................ ................................ ............................... 102 Strengths and limitations ................................ ................................ ................................ ..... 104 Policy implications ................................ ................................ ................................ .............. 106 REFERENCES ................................ ................................ ................................ ........................... 108 C HAPTER 4: C ONCLUSION ................................ ................................ ................................ ... 113 Revisiting research questions ................................ ................................ ................................ .. 113 Additional thoughts about the practical implications ................................ .............................. 115 Limitations and future work ................................ ................................ ................................ .... 116 REFERENCES ................................ ................................ ................................ ........................... 119 ix LIST OF TABLES Table 1: Descriptive analysis of samples ................................ ................................ ...................... 17 Table 2: Average total PE at Wave 1 and Wave 2 ................................ ................................ ........ 18 Table 3: Social influence model results ................................ ................................ ........................ 20 Table 4: Social influence model with interactions results ................................ ............................ 23 Table 5: D escription of effects in SAB friend selection and SAB behavior submodels .............. 41 Table 6: Descriptive statistics of two sample schools (percent in parentheses) ........................... 43 Table 7: Descripti ve statistics of friend networks ................................ ................................ ......... 44 Table 8: SAB selection model ................................ ................................ ................................ ...... 47 Tabl e 9: SAB coevolution model - School A ................................ ................................ ............... 49 Table 10: SAB coevolution model - School B ................................ ................................ .............. 51 Table 11: Descriptive statistics of students from the sample school ................................ ............ 80 Table 12: Significant coefficients from SIENA model ................................ ................................ . 81 Ta ble 13: PG - related point density in Boston ................................ ................................ ............... 84 Table 14: Summary of scenario tests ................................ ................................ ............................ 93 x LIST OF FIGURES Figure 1: Home location of sample students from School A ................................ ........................ 59 Figure 2: Home locations of sample students from School B ................................ ...................... 60 Figure 3: Distribution of total physical activity and change between Wave 1 and Wave 2 of sample students from School A ................................ ................................ ................................ .... 61 Figure 4: Distribution of total physical activity and change between Wave 1 and Wave 2 of sample students from School B ................................ ................................ ................................ ..... 62 Figure 5: Distribution of neighborhood built environment of sample students from School A ... 63 Figure 6: Distribution of neighborhood built envir onment from School B ................................ .. 64 Figure 7: Flowchart of PGABM ................................ ................................ ................................ ... 87 Figure 8: Illustration of scenario 3 ................................ ................................ ................................ 89 Figure 9: Distribution of simulated weekly total PA (boxes) and observed value at Wave 2 (solid line) ................................ ................................ ................................ ................................ ............... 90 Figure 10: Distribution of simulated in - degree (boxes) and observed network at Wave 2 (solid line) ................................ ................................ ................................ ................................ ............... 91 Figure 11: Distribution of simulated out - degree (boxes) and observed network at Wave 2 (solid line) ................................ ................................ ................................ ................................ ............... 92 Figure 12: Scenario 1 - Effects of different scales of the program (dots: mean of 20 models runs; bars: ± 1 standard deviation of simulation means) ................................ ................................ ....... 96 Figure 13: Scenario 2 - Effects of targeting students with larger BMI (dots: mean of 20 models runs; bars: ± 1 standard deviation of simulation means) ................................ .............................. 98 Figure 14: Scenario 3 - Effects of distance to community center (dots: mean of 20 models runs; bars: ± 1 standard deviation of simulation means) ................................ ................................ ..... 101 1 INT RODUCTION Statement of the Problem This study stems from the prevalence of obesity among adolescents in the US, which is a severe public health issue. The prevalence of obesity in the US has been rising since 1999 with only a temporary pause between 2009 and 2012, and it is predicted that a bout half of the adolescents aged 12 19 will be obese or overweight by 2030 (Wang et al. 2020) . Usually, obesity and overweight are due to imbalance of caloric intake and expenditure, thus dieting and promoting physical activity are considered the most i mportant and effective methods for obesity treatment and prevention methods. However, obesity is a very complex problem that involves various driving forces. reasons. Fi - year (2004 2009) longitudinal study (Neumark - Sztainer 2006) of adolescents shows that most dieters were back to their original weight and about 40% of them even gained more weight than before the study. Dieting and unhealthy weight control behavior may lead to eating disorders or disordered eating. Similar conclusion was also drawn by Field et al. (2003) , whose longitudinal study of children and adolescents showed that dieting is not effective in w eight control and may lead to weight gain. Secondly, in addition to preventing obesity, PA offers many other health benefits, such as Many ado lescents in the US do not do enough PA. While adolescents (age 6 - 17) are suggested to do at least an hour of PA per day, in 2017, only 26.1% of high school students met 2 this requirement (Kann et al. 2018a) . Although schools provide elective Physical Educat ion (PE) classes, only 51.7% of high school students take these classes in an average week and less than a third students took PE classes daily (Kann et al. 2018a) . Recognizing inadequacy of adolescent PA, many scholars have investigated the variation am ong adolescents based on gender, different ethnic background, and socioeconomic status (SES). For example, in 1996, the National Longitudinal Study of Adolescent Health (NLSAH) data showed that female and minority adolescents in grades 7 to 12 (except for Asian females) were most inactive (Gordon - Larsen 1999) . In a different study of high school students in San Diego, Sallis et al. (1996) demonstrate that high socioeconomic status can be associated with higher frequency of participating in PE classes and ex tracurricular PA. While ethnic differences could be observed on some specific activities, there was no significant ethnic or socioeconomic status difference on vigorous exercise outside of school. Participation in PA is not only related to demographic cha racteristics and personal social network impacts. For example, in a study using data from NLSAH, Mueller et al. (2010) buil d a number of different multi - le vel models to investigate the influence of social comparison in a school context. Their findings show that girls who have similar Body Mass Index (BMI) different BMIs. They also illustrate that the school context matters with more overweight girls, chances of an individual trying to lose weight decrease and vice versa. In another study, Zhang et al. (2015b) use the Add Health data (Harris et al. 2009) to build an Agent - Based Model (ABM) to study the role of adolescent social network. Their simulation demonstrates that peer influence can impact the prevalence of overweight, but the effect is dependent on the distribution of BMI. 3 Given the significant impacts of soc ial network on PA of youth, scholars propose interventions that explicitly employ social networks to address obesity prevalence. For instance, a study by Bahr et al. (2009) illustrates that it is important to consider larger network impacts. Targeting indi viduals at the edges of a network cluster can better control the prevalence of obesity. They In addition to the school environment, another important space where adolescents spend most o f their time is the neighborhood around their homes. Studies have shown that built environment also affects individual PA. Yang et al. (2012) demonstrate that, for a group with low SES and the associated low level of PA, when the positive attitude towards walking is increased, this positive attitude will gradually fade over time if the environment is not walkable. However, if walkability of the neighborhood is improved, there is a potential of increase in walking of youth, which can effectively increase the ir total PA (Carlson et al. 2015) . Apart from walkability, accessibility to amenities and natural space (parks, beaches etc.) is also positively associated with physical activities of young people (Edwards 2014, Floyd 2011) . Safety has also been identified as influential on adolescent outdoor activity (Molnar et al. 2004a) . Despite the proliferation of studies on adolescent PA, the distinctive role of the built environment and social networks is unclear as contradictory findings have been reported (Voorhees et al. 2005, Christakis and Fowler 2007a, Cohen - Cole and Fletcher 2008) . Also, although scholars provide suggestions on interventions involving environment and/or social network, it remains to be seen whether these interventions are effective when the entangled impacts of space and social networks are considered. More studies are needed to investigate the joint impacts of social network and environment to facilitate designs of effective policies and interventions to promote PA and prevent the prevalence of obesity among adolescents. 4 Purpose of the Research The overarching goal of this study to investigate the joint impact of social network and built - environment on high - and , with this joint impact, how PA - promoting interventions would affect participants and non - participants. We examine PA from Physical Education (PE) separately as it is different from leisure - time PA . PE is also little influenced by the neighborhood environment. In this research, we are trying to answer three researc h questions: 1) Does the social influence in a school context play an important role in affecting adolescents to conform in taking PE classes? 2) H ow does the neighborhood environment and friendship network jointly influence PA? 3) How can PA - promoting interventions would affe ct participants and non - participants given the joint impact of social network and space? Organization of the Research The dissertation is organized as follows. In Chapter One , I buil d a social influence model to Chapter Two , I use a stochastic actor - based model called Siena to analyze Add Health data to investigate the influence of the home location and neighborhood characteristics on high school Three , I extend an ABM derived from a Siena model by testing the Pokémon Go mobile game as an PA - promotion intervention to investigate the spillover effect s on non - players due to social network dynamics and social influence. In terms of format, Chapter One, Two, and Three are presented as standalone manuscripts, 5 independently addressing each of the three research questions mentioned above . In Conclusion , I summarize key findings of this research, point out limitations, and discuss directions for future research. 6 REFERENCES 7 REFERENCES Andersen, L. B. (2006) Physical activity and clustered cardiovascular risk in children: a cross - sectional study (The European Youth Heart Study). Lancet, 368, 299 - 304. Bahr, D. B., R. C. Browning, H. R. Wyatt & J. O. Hill (2009) Exploiting Social Networks to Mitigate the Obesity Epidemic. Obesity, 17, 723 - 728. Carlson, J. A., B. E. Saelens, J. Kerr, J. Schipperijn, T. L. Conway, L. D. Frank, J. E. Chapman, K. Glanz, K. L. Cain & J. F. Sallis (2015) Association between neighborhood walkability and GPS - measur ed walking, bicycling and vehicle time in adolescents. Health & Place, 32, 1 - 7. Christakis, N. A. & J. H. Fowler (2007) The Spread of Obesity in a Large Social Network over 32 Years. New England Journal of Medicine, 357, 370 - 379. Cohen - Cole, E. & J. M. Fle tcher (2008) Is obesity contagious? Social networks vs. environmental factors in the obesity epidemic. Journal of Health Economics, 27, 1382 - 1387. Edwards, N. J. (2014) The Effect of Proximity on Park and Beach Use and Physical Activity Among Rural Adolesc ents. Journal of physical activity & health, 11, 977 - 984. Field, A. E., S. B. Austin, C. B. Taylor, S. Malspeis, B. Rosner, H. R. Rockett, M. W. Gillman & G. A. Colditz (2003) Relation Between Dieting and Weight Change Among Preadolescents and Adolescents. PEDIATRICS, 112, 900 - 906. Floyd, M. F. (2011) Park - Based Physical Activity Among Children and Adolescents. American journal of preventive medicine, 41, 258 - 265. Gordon - Larsen, P. (1999) Adolescent physical activity and inactivity vary by ethnicity: The Na tional Longitudinal Study of Adolescent Health. The Journal of pediatrics, 135, 301 - 306. Harris, K. M., C. T. Halpern, E. Whitsel, J. Hussey, J. Tabor, P. Entzel & J. R. Udry. 2009. The National Longitudinal Study of Adolescent to Adult Health: Research Design [WWW document]. Kann, L., T. McManus, W. A. Harris, S. L. Shanklin, K. H. Flint, B. Queen, R. Lowry, D. Chyen, L. Whittle, J. Thornton, C. Lim, D. Bradford, Y. Yamakawa, M. Leon, N. Brener & K. A. Ethier (2018) Youth Risk Behavior Surveilla nce - United States, 2017. MMWR Surveill Summ, 67, 1 - 114. 8 Molnar, B. E., S. L. Gortmaker, F. C. Bull & S. L. Buka (2004) Unsafe to Play? Neighborhood Disorder and Lack of Safety Predict Reduced Physical Activity among Urban Children and Adolescents. Americ an Journal of Health Promotion, 18, 378 - 386. Mueller, A. S., J. Pearson, C. Muller, K. Frank & A. Turner (2010) Sizing up Peers. Journal of Health and Social Behavior, 51, 64 - 78. Neumark - Sztainer, D. (2006) Obesity, Disordered Eating, and Eating Disorders in a Longitudinal Study of Adolescents: How Do Dieters Fare 5 Years Later? Journal of the American Dietetic Association, 106, 559 - 568. Sallis, J. F., J. M. Zakarian, M. F. Hovell & C. R. Hofstetter (1996) Ethnic, socioeconomic, and sex differences in physi cal activity among adolescents. J Clin Epidemiol, 49, 125 - 34. Ussher, M. H., C. G. Owen, D. G. Cook & P. H. Whincup (2007) The relationship between physical activity, sedentary behaviour and psychological wellbeing among adolescents. Social Psychiatry and Psychiatric Epidemiology, 42, 851 - 856. Voorhees, C. C., D. Murray, G. Welk, A. Birnbaum, K. M. Ribisl, C. C. Johnson, K. A. Pfeiffer, B. Saksvig & J. B. Jobe (2005) The Role of Peer Social Network Factors and Physical Activity in Adolescent Girls. American Journal of Health Behavior, 29, 183 - 190. Wang, Y., M. A. Beydoun, J. Min, H. Xue, L. A. Kaminsky & L. J. Cheskin (2020) Has the prevalence of overweight, obesity and central obesity levelled off in the United States? Trends, patterns, disparities, and fut ure projections for the obesity epidemic. International Journal of Epidemiology, 49, 810 - 823. Yang, Y., A. V. Diez Roux, A. H. Auchincloss, D. A. Rodriguez & D. G. Brown (2012) Exploring walking differences by socioeconomic status using a spatial agent - bas ed model. Health & Place, 18, 96 - 99. Zhang, J., L. Tong, P. J. Lamberson, R. A. Durazo - Arvizu, A. Luke & D. A. Shoham (2015) Leveraging social influence to address overweight and obesity using agent - based models: The role of adolescent social networks. Soc ial Science & Medicine, 125, 203 - 213. 9 CHAPTER 1 : MODELING THE SOCIAL INFLUENCE ON HIGH SCHOOL Abstract for weight control and providing other health benefits. However, the enrollment rate of PE classes is not high in US high schools, especially in higher grades. We hypothesized that observing friends one of the reasons that influenced Adolescent Health and a regression - ollment. Specifically, we investigated whether PE enrollment of enro llment was significantly (p<0.001) associated with their enrollment in the following year. Higher grade was associated with lower enrollment rate. PE enrollment of close friends showed a ar others (i.e. peers of the same gender and the same grade) may exert impacts. This study sheds light on understanding the decision - makers to seek effective interv entions for promoting PE taking and preventing obesity among high school students. Keywords: Physical Education; friendship; social influence; adolescence 10 Introduction Obesity among adolescents is a serious public health problem. In 2015 - 2016, the prevalence of obesity among adolescents (12 - 19 years) in the US was 20.6%, and there was a significant increase in obesity rate from 1999 - 2000 through 2015 - 2016 (Hales et al. 2017) Regular physical activity can not on ly help with weight control (Tappy, Binnert and Schneiter 2003) but provide other physical health (Janssen and LeBlanc 2010b) and mental health (Eime et al. 2013a) benefits. Physical Education (PE) is recognized as the primary source of physical activity f or adolescents (Kann et al. 2018b, USDHHS 2001) . Besides, PE and other school sports benefit children in many other aspects such as engendering positive social behaviors, improving psychological health, enhancing academic performance etc. (Bailey et al. 20 09) adolescents did not do enough physical activity on regular basis (USDHHS 2001, Troiano et al. 2008) . According to a national survey in 2017, less than a third of studen ts were physically active for at least an hour per day on all seven days before the survey, and less than half of students were active for at least an hour on five or more days in the week (Kann et al. 2018b) . Also, only 51.7% of students went to a PE clas s on one or more days in an average week (Kann et al. 2018b) . In the US, many high school students no longer choose to take elective PE classes 11 after they fulfill the PE credit requirements for graduation thus PE participation rate decreases with age in hi gh schools (Shen 2010, Kann et al. 2018b, Ahima and Lazar 2013) . Given the prevalence of adolescent obesity and the benefit of physical activity (including behavio ral interventions. Many studies have identified the influences from peers and/or friends (Fitzgerald, Fitzgerald and Aherne 2012) . As a major form of adolesc this study we hypothesize that taking PE can also be influenced by the enrollment status of peers in the school. Background Friendship may affect PE enrollment because taking a PE class with friends could be a way of maintainin g and strengthening friendship for adolescents. School is a bounded environment school context, conforming to the norms and behavior of others could help a st udent gain acceptance of other students and obtain his/her social status (Coleman 1961) , which in turn, (Crosnoe, Frank and Mueller 2008) . Friendship, as part of the social opportun ities, is of great value to adolescents as it provides socioemotional resources such as comfort and support as well as instrumental resources such as help for coursework (Frank et al. 2008) . A recent study showed that the amount of physical activity from P E was significantly associated with perceived acceptance among adolescents (Lee, Shin and Smith 2019) . 12 friends as they behave like their friends over time, i.e. a result of social influence. For example, close friends may encourage an individual to take the same c lass together as companions over observation. When an individual observes others taking PE classes, who were existing friends or considered as potential friends, the individual may enroll in the class as well. The homophily theory, a phenomenon of individual inclining to associate with similar others (John, Rodgers and Udry 1984, Joyner and Kao 2000) , may also imply the potential relationship between friendship and tak ing/maintaining participation in PE. For example, it was found that body size had an influence on friend selection among adolescents (Crosnoe et al. 2008) . Non - overweight students were more likely to be friends with non - overweight others (Schaefer and Simp kins 2014) . Given the role of homophily, students who share similar characteristics such as possible that physically active students tend to be friends with other active students, while physically inactive students would like to associate with inactive students. This may lead to reinforcing feedback of the social influence on behaviors, in which case, physically active students became more active. In contrast, inactive students got more inactive after they were influenced by friends and conformed to similar behaviors. Apparently, besides influence from peers and the school context, there are als o other factors - level driving forces, such as interests in sports or pursuing a more appealing physical appearance through physical activities (Crosnoe et 13 al. 2008) , could lead to the enrollment of PE. Influence could also come from family and acquaintances outside school via communication or observation. Research question effective strategies of promoting futu re enrollment. Among many driving forces, our research question is that whether the social influence in school context plays an important role in affecting adolescents to conform in taking PE classes. Specifically, in this study , we built a social influenc e model to test the following hypothesis: observing PE enrollment of friends and cohorts following year. Methods Data In this study we used the Add Health data - The National Longitudinal Study of Adolescent to Adult Health data (Harris 2009) - to test our hypothesis. Add Health is a nationwide school - based longitudinal data with the first wave data collected in the 1994 - 95 school year (Wave 1) and the second wave in the 95 - 96 school year (Wave 2). More details about Add Health study design and additional information could be found elsewhere (Harris et al. 2009) . Given the difficulty of collecting data of a complete longit udinal social network of adolescents in a school context, Add Health was the most suitable dataset that we could access and use to test our hypothesis. Among all Add Health sample schools, students from 16 selected schools were interviewed at home and the y were asked to provide the names of up to five male and five female friends. 14 These nominated friends were identified and linked with their corresponding participant ID i f they enrolled in the Add Health project. These schools are called saturated schools as they have completed social network data. In the study, we chose the two largest saturated schools (called School A and School B throughout this paper) to test our hypotheses. Data Preparation To prepare data for our analysis, a few data filtering steps were undertaken. In the raw data, there were 832 students from School A and 1721 students from School B of Wave 1. Since we focus on high school students with both Wave 1 and Wave 2 data, students who were in 12 th grade or under 9 th grade a nd those who had missing data in either wave were removed from the dataset. We also excluded students with incomplete PE enrollment information in Wave 1 and Wave 2. To investigate peer influence, a social network was built based on nominations in the surv ey at Wave 2 because friendship nomination at Wave 2 was considered to reflect experience between Wave 1 and Wave 2. We then excluded nominations that were not in the two selected schools of this study. In our final dataset, there were 447 observations fro m School A and 626 observation from School B. contains information about whether, when and what type of PE classes participants took between enrollment and 0 otherwise . After plotting the data, then maximum enrollment was two PE of 1 if a student enrolled in one or more types of PE classes within a school year, and a value of 15 0 describe the exposure to PE enrollment of students not nominated as fri ends, which we called the Data preparation and data analyses were done in R (R Core Team 2018) . Social Influence Model To test our hypothesis mentioned in the research question section, we proposed a logit social influence model defined in Equation (1). Based on the social influence theory, we hypothesized close friends as well as similar others. Specifically, we hypothesized tha friends (nominated at Wave 2) in the school, as well as the PE enrollment of similar others who were of the same gender in the same grade between W PE enrollment and grade at Wave 1. 16 Equation ( 2 ) below. Version two is the social influence model with only the exposure to average PE enrollment of similar others shown in Equation (3). Lastly, version three is the proposed full social influence model shown in Equation (1). Results Table 1 shows the descriptive statistics of sample students in School A and B. There was approximately the same amount of male and female students in both schools. School A was dominated by White students while school B had a more diverse student compositi on. After data 17 filtering, more samples from school A were in grade 9 (39%) and fewer in grade 11 (27%), but in School B the majority of samples were from grade 10 and 11. Table 1 : Descriptive analysis of samples School A School B Sample size 447 % 626 % Gender Male 231 51.7 315 50.3 Female 216 48.3 311 49.7 Race (more than 1 categories allowed) White 442 98.8 147 23.5 Black or African American 0 - 140 22.4 Asian or Pacific Islander 6 1.3 222 35.5 American Indian or Native American 19 4.3 25 4.0 Other 2 0.4 142 22.7 Birth year 1976 5 1.1 8 1.3 1977 61 13.6 94 15.0 1978 139 31.1 315 50.3 1979 153 34.2 208 33.2 1980 89 19.9 1 0.2 According to the PE records shown in Table 2, in general both schools showed that PE enrollment decreased as students entered higher grades, especially among male students as they 18 transitioned from grade 10 to 11. Compar ed to school A, grade 11 students from school B had a relatively higher average PE. After applying the proposed influence model on the network datasets of the two schools separately, we received slightly different results for the two tests. Table 2 : Averag e total PE at Wave 1 and Wave 2 School Grade at Wave 1 Average PE enrollment Wave 1 Average PE enrollment Wave 2 Male Female Male Female A 9 0.951 0.977 0.939 0.943 10 0.976 0.945 0.083 0.164 11 0.138 0.218 0.046 0.145 B 9 1.000 1.000 1.000 1.000 10 0.973 0.974 0.453 0.409 11 0.598 0.487 0.451 0.327 Table 3 shows the results for both schools. Based on the results of full models , we can infer their PE enrollment at Wave 1 (prior), their grade, and the behavior of similar others. The association with the prior year enrollment was positiv e, which indicated that students who take PE activities in Wave 1 are more likely to enroll in PE in Wave 2. PE enrollment at Wave 2 grades have a lower total enroll ment. PE taking status was also negatively associated with that of 19 peers of the same gender and grade, which suggested that an increase in PE taking among similar others was associated with less likelihood that one took PE in the following year, or vice ve rsa. At School B, total PE at Wave 2 was strongly associated with prior year enrollment , which is similar to School A. However, the results of School B did not show significant association with the social influence from close friends or similar others, no r was it associated with the grade. For both schools, the coefficients and standard errors of both exposure terms did not vary a lot in sub - models compared to the full model, indicating that the re is no multicollinearity issue caused by these two independe nt variables. 20 Table 3 : Social influence model results School A Full model - Equation (1) Sub - model - Equation (2) Sub - model - Equation (3) Independent variable Coefficient Standard error P value Coefficient Standard error P value Coefficient Standard error P value intercept - 127.359 15.369 <0.001*** - 113.965 13.488 <0.001*** - 128.997 15.213 <0.001*** prior 2.584 0.588 <0.001*** 1.894 0.488 <0.001*** 2.661 0.579 <0.001*** mean exposure to friends 0.231 0.352 0.511 0.229 0.347 0.508 NA NA NA exposure to similar others - 1.457 0.676 0.031* NA NA NA - 1.460 0.677 0.031* birth year 1.599 0.198 <0.001*** 1.421 0.172 <0.001*** 1.622 0.195 <0.001*** School B Full model - Equation (1) Sub - model - Equation (2) Sub - model - Equation (3) Independent variable Coefficient Standard error P value Coefficient Standard error P value Coefficient Standard error P value intercept 6.532 11.844 0.581 16.488 9.715 0.09 6.436 11.823 0.586 prior 1.835 0.261 <0.001*** 1.701 0.248 <0.001*** 1.836 0.261 <0.001*** mean exposure to friends 0.024 0.184 0.894 0.014 0.183 0.939 NA NA NA exposure to similar others - 0.892 0.534 0.095 NA NA NA - 0.890 0.534 0.095 birth year - 0.098 0.155 0.525 - 0.233 0.125 0.063 - 0.097 0.154 0.53 Two observations with null exposure to similar others in School B were removed from analysis 21 Discussion The results from the social influence model, as applied to the two schools in our study, indicated the PE enrollment among the high school students in the second year was positively associated enrolled in PE classes at a showed a dramatic decrease in PE enrollment at higher grades, which is consistent with the observation that after students fulfilled th e minimum PE credits requirement, they would prefer to use that time for other classes and prepare for college (Shen 2010, Kann et al. 2018b, Ahima and Lazar 2013) . the average PE of students of the same gender and grade at Wave 1 in School A. The relationship was positive but not significant in School B. The average PE taking of students of similar others was introduced to the model as a variable representing the exposu re to potential friends who were not nominated as friends in the survey. A possible reason for this negative relationship in School A might be that while there was an overall trend that fewer high school students took PE classes when they entered higher gr ades, many students who were actively engaged in the PE classes had a developed habit and were more likely to enroll in a PE course in the following years. Another explanation might be that there were limited PE resources in school A thus the s at Wave 2 has a positive relationship with this friends was not significant. This may indicate that direct observation of PE enrollment behavior of nominated stu dents did not serve as a major driving force that motivated students to keep 22 enrolling in PE courses in these two selected sample schools. However, the influence from friends on PE taking behavior may be effective in other forms, such as social supports vi a verbal encouragement. A study showed that social support from friends could predict intention for vigorous physical activity as well as partly buffer lack of self - efficacy (Hamilton, Warner and Schwarzer 2017) E classes themselves. However, as taking PE classes in the following year). PE enrollment from combined data Given the inconsistency of results in the two sampl e schools and their difference in student compositions in terms of grade and race, we combined data for the two schools. We then tested the interaction between schools and exposures (to nominated friends and to other students of the same gender and grade). Table 4 shows the results of the influence model with interaction terms using data from both schools. The exposure effect from nominated friends was not significant, and their coefficients ssociated with PE enrollment at Wave 2, indicating the PE enrollment status varied in different school conte xt s. The exposure to similar others was significantly and negatively associated with PE enrollment status in Wave 2. Such association was affected b y school contexts which was indicated by a significant exposure to similar others was significant for School A but not for School B. Based on this extended model wit h interaction terms, we can conclude that the influence from nominated enrollment status varied in different school contests. 23 Table 4 : Soc ial influence model with interactions results Combining School A and School B Independent variable Coefficient Standard error P value intercept - 55.947 8.791 <0.001*** prior 1.906 0.239 <0.001*** mean exposure to friends - 0.038 0.187 0.838 exposure to similar others - 2.559 0.500 <0.001*** birth year 0.692 0.112 <0.001*** school - 2.543 0.263 0.003** mean exposure to friends * school 0.559 0.362 0.122 exposure to similar others * school 2.781 0.614 <0.001*** Significance codes: P< Exposure terms were centered on their means before being entered in the above model. Two observations with null exposure to similar others in School B were removed from analysis. Conclusions from results Given the classes, it is important to seek effective strategies to engage more students in exercise in higher grades. The social influence effect from nominated friends was not stron g based on our data but there might be other aspects where social influence might work. For example, friends could exert influence through encouragement instead of the actual behavior of taking PE courses. Furthermore, friends outside school were not inclu ded in the analysis but their behaviors and 24 attitudes could also have impacts. We also did not include family influences, such as education and the physical activity level of parents and siblings. Students who were not enrolled in PE might still be physica lly active via other paths. However, to keep simplicity and to focus on our hypothesis, and also due to the limited information provided in the dataset, we did not investigate other social influences. Our study was also limited by the age of the data, as t he way high school students interact has greatly changed compared to the 19 90s. For instance, studies have shown that online social networks, such as Facebook TM groups, could provide social support and serve as promising intervention tools to promote phys ical activity (Cavallo et al. 2012, Todorovic et al. 2019) . As shown in this study, exposure to other observation of posts from social networking systems could also lead to attitude and behavior change. For example, there was a n association between wanting to look like model figures in the media and an increased level of physical activity among adolescents (Taveras et al. 2004) . Given the potential impact of online social networks on adolescents nowadays, collecting comprehensiv e longitudinal social network data of adolescents in the near future would be of great value to further investigate the influence of peers and understand how this influence has changed over the years. Conclusion This study used Add Health longitudinal data year PE enrollment had a significant influence on his/her enrollment in the following year. Higher grade was a ssociated with a low enrollment rate, and such a relationship was significant 25 choice. However, the overall enrollment status of students of the same gender and grade might Our findings contribute to a better understanding of the driving forces of PE enrollment in high schools with a focus on social influence in school contexts. Unlike some other behaviors, ment did not seem to be greatly influenced by friends. On the other hand, the requirement of PE credits and previous experience might be the key driving forces in future enrollment. Requiring PE credits at high grades and engaging students in PE classes at lower 26 REFERENCES 27 REFERENCES Ahima, R. S., & Lazar, M. A. (2013). The Health Risk of Obesity - Better Metrics Imperative. SCIENCE, 341(6148), 856 - 858, doi:10.1126/science.1241244. 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Rockville, MD: U.S. Department of Health and Human Services, Public Health Service, Office of the Surgeon General. 30 CHAPTER 2: HIGH ACTIVITY AND RESIDENTIAL LOCATIONS Abstract Evidence shows that adolescents do not do enough physical activity (PA). We used a stochastic actor - based model to analyze Add Health data to investigate the influence of the home location and neighborhood together, increased the likelihood of forming friendships. This study informs policy makers o f of PA. Keywords : Adolescents, Stochastic actor - based model, physical activity, social network, built environment 31 Introduction Obesity, physical activity, environment, and social network Obesity has been one of the leading public health problems in the U.S. in the past few decades (Flegal et al. 2016). Obesity among adolescents is also a serious health issue. Between 2015 and 2016, nearly one - fifth of all U.S. adolescents were obese (prevalence rate = 18.5% ) (Hales et al. 2017). As obesity and overweight are due to an imbalance of caloric intake and expenditure, the lack of exercise is a major direct cause of unhealthy weight. While exercising provides ma ny physical and mental health benefits (Janssen and LeBlanc 2010a, Eime et al. 2013b) , U.S. adolescents do not do enough physical activity (PA) regularly (Kann et al. 2018b, Troiano et al. 2008) . A national sample of 24800 U.S. high school students between 2013 and 2015 showed that about 66% of boys and 75% of girls did not get daily PA. On the contrary, approximately one - fifth of students spent over 5 hours on screen devices (e.g. computers, smartphones etc.) per day (Kenney and Gortmaker 2017), an activi ty counter - productive to exercise. Among many factors that are associated with obesity and PA, built environment is an public health outcomes, in particular obes ity, and the low - density, automobile - dependent urban form in the U.S., and an increasing number of studies started to investigate the influence of built environment on PA (Ledoux et al. 2016). Studies revealed that a pedestrian and bicycle - friendly built e nvironment, which is characterized by high population and housing density, mixed land Availability and accessibility to PA facilities (Powell et al. 2006, Mason, Pearce and Cummins 2018) , as well as neighborhood safety (Harrison, Gemmell and Heller 2007, Molnar et al. 2004b) , also exert a positive influence on PA. Meanwhile, travel behavior, accessibility, safety, 32 and PA are also shaped by socio - demographic variables includin g class, ethnic, and racial composition (Vojnovic et al. 2019). In the last decades or so, an increasing number of studies started to investigate the relationship between obesity and social networks. In the longitudinal Framingham Heart Study, Christakis a nd Fowler (2007b) conducted a social network analysis, and their findings suggested networks was also found to be associated with other health - related factors, suc h as smoking (Christakis and Fowler 2008), happiness (Fowler and Christakis 2008), and loneliness (Cacioppo, Fowler and Christakis 2009) attention and aroused public debates (Zhang et al. 2018). Cont roversial arguments suggested that the clustering of obesity observed in a social network could result from the shared environment (Cohen - Cole and Fletcher 2008, Lyons 2011) , or the friendship selection process, i.e., the homophily effect where people tend to associate with those who share similar characteristics (Lyons 2011). These debates inspired researchers to further investigate the complex relationship between social networks and health. In terms of social networks and obesity, studies were conducted to disentangle social influence from social selection as well as other confounding processes (Zhang et al. 2018). SAB models of obesity and PA: a brief review Among studies exploring the underlying causal relationship between obesity (and obesity - related b ehaviors) and social networks, a commonly used method is called a Stochastic - data to simulate the evolution of a network as a stochastic process driven by actors wh o decide on their outgoing ties (e.g., friendship). Network dynamics are affected by its structure and 33 exogenous factors, i.e., the characteristics of actors or dyads (ties). SAB models have the advantage to simultaneously analyze the coevolution of the ne twork and the behavior(s) of its actors. This dynamic system is the outcome of a Markov process, where a number of unobserved small changes are assumed to occur between each of the successive observed states of a network and behavior. A SAB model has two d dynamic model. More details about the SAB model can be found in Snijders (2001) and Snijders et al. (2010). Most studies on social networks and obesity using SAB models are about children and adolescents. To demonstrate how the SAB model was applied in studies about the relationship between social network and obesity, we reviewed research articles included in tw o recently published systematic review papers (Zhang et al. 2018, Prochnow et al. 2020) . De La Haye et al. (2011a) used longitudinal data of four waves from a high school in Australia. They found that similarities in the weights of friends were mainly driv en by friend selection (both homophily and weight - between social network and body weigh in a virtual space through analyzing social network data collected from a social n etworking site for weight management. The results indicated that 2016) . Two studies (Shoham et al. 2012, Simpkins et al. 2013) both using the National Longitudinal Study of Adolescent Health (Add Health) data and the SAB models, found evidence of the homophily effect based on PA and social influence from peers. The effect was in the form of assimilation, i.e., over time, individu 34 among friends were also found in an Australian study (De La Haye et al. 2011b). Different from the above studies, Gesell, Tesdahl, and Ruchman (2012) found that PA had no impact on forming or dissolving friendships in an after - school friendship network. They found that students would adjust their PA level to emulate the activity levels of their peers. Although the sa me sample of schools from Add Health data were used, the study by Long, Barrett, and Lockhart PA on friend selection. Purpose of study The review of existing studies points to a gap in the literature. Previous longitudinal studies using SAB models on PA among adolescents yielded mixed results, even those that used the same datasets. More importantly, existing studies using social network analysis did not empha environmental influence was not considered and tested. Since little research has been conducted to investigate the combined influence of the environment and social net work on adolescent PA using longitudinal data, this study aims to integrate the environmental drivers within the social network models to investigate their joint impact. Specifically, we aimed to test the following hypotheses: (1) home location has a signi friendships, and (2) neighborhood environment has a significant influence on high school We used the SAB model to extend the existing studies by including the environmental variables and the home distance to schools. The SAB model was implemented using the 35 Simulation Investigation for Empirical Network Analysis package in R (R - SIENA version 4) (Ripley and Snijders 2009). Method Study population This study used the Add Health Data a nationwide school - based longitudinal dataset with the first wave data collected in the 1994 - 95 school year (Wave 1) and the second wave in the 95 - 96 school year (Wave 2). More details about Add Health sampling methodology and study d esign can be found elsewhere (Harris et al. 2009). Among all Add Health sample schools, students from 16 selected schools were interviewed and they were asked to nominate up to five male and five female friends they considered to be close , i.e., a maximum of 10 friends in total. In this research, Wave 1 and Wave 2 data of students from two largest schools were used for analysis. These two selected schools are good for comparative analysis because one is in a mid - sized town dominated by non - Hispanic white s tudents while the other one is in an urban setting with more diverse population (Shoham et al. 2012). The Institutional Review Board of Michigan State University approved the use of Add Health data for this study (IRB# x16 - 380e). There were 2553 samples in total from Wave 1 in - home survey (school A: N = 832; school B: N = 1721). We excluded students in grade 12 because they would not be at school in Wave 2 due to graduation; thus, 756 students were removed (192 from school A and 564 from school B). After me rging with Wave 2 data, 222 students were removed (78 from school A and 144 from school B) due to no observations at the second wave. Lastly, we examined the friendship data and excluded students who did not nominated any other student as their friends or were nominated by others in both waves. This is because this study simultaneously focused both 36 on the dynamics of the social network and the influence of peers. In the final sample set used in this study, there were 557 students from school A and 948 stude nts from school B. Measurements a) Friendship network During the in - home interviews in both waves, students were asked to nominate up to five male and five female closest friends. Among all the nominees, we excluded those who were not students in the two sel ected sample schools. As mentioned earlier, students who did not nominate any friends in their school and were not nominated by any other participants were dropped from this study. b) PA - blading, roller skating, skate - rt, such as baseball, softball, such PA at all, 1 indicates 1 or 2 times, 2 indicates 3 or 4 times, and 3 indicates 5 or more times in a week. We calculated the sum of all three variables as the Total PA, of which value ranged from 0 c) Spatial data The coordinates of home addresses were collected during Add Health survey and GPS reads were converted to relative coordinates based on the central point of a community to ensure anonymity among the students. Samples of the same school are in the same comm unity in this research. We calculated the Euclidian distance between home locations of each pair of students 37 from School A and School B respectively to control for propinquity among students affected by where they lived. The Obesity and Neighborhood Envir onment (ONE) database linked Add Health - level data spatially and temporally, behavior. Among all the available me asures, we extracted five variables that we hypothesized to (1) distance from home to school; (2) counts of all types of PA resources within 3, 5 and 8 km road network radius; (3) road connectivity index within 3, 5, and 8km of Wav e I respondent locations, i.e. the Gamma index, which is the ratio of actual links over the maximum number of all possible links between nodes in the road network; 8k m radiuses, with a higher value indicating greater land cover diversity; (5) the population of year 1990 within 3, 5, and 8km buffers around each residential location. Distance to school could affect available time for extracurricular sports. Amount of PA facilities might influence the availability and accessibility to PA resources. Road connectivity, land - use diversity, and population density were related to neighborhood walkability (Handy et al. 2002) eighborhood environment variables included in this study were mapped and can be found in Appendix A . d) Other related measurements (1) Sex. 38 (2) Race and ethnicity. Race information was stored in five different binary variables (White, Black or African American, American Indian or Native American, Asian or Pacific Islander, and Other). We integrated all five variables and recoded values (1 = White, 2 = Black or Africa n American, 3 = American Indian or Native American, 4 = Asian or Pacific Islander, 5 = Other, 6 = missing value). Ethnicity was a binary variable with value 1 indicating Hispanic or Latino origin and 0 as not. (3) Body Mass Index (BMI) . Students reported the ir height and weight in both waves. The BMI value was calculated using the weight (kg) and height (m) reported in the survey (BMI = weight/height 2 ). BMI at Wave 1 was used as a constant covariate in our models. (4) Motivation. During the in - home survey, partic ipants were asked whether, in the past seven days, they exercised to 1) lose weight/keep from gaining weight, or 2) gain variables was set to 1 if the answer to the corresponding motive was true and to 0 otherwise. (5) Course overlapping. Add Health data provide information about the extent of courses common to each pair of students. A weighted cours e - overlap measure was used in this study to control for the influence of taking the same course on friend selection. Weights were determined based on the number of Carnegie units taken by students and the number of classes per course. Analytic plan In this study, we adopted the SAB models to understand the relationship among high school 39 evolution of a network is treated as a stochastic process driven by actors (i.e. students) who decide on their outgoing ties (i.e. friend nominations). SAB model assumes many unobserved micro - steps between two consecutive observations (in our case, a certain number of micro - steps between Wave 1 and Wave 2). A rate parameter dete rmines the number of micro - steps. In each micro - step, one change occurred in the network (forming a new tie, dropping an existing tie, or no change to current network). Which tie and how it will change is captured by a linear additive objective function, c onsisting of many effects, whose value can be translated into an expected probability. To test our first hypothesis about the influence of home location on friend selection, we included Euclidean distance between home locations of each pair of students fro m the same school as a covariate in the SAB selection. A significant coefficient would reject our null hypothesis that residence distance between two adolescents has no impact on forming or maintaining friendship between them. Other effects in the selectio n model include (1) structured effects that represent the endogenous network processes; (2) homophily effects that captures the assimilation process during friend selection; and (3) behavior effects, which helped to investigate the influence of PA on the d ynamics of a social network. Descriptions of effects included in the model is shown in Table 5 . Coevolution of behavior is also integrated into the SAB model, which enabled us to , the SAB behavior model also has a rate parameter and a linear additive objective function describing how different change per micro - step). To test our second hy pothesis about the influence of the built environment on PA, we included five environmental effects (see Table 5 ) at three different geographic scales (3km, 5km, and 8km) with each scale as a separate SAB behavior model. 40 To test our hypotheses, we built S AB models using the RSiena package in R. We used a forward selection process (Snijders et al. 2010) and only kept the significant effects in the selection model before we modeled the coevolution of selection and behavioral change. Since there were two scho ols and three geographic scales of environmental effects, a total of six models were tested. Detailed model specifications for both SAB selection and behavior model can be found in Appendix B . 41 Table 5 : Description of effects in SAB friend selection and SAB behavior submodels Effects on friendship dynamics Description structural effects out - degree effect the tendency to send out a tie a random alter reciprocity effect The inclination of a nominee to form a friendship tie back to the nominator transitive triplets effect the tendency of network closure ("becoming a friend with friend's friend") in - degree relate popularity effect the tendency of an individual to attract more incoming ties homophily effects same sex preference to nominate friends of the same sex same grade preference to nominate friends of the same grade same race preference to nominate friends of same the race same ethnicity preference to nominate friends of the same ethnicity BMI similarity preference to nominate friends based on similar BMI C ourse overlapping preference to nominate friends taking the same courses behavior effects PA ego effect of actor's PA on friendship nominations PA alter effect of alter's PA on friendship nominations PA similarity preference to nominate friends based on similar PA level spatial effect distance to friends effect of home distance on friend nominations Effects on PA dynamics Description Shape effects linear shape, quadratic shape two effects of PA upon itself Friend effect PA similarity effect of friends' PA on actor's PA based on similarity Motivation effects lose weight effect of actor's intention to lose weight via exercising gain muscle effect of actor's intention to gain muscle via exercising Environment effects distance to school effect of actor's home distance to school PA resources (3km, 5km, 8km) effect of counts of PA resources within 3km/5km/8km neighborhood road connectivity (3km, 5km, 8km) effect of road connectivity within 3km/5km/8km neighborhood land use mix (3km, 5km, 8km) effect of land use mix within 3km/5km/8km neighborhood population density (3km, 5km, 8km) effect of population den sity within 3km/5km/8km neighborhood SAB stochastic actor - based; BMI body mass index; PA physical activity 42 Results Descriptive statistics Table 6 shows the descriptive statistics of the characteristics of students from two schools. There was about an equal number of male and female students in both schools. School A was dominated by white students, while School B was more diverse in terms of race a nd ethnicity. In both sample schools, we observed a slight increase in average BMI and a small decrease in average total PA from Wave 1 to Wave 2. Specifically, among 557 students in School A, 254 students (45.6%) had a decrease in PA, 186 students (33.4%) had an increase in PA, and 117 students (21.0%) had no change in their reported total PA from Wave 1 to Wave 2. Among 948 students in School B, 458 students (48.3%) had a decrease in PA, 294 students (31.0%) had an increase in PA and 196 students (20.7%) reported no change in total PA. In both schools, more than half of the students indicated motivation to increase PA at Wave 1. Also, on average, students from School A had lower BMI and more PA than School B. In terms of environmental variables, there we re no dramatic differences among index type variables (road connectivity and land cover diversity) at different scales while count - type variables (total PA resources and population) increased along with the scale. 43 Table 6 : Descrip tive statistics of two sample schools (percent in parentheses) School A School B (N = 557) (N = 948) gender (%) male 297 (53.3) 478 (50.4) ethnicity (%) Hispanic 5 (0.9) 385 (40.6) race (%) White 525 (94.3) 178 (18.8) Black 0 (0) 200 (21.1) American Indian 23 (4.1) 34 (3.6) Asian 6 (1) 312 (32.9) other 3 (0.5) 224 (23.6) motivation (%) lose/maintain weight 473 (56.2) 259 ( 27.3 ) gain muscle 54 (9.7) 93 (9.8) distance to school in meter (sd) 4614.42 (3634.31) 2648.19 (3814.25) PA resources count (sd) 3km 2.09 (1.66) 10.99 (3.85) 5km 3.26 (1.85) 18.40 (4.62) 8km 4.33 (1.86) 33.40 (5.36) road connectivity index (sd) 3km 0.49 (0.04) 0.46 (0.02) 5km 0.47 (0.02) 0.47 (0.01) 8km 0.46 (0.01) 0.49 (0.01) land cover diversity index (sd) 3km 0.65 (0.08) 0.65 (0.02) 5km 0.64 (0.07) 0.65 (0.01) 8km 0.64 (0.05) 0.65 (0.01) population (sd) 3km 5819.73 (3131.82) 67489.37 (18620.52) 5km 11423 (5665.17) 180667.80 (26695.65) 8km 21637.69 (10429.76) 481745.00 (72757.53) Wave 1 Wave 2 Wave 1 Wave 2 BMI* (sd) 22.86 (4.34) 23.23 (4.52) 23.51 (4.67) 23.86 (4.88) PA (sd) 3.87 (2.09) 3.49 (2.04) 3.69 (2.02) 3.26 (1.93) BMI body mass index; PA physical activity *Due to missing BMI values, N differed between Wave 1 and 2; N = 556 in Wave 1 and N = 552 in Wave 2 for School A; N = 931 in Wave 1 and N = 935 in Wave 2 for School B. Both schools had very sparse social net works. In School A (Table 7 ), the network density was, on average, 0.0065 (including both Waves). In School B, the network density was 0.002 in both Waves. The overall average degree was 3.513 for School A, and 1.76 for School B. Both 44 schools had a slightl y higher average degree in Wave 1 (School A: 3.711; School B: 1.92) than Wave 2 (School A: 3.316; School B: 1.608). Because Wave 1 had more nominations (School A: 2067; School B:1820) than Wave 2 (School A: 1847; School B: 1524), there were more dropping t ies (School A: 1275; School B: 1209) than forming ties (School A: 1055; School B: 913). The Jaccard similarity indices of both schools were not high (School A: 0.254; School B: 0.224), which is associated with network sparsity. Table 7 : Descriptive statistics of friend networks SAB friend selection model Table 8 shows the results of the SAB friend selection model. The overall convergence ratios of both schools were under 0.25. All the convergence t - ratios were under 0.1. Together they indicate an adequate convergence of the model for two sample schools. First, t he spatial effect we examined in the friend selection model - the distance between - had a significantly negative coefficient in both schools. This important finding suggests that an alter living far apart from the ego w as slightly less likely to be selected as a friend (estimate = - 0.0712, esp( - 0.0712) = 0.93). Consequently, we reject our School A School B Wave 1 2 1 2 Density 0.007 0.006 0.002 0.002 Average degree 3.711 3.316 1.92 1.608 Number of ties 2067 1847 1820 1524 Tie change from Wave 1 to Wave 2 Create a new tie (0 - >1) 1055 913 Drop an existing tie (1 - > 0) 1275 1209 No change 0 - > 0 306570 0 - > 0 895023 1 - > 1 792 1 - > 1 611 Jaccard similarity 0.254 0.224 45 first null hypothesis and conclude that home location had a significant impact on the dynamics of the friendship network. In terms of other effects, all included structural effects exerted significant influence (p < 0.05) on the network dynamics and the results of two schools were consistent with each other. According to the estimates, outdegree had a significant negative coefficient, su ggesting that the actors in the network were not inclined to make friends with random alters. The significant positive coefficients of reciprocity indicated that students liked to maintain existing friendship ties or nominated those who nominated them as f riends. Estimates for transitive triplets and popularity were also significant and positive. The former suggests that the individual was received a lot of nomina tions would attract more incoming ties. In terms of the homophily effects, for School B, all variables included in the selection model exerted significant (p<0.05) influence on forming or maintaining ties. However, race, ethnicity, and BMI homophily effect s were not significant for School A. Students who had more course overlapping were more likely to be friends. If two students were of the same gender, they would be 19% (School A) and 61% (School B) more likely to be friends than students of different gend er (School A: estimate = 0.1747, exp (0.1747) = 1.19; School B: estimate = 0.48, exp (0.48) = 1.61). For School A, students from the same grade were 1.74 times more likely to form or maintain a friendship tie (estimate = 0.5547, exp (0.5547) = 1.74). For S chool B, the chance of being friends was 1.63 times,1.51 times, and 2.14 times higher, if students were in the same grade (estimate = 0.4887, exp (0.4887) = 1.63), of the same race (estimate = 0.4093, exp (0.4093) = 1.51), and of the same ethnicity (estim ate = 0.7610, exp (0.7610) = 2.14), respectively. Students from School B who had similar BMI value were more likely to become 46 friends or keep their existing friendship. However, such associations were not significant in The behavior effects included in the selection model were used for testing if different effect was not significant, indicating that a physically active student and a physically inactive student had no difference in terms of being nominated as a friend by others, with all other characteristics unchanged. Also, the insignificant coefficient of PA similarity suggested that similar PA level had no impact on attracting mo re incoming ties. The estimate of PA ego was active students in that school were less likely to form or maintain friendship ties with others. Following our anal ysis plan, only significant covariates in the selection model were kept in developing the network - behavior coevolution model. Given the inconsistency in the results of two sample schools, the coevolution model of School A had fewer covariates than School B . 47 Table 8 : SAB selection model *Absolute value of the estimated coefficient was greater than 1.96 standard error (SE), suggesting p < 0.05. School A convergence t ratios all < 0.05; Overall maximum convergence ratio 0.1044. School B convergence t ratios all < 0.09; Overall maximum convergence ratio 0.1668. SAB coevolution model In the SAB network - behavior coevolution model, PA was treated as another dependent variable significance test results were consis tent with the selection model that the coevolution model is built from, we only focused on the results of the behavior model in this section. For School A (Table 9 ), the PA total similarity effects were positive and significant (p<0.05) in all models of different spatial scales (3km, 5km, 8km), indicating an assimilation School A School B Parameter Estimates SE Estimates SE Rate 13.0037 0.6008* 7.011 0.0006* Structural effects Outdegree - 3.4596 0.1589* - 6.0472 0.1151* Reciprocity 2.2063 0.0693* 2.3885 0.0895* Transitive triplets 0.4565 0.0258* 0.5047 0.0377* Popularity (alter sqrt) 0.1262 0.0377* 0.4794 0.0355* Homophily Effects Course overlap 0.0415 0.0096* 0.2398 0.0568* Same sex 0.1747 0.0378* 0.48 0.0544* Same grade 0.5547 0.0377* 0.4887 0.0539* Same race - 0.1062 0.0608 0.4093 0.0528* Same ethnicity - 0.202 0.1349 0.761 0.0704* BMI similarity 0.1484 0.1427 0.5445 0.2000* Behavior effects PA ego 0.0041 0.0099 - 0.0452 0.0165* PA alter 0.0123 0.0093 - 0.0042 0.0165 PA similarity 0.0615 0.1035 0.069 0.1237 Spatial effect Distance to friends - 0.0113 0.0039* - 0.0712 0.0111* 48 process where adolescents tended to adopt a similar level of PA of their friends. In our model w e used and reported the total similarity effect which means the total influence of nominated friends was proportional to the number of nominations. We also tested the average similarity effect at different spatial scales while holding all other effects the same, and results showed that the average similarity effect of PA remined significant. For school B (Table 10 ), the PA total similarity effect showed a consistent result as in School A, i.e. the effect was significant at all three geographic scales (p < 0 .05). All estimates were positive thus we concluded that like in In terms of other direct effects (motivation and environmental effects), we did not observe any signi ficant influence for both schools among different spatial scales. Thus, in this study, we were not able to reject our second null hypothesis (i.e., built environment exert no een Wave 1 and Wave 2). 49 Table 9 : SAB coevolution model - School A School A 3km neighborhood 5km neighborhood 8km neighborhood Parameter Estimates SE Estimates SE Estimates SE Network Dynamics Rate 13.0146 0.5564* 13.0086 0.4500* 13.0169 0.5832* Structural effects Outdegree - 3.7746 0.0838* - 3.7740 0.0865* - 3.7745 0.0873* Reciprocity 2.2025 0.0658* 2.2000 0.0683* 2.2022 0.0768* Transitive triplets 0.4573 0.0256* 0.4567 0.0287* 0.4574 0.0267* Popularity (alter sqrt) 0.1385 0.0331* 0.1389 0.0360* 0.1378 0.0339* Homophily Effects Course overlap 0.0405 0.0112* 0.0408 0.0094* 0.0409 0.0095* Same sex 0.1764 0.0380* 0.1753 0.0375* 0.1772 0.0408* Same grade 0.5564 0.0390* 0.5574 0.0423* 0.5576 0.0415* Same race - - - - - - Same ethnicity - - - - - - BMI similarity - - - - - - Behavior effects - - - - - - PA ego - - - - - - Spatial effect - - - - - - Distance to friends - 0.0117 0.0043* - 0.0118 0.0044* - 0.0120 0.0042* Behavior Dynamics Rate 9.6362 1.0774* 9.6221 0.8355* 9.6869 1.5003* Shape effects Linear shape - 0.0943 0.0209* - 0.0944 0.0194* - 0.0936 0.0269* Quadratic shape - 0.0129 0.0098 - 0.0138 0.0112 0.0141 0.0112 Friend effect PA total similarity 0.6436 0.1764* 0.6342 0.2022* 0.6325 0.2355* Motivation effects Exercise to lose weight 0.0268 0.0496 0.0266 0.0485 0.0272 0.0526 Exercise to gain muscle - 1.1171 0.0889 - 0.1123 0.0811 - 0.1079 0.1099 50 Table 9 Environmental effects Distance to school 0.0008 0.0079 - 0.0069 0.0094 - 0.0122 0.0108 Amount of PA resources - 0.0058 0.0133 - 0.0177 0.0150 - 0.0028 0.0165 Road connectivity - 0.4755 0.5386 - 0.9994 1.1947 - 2.9467 3.8037 Land use diversity - 0.5108 0.3808 - 0.4676 0.4033 - 0.4108 0.5583 Population density 0.0078 0.0124 0.0116 0.0084 0.0064 0.0041 *Absolute value of the estimated coefficient was greater than 1.96 standard error (SE), suggesting p < 0.05. Convergence t ratios all < 0.1; Overall maximum convergence ratio all <0.25. 51 Table 10 : SAB coevolution model - School B School B 3km neighborhood 5km neighborhood 8km neighborhood Parameter Estimates SE Estimates SE Estimates SE Network Dynamics Rate 7.0505 0.3360* 7.0215 0.3294* 7.0301 0.4004* Structural effects Outdegree - 6.0327 0.1126* - 6.0340 0.1185* - 6.0366 0.1383* Reciprocity 2.3922 0.1015* 2.3864 0.0883* 2.3861 0.0891* Transitive triplets 0.5056 0.0365* 0.5052 0.0405* 0.5045 0.0438* Popularity (alter sqrt) 0.4781 0.0368* 0.4779 0.0348* 0.4795 0.0363* Homophily Effects Course overlap 0.2410 0.0516* 0.2388 0.0519* 0.2434 0.0553* Same sex 0.4783 0.0516* 0.4795 0.0495* 0.4817 0.0560* Same grade 0.4830 0.0544* 0.4849 0.0536* 0.4829 0.0513* Same race 0.4093 0.0474* 0.4106 0.0554* 0.4100 0.0505* Same ethnicity 0.7564 0.0651* 0.7564 0.0897* 0.7579 0.0896* BMI similarity 0.5324 0.2190* 0.5394 0.2047* 0.5354 0.2131* Behavior effects PA ego - 0.0465 0.0145* - 0.0462 0.0155* - 0.0463 0.0141* Spatial effect Distance to friends - 0.0708 0.0120* - 0.0707 0.0128* - 0.0701 0.0135* Behavior Dynamics Rate 10.7074 0.9316* 10.6890 0.7664* 10.6794 0.8970* Shape effects Linear shape - 0.0983 0.0175* - 0.0985 0.0151* - 0.0983 0.0168* Quadratic shape - 0.0424 0.0066* - 0.0424 0.0070* - 0.0421 0.0070* Friend effect PA total similarity 0.4653 0.2170* 0.4632 0.2269* 0.4695 0.1998* Motivation effects Exercise to lose weight 0.0084 0.0090 0.0092 0.0097 0.0084 0.0105 Exercise to increase muscle 0.0008 0.0091 0.0016 0.0100 0.0011 0.0111 52 Table 10 Environmental effects Distance to school - 0.0052 0.0049 - 0.0076 0.0044 - 0.0065 0.0043 Amount of PA resources 0.0077 0.0053 0.0044 0.0044 0.0010 0.0032 Road connectivity - 0.8073 0.7468 - 1.0438 1.4494 - 1.1876 2.0609 Land use diversity - 0.5558 1.3342 - 2.7064 2.2493 - 1.1432 1.6769 Population density - 0.0011 0.0016 - 0.0011 0.0013 - 0.0001 0.0005 *Absolute value of the estimated coefficient was greater than 1.96 standard error (SE), suggesting p < 0.05. Convergence t ratios all < 0.1; Overall maximum convergence ratio all <0.25. 53 Discussion This study extended prior research conducted by other scholars and contributed to the physical inactivity and childhood obesity literatures by using the combined social, spatial, and environmental variables to test their influences on the dynami cs of friend selection and adolescent PA. Our results show that, in the friend selection model, home distance between high school students was significantly and negatively associated with tie creation and maintenance, which means that students who live clo ser together are more likely to be friends. This can indicate that students interact outside of school contexts, such as spending time together after school or during summer and winter breaks , and perhaps even walking to and from school together . We also f an assimilation process. Together, these two findings imply that intervention outside school, such as PA involved activities in the community centers or self - organized outdoor sports arranged by par ents , might be able to facilitate promoting PA of adolescents by direct participation or indirect influence via a change in the behavior of friends. existing studies which showed the built environment had trivial to small impacts on P A among youth (McGrath, Hopkins and Hinckson 2015) . However, other reasons could contribute to an insignificant association between the built environment and PA dynamics in this study. One might be that the Wave 1 and Wave 2 were only one year apart, but t he shaping effects of the environment on behavior may take a longer time. Another possible reason is that for students participating in Add Health survey, the neighborhood outdoor environment was not their primary location for PA. Without further detailed information, we were not able to figure out if the PA reported in the survey took place near home or mostly in school. Unlike adults who may largely rely on public amenities such as parks to do certain 54 sports, adolescents spend a great amount of time in sc hool and have easy access to facilities available for students provided by the school. It is also possible that the features of decision making about PA in their neig hborhood. In future studies, it may be useful to examine other variables such as safety. Some of our results are consistent with the findings of Simpkins et al. (2012) and Shoham et al. (2012) who used the same dataset. These include homophily effects of g rade and gender, and the effects, of course, overlapping in friend selection. However, we also ended up with some inconsistencies. For instance, in our study, the PA ego effects and BMI similarity effects in SAB selection model were only significant in Sch ool B, whereas they were both significant in the work of Simpkins et al (2012). We hypothesize that these disparities can be attributed to differences in data filtering and the selection of explanatory variables due to different research questions. In the model of Simpkins et al (2012), BMI was classified whereas we used raw (numerical) BMI values, which may also cause differences in the level of significance. This study has some limitations. First, in our analysis, we used secondary data collected in 1994 /1995. We realize that, after 30 years, the way that high school students interact with peers may have changed, or not. Compared to millennials, the lifestyle of centennials (people born between the late 1990s and 2010) is greatly influenced by online inte raction, which may have a varying effect on PA. Online social network is playing an obstructive for the interaction and communication between children living farther apar t. According to the United States Census Bureau (2010), in 1993, only 22.9% of households in the U.S. owned computers, whereas now, computers are ubiquitous. In 1997, 18% of households had access to the internet. After ten years, in 2007, that percentage i ncreased to 55 61.7%. Based on a survey from 2015, around three - quarters of teenagers had cellphones (Lenhart 2015). The popularization of computers, cellphones and internet not only greatly influence the social network of adolescents, but also contribute to their screen time, which might otherwise be devoted to PA. Friendships and their influence on students may also be moderated by screens and how influential a friend is compared to one - on - one contact relationships. Given these changes in the society and cul ture, samples used in this study might not well represent the behavior pattern and attitudes of adolescents in current times. More recent large - scaled longitudinal data with complete social network will be of great value for future studies. Another limitat ion is that the data was self - reported rather than measured. For example, the key variable that we used in our analyses, total PA, only reflected the reported frequency of PA in seven days preceding the survey. However, the duration and intensity of the ac tivity were unknown. This could lead to inconsistency and uncertainty when trying to investigate the changes in PA and the difference of PA between a pair of students. these associations. There is a lack of information about whether or not the rep orted PA was It is possible that a student was frequently invited by friends to participate in PA together after school, which boosted her PA to be similar to he r physically active friends. Or, on the contrary, she could be invited to watch TV or play video games together which borrowed her leisure time for PA and made her less physically active. A student could also be influenced by friends by simple observation or verbal communication. A student may not participate in PA with her friends together, but she might see her physically active friends as role models 56 and mimic their behavior when she is in a more private setting. It is also possible that she devoted more time to certain activities, such as doing sports or watching TV, in order to have a conversation with friends as a way of maintaining the friendship or becoming more popular among peers. Regardless of these limitations, we believe that this study lays a strong foundation to further our understanding of the joint impact of social network and neighborhood Summary e built SAB models to investigate the relationship among friend network, home location, neighborhood those who lived closer, but we failed to detect a significant inf luence of the built environment research via incorporating spatial and environmental variables in the analysis. Due to limitations of this study, the relationship between environment, PA and obesity is still not clear and further research with more recent data are required in the future. 57 APP ENDICES 58 APPENDIX A : Distribution of Environment Variables 59 APPENDIX A: Distribution of Environment Variables In this document, we presented the distribution maps of home locations , physical activity (PA), and neighbourhood environment characteristics of sample students from two sample schools included in our study. Figure 1 : Home location of sample students from School A 60 Figure 2 : Home locations of sample students from School B 61 Figure 3 : Distribution of total physical activity and change between Wave 1 and Wave 2 of sample students from School A 62 Figure 4 : Distribution of total physical activity and change between Wave 1 and Wave 2 of sample students from School B 63 Figure 5 : Distribution of neighborhood built environment of sample students from School A 64 Figure 6 : Distribution of neighborhood built environm ent of sample students from School B 65 APPENDIX B : Specification of the SAB Model 66 APPENDIX B : Specification of the SAB Model The Stochastic Actor - based (SAB) Model used in this study had two sub - models, a friend selection describing the dynamics of the friend network, and a behavioral evolution model predicting chang es ivity (PA). SAB friend selection model As shown below, the SAB selection model is a linear combination of many components, effect on the network, thus the selection model helped us investigate how acto characteristics influence the network dynamics. We classified these components into five categories based on different types of covariates included in the model. In the SAB selection model, the function measures the status of dyad in friendship adjacency matrix of student . represents covariates in the model and behavior (i.e. PA in this study). For the friendship adjacency matrix, if student nominated as a friend, then , else . = + + + + + + + + + + + + . ehavior Effects + ......... ... Spatial Effects Structural effects The structural effects represent the endogenous network processes, i.e. effects depending on the network only. The evolution of a social network is greatly influenced by the existing network ties thus these endogenous effects need to be controlled in the network evolution model. We included: 1) the out - degree effect (density effect); means that there is a tie from to . A strong positive coefficient ( ) indicates a greater tendency to send out a tie to a random alter. In our case, that is a tendency to create or maintain a friendship tie. 67 2) the reciprocity effect; this effect describes the inclination of a nominee to form a friendship tie back to the nominator . 3) the transitive triplets effect; this effect describe the tendency of network closure thr ough the number of transitive triplets in the network. Significant positive 4) in - degree related popularity (sqrt) effect; it express es th e tendency of a popular individual to attract more incoming ties (i.e. getting more nominations) than others. Homophily effects Studies have shown that people tend to make friends with those sharing similar characteristics, such as age and gender. To control for the homophily effects on friendship network dynamics, we included homophily effects for participant attributes and total PA. By default, covariates were centered in RSiena by subtracting the mean. 1) , , , and these four homophily effects are covariate - grade (g), race (r) and ethnicity (e), respectively. The effect is defined by the number of ties where actor and had the same value on a selected attribute. 2) this component in the function controls for the homophily effect of body image, which is represented by BMI value. It is defi ned by the sum of centered BMI similarity scores between actor . The similarity score is a function of the absolute difference between two values and is normalized between 0 and 1, where 1 indicates equal values. 3) this component was introduced to the model to control for the influence of course overlapping. We viewed it as an inbreeding homophily introduced by by sharing the environment and receiving education in the same classes. Behavior effects These effects were included in the model specifically to investigate the influence of PA on 68 1) the covariate - ego effect is defined by the outdegree of actor weighted by its PA value. A significant positive coefficient would then indicate that physically active student tends to select more friends. 2) this is a c ovariate - alter effect, also called the covariate - related popularity effect. It is defined by the sum of PA over all students that nominated as a friend. Based on its definition, a significant positive coefficient would suggest that the physically activ e students are more likely to be selected as a friend. 3) like the homophily effect of PA, this effect captures the likelihood of forming or maintaining friendship tie depending on similarity in total PA. Spatial effect To investigate the influence of physical distance between a pair of actors in the network, we included a spatial effect in the SAB selection model. A significant coefficient would reject our null hypothesis that residence distance between two adolescents has no impact on forming or maintaining friendship between them. SAB behavioral evolution model Our SAB behavioral evolution model consists of nine components that we classified into three types of effects neighborhood environment. This model was utilized for us to identify the driving forces of ado is defined as: = + . + . .. + + ... + + + + + Shape effects In our Siena behavioral evolution model, we included a linear shape effect ( ) and quadratic shape effects ( on the behavior in Wave 2, i.e. control for the prior. Variable is centered, which means it is the original total PA minus the overall mean of all observations. 69 Friend effect - the average similarity effect is defined by the average centered similarity scores between actor and alters that has ties with. A significant positive coefficient suggests that if friends are more physically active, the stude promoted. Together with the PA effects in the selection model, the friend effect in the a feather flock together" effect . Motivation effects and were included to control for self - motivation of losing or gaining weight through PA. Environment effects was included to control for self - motivation of losing or gaining weight through PA. To related components in the model, including distance to school ( , amount of PA resources in the neighborhood ( ), road connectivity ( ), land use mix ( ) and population density ( neighborhood environment measures were of different scales (3, 5, and 8 km s ) thus we created three versions of the model to test each spatial scale separately. 70 REFERENCES 71 REFERENCES Cacioppo, John T., James H. Fowler, and Nicholas A. Christakis. 2009. "Alone in the Crowd: The Structure and Spread of Loneliness in a Large Social Network." Journal of Personality and Social Psychology 97 (6):977 - 91. doi: 10.1037/a0016076. Christakis, Nicholas A., and James H. Fowl er. 2007. 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Obesity Reviews 19 (7):976 - 88. doi: 10.1111/obr.12684. 75 C HAPTER 3: EFFECTS OF POKÉMON GO AS AN INTERVENTION TO - A SPATIAL STOCHASTIC AGENT - BASED MODEL SIMULATION Abstract Studies have shown that the location - based augment ed reality mobile game Pokémon Go could be a promising tool to promote physical activity. In this research, w e built an agent - based model (ABM) based on a stochastic actor - based social network model (Siena) as a baseline model to simulate the dynamics of friendship and physical activity (PA) among students from a sample high school. We then introduced a game - based intervention that is similar to P okémon Go to convert the baseline model to a spatial ABM . Three scenarios were tested: enrolling different number of players, enrolling students with large body mass index (BMI), and enrolling student s based on home distance to community center. Result s of the computational experimentation indicate that 1) the intervention could lead to an increase in non - ; 2) enrolling more students would lead to greater impacts on non - players, which we called a spillover effect ; 3) targeting students with large BMI proved to be not effective in terms of promoting the average PA of the entire school, but it had the greatest ; and 4) t he spillover effect on non - players was the gre atest by enrolling far - from - community - center students, and the weakest by enrolling close - to - community - center students. Keywords : s patial agent - based model , game - based intervention , Pokémon Go , spillover effec t 76 Introducti on Prevalence of obesity and overweight among adolescents is a public health issue worldwide. In the U.S., research has shown that the prevalence of obesity among adolescents (between 12 and 19 years old) was 20.6% in 2015 2016 (Hales et al. 2017) . Promotin g physical activity (PA) is one of the most well - accepted and effective approaches to prevent and control obesity, and regular exercises also provide other health benefits such as lowering risks of depression, cardiovascular disease, type 2 diabetes, and s ome cancers (CDC 2020) . Various interventions have been designed and adopted to motivate and encourage adolescents to engage in PA, often combin ed with interventions on dietary intake and sedentary behaviors. Some common forms of PA interventions on child ren and adolescents include behavior change counseling, group session therapy, discussion with or without parents, lifestyle education, group physical activity, and games such as team sports and running games (Cliff et al. 2009) . Recently , video games have turned into a very common and popular activity among children and adolescents. Active video games, which engage players to participate through movement, have been increasingly explored as an approach to induce light to moderate PA among children and adole scents (Biddiss and Irwin 2010, Graf et al. 2009, Norris, Hamer and Stamatakis 2016) . More recent studies indicate that active video games are effective, as well as more acceptable and sustainable tools than many conventional approaches, to promote PA amon g adolescents (Williams and Ayres 2020, Gao et al. 2020, Merino - Campos and Del Castillo Fernández 2016) . W hen augmented reality came into being and was applied to games, more possibilities were offered to mobile game - based intervention for PA promotion. A n interesting case is the launch of an augmented reality game called Pokémon Go (PG) released in the summer of 2016. The game was not meant to be a health and fitness app . However, due to its location - based features requiring players to explore outdoor spa ces to play the game, it has proved to 77 be useful in p romoting both physical and mental health (Khamzina et al. 2020, Baranowski and Lyons 2019, Watanabe et al. 2017, Liu and Ligmann - Zielinska 2017) . When evaluating , most of the studies am ong young adults or adolescents indicated that the game led to an increase in PA (Baranowski and Lyons 2019) . Mobile games , like PG , provide new possibilities for PA promotion interventions . It also possible to induce spillover effects of the - PG players due to the ir social network dynamics. Studies have found evidence that individuals would adjust their weight - due to social influence (Eisenberg et al. 2005, Marks et al. 2015) . T hus, an increase in PA of PG players may also exert effects on non - players. Investigating the scale of the spillover effect of PA promotion intervention could help with a more comprehensive assessment and evalua tion of the intervention program. Moreover, the geographical scale and distribution of such a spillover effect are not always incorporated in PA promotion intervention studies. One approach to investigating the potential impacts of an intervention in term s of both magnitude and distribution is to build a computational simulation model, such as a spatial Agent - community of heterogeneous and interacting individuals distributed wit hin a shared (Ligmann - Zielinska 2010, 28) . ABM is a bottom - up modeling approach to simulate individual behavior and interaction s, while introduced ing changes (such as modification to the enviro nment, rules, policies, or interventions) at the system level. The decision - making rules and behaviors of these individuals, like game agents, and their environment (game space) can be defined by the model maker, which enable ABMs to be employed in both th eoretical and empirical (An 2012). 78 activity, tested interventions, and/or incorporated so cial network in the model (Yang 2019) . For example, several ABMs were developed with social network components to test network - based intervention on behavior change, e.g. intervening the most connected individuals within the social network . Interestingly, the ir simulations yielded controversial results , which showed that targeting the highly networked individuals in the intervention did not always outperform an at - random intervention (El - Sayed et al. 2013, Zhang et al. 2015b, Zhang et al. 2015a, Van Woudenberg et al. 2019, Shi, Zhang and Lu 2020) . In addition, m any ABMs of obesity focus on social influence yet lack health behavior components built into the model (Li et al. 2016) . ABMs have also been used to investigate the influence of environment on travel to school (Yang et al. 2011, Yang et al. 2012, Yang et al. 2014) . Their limitations are the lack of empirical ly grounded social network representations . Althou gh an increasing number of ABMs have been developed in the field of non - communicable disease control (Tracy, Cerdá and Keyes 2018) , few ABMs in public health have integrated both empirical data based social network, health behavior such as physical activit y, and geographic components in one integrated complex system model to explore health outcomes. Consequently, our goal for this study is twofold: (1) using a spatial ABM to simulate and investigate the impact and the spillo ver effect s of PG on promoting PA of high school students; (2) demonstrating the advantages of using ABM public health by providing an example of a model that integrates empirical social network data, spatial components, and interventions that bring about behavior change. 79 Methods Baseline Model and Empirical Data Analysis In this study, we used a national longitudinal survey data (Harris et al. 2009) called Add Health (National Longitudinal Study of Adolescent Health). Two waves of data for consecutive years (Wave 1: 1994 - 95 school year; Wave 2: 1995 96 school year) from a selected saturated school were analyzed in R. A saturated school is a sample school with a complete social network dataset where each participant was asked to nominate up to five male and five female friends. Descriptive analysis of students in the selected sample school is provided in Table 11 . M ore details about Add Health data can be found elsewhere (Harris et al. 2009) . We used Wave 1 data as the ABM input to allow the model to simulate one school year and then compare the simulation results with the Wave 2 data for baseline model validation. 80 Table 11 : Descriptive statistics of students from the sample school Sample School (i.e., School B in Chapter 1 & 2) (N = 948) gender (%) male 478 (50.4) ethnicity (%) Hispanic 385 (40.6) race (%) White 178 (18.8) Black 200 (21.1) American Indian 34 (3.6) Asian 312 (32.9) other 224 (23.6) distance to school in meter ( SD ) 2648.19 (3814.25) Average BMI ( SD ) Wave 1 Wave 2 23.51 (4.67) 23.86 (4.88) Average total PA ( SD ) 3.69 (2.02) 3.26 (1.93) BMI body mass index; SD standard deviation. Our baseline model was created based on the design of the ABM of an existing study (Zhang et al. 2015a) , which was derived from a SIENA social network model. SIENA social network model is a stochastic actor ( aka agent ) based model that simulates the dynamics of change (in our case, change in total PA). W e built and calibrated our own SIENA social netwo rk model in R using the R - SIENA package and the first two waves of Add Health data of the selected sa mple school to identify key factors that influence networks and behaviors. Only effects with statistically significant (p<0.05) coefficients were included in the final model which include factors affecting network dynamics like network structure effects, homophily effects, behavior effects, and spatial effects. Structure effects account for endogenous impacts coming from the network itself. Homophily effects (the tendency for people to have social ties with people who are similar to themselves) consist of same sex, same grade, same race, same ethnicity, BMI similarity, and course overlapping. Behavior effect refers to the PA ego effect, which is 81 the effect of the actor's PA on friendship nominations. The spatial effect captures the influence of home distance on friend selection. In terms of behavior dynamics, effects include shape effects (i.e. linear and quadratic shape effects that capture the endogenous tre nd of change) and a 12 . Table 12 : Significant coefficients from SIENA model Since our baseline model was designed based on the ABM by Zhang et al. (2015b) , we will not elaborate too much on how SIENA model parameter estimates were translated into probabilities for network and behavior dynamics in the ABM. However, we want to briefly describe three aspects where our baseline model different from the model by Zhang et al. (2015b) . First, our outcome variable is different. Instead of modeling change in BMI as Effects Coefficients Network dynamics Basic rate 7.0422 Structural effects Outdegree - 6.0322 Reciprocity 2.3882 Transitive triplets 0.5051 Popularity (alter sqrt) 0.4777 Homophily Effects Course overlap 0.2431 Same sex 0.4834 Same grade 0.4862 Same race 0.4102 Same ethnicity 0.7517 BMI similarity 0.5403 Behavior effects PA ego - 0.0458 Spatial effect Distance to friends - 0.0700 Behavior dynamics Basic rate 10.6079 Shape effects Linear shape - 0.0981 Quadratic shape - 0.0408 Friend effect PA average similarity 0.4769 82 behavior dynamics, our model simulates changes in total PA (an ordinal variable that indicates the amount of different kinds of PA in a week). Second, our model consists of di fferent effects that influence social network and behavior dynamics. Third, we used empirical data from a different sample school. The sample high school (number of respondents = 948) we chose to simulate was a school located in an urban area with racial h eterogeneity, whereas the one simulated by was a rural school primarily dominated by white students. More details of the social network model used to construct our baseline mode can be found in Chapter 2 of this dissertation . Baseline model validation In t he baseline model validation, we compared the simulated total weekly PA and the empirically - driven social network PA at the end of one simulated year. In terms of network structure measures, we compared the edge density, the distribution of in - degree (an i n - degree means that the agent is nominated as a friend by another agent in the school), and the distribution of out - degree (an out - degree mean s that the agent nominated one student as a friend) with values calculated from Wave 2 observed data. We also chec ked the triad census, which are counts of different types of tie - configuration among three agents. There are 16 possible types of triads in a directed network (Holland and Leinhardt 1970) . Specifically, we inspected if the model over - simulat ed 3 - cycles (Ho - simulat ed the complete graph (Holland and (Davis 1970, Snijders et al. 2010, Zhang et al. 2015b) . 83 Extended baseline model with PG intervention the PGABM 1. Game environment After validating the baseline ABM, w e introduced PG to the model as an intervention to , and we called this extended ABM as PGABM . PG is a location - based augmented reality game where players need to move around and explore places to capture a randomly spawned Pokémon creature. Three types of features in PG could influence the game activity of players: spawnpoints, Pokéstop, and Gyms. Spawnpoints are locations where new Pokémons appear in the game , and either disappear in 30 minutes or are ught by the player . Pokéstops and Gyms were associated with the landmarks in geographic space, where players can collect items, such as Poké B alls used to capture more Pokémon, or where they can train their Pokémon ( t raining happens in Gyms within the game ). To simulate PG interventions and implement the aforementioned game features , whenever possible, we used secondary data from other published studies. If data was not available, we resorted to best guess values. To set up the game environment, we parametrized it using secondary data from the study by Juhász and Hochmair (2017) , whose PG - related point data was collected in two areas, South Florida and Boston . Based on the demographic statistics, the sample school was more likely in an urban setting with a diverse population, thus we assumed that the Boston point density data is more accurate to account for the actual game feature distribution in our sample school commun ity. Due to unknown landcover of the sample school community , we used the average density (i.e., total observation counts divided by total area) of three major land use types (commercial, public, residential) to initialize game features in the PGABM enviro nment as shown in Table 1 3 . 84 Table 13 : PG - related point density in Boston Land - use Area (km2) Pokéstop counts Spawnpoint counts Gym counts Commercial 6.8 589 1249 35 Public 6.0 544 1112 41 Residential 17.2 305 1806 25 Total 30.0 1438 4167 101 Average density (count/km2) 48 139 3 * Calculated based on field data reported in Juhász and Hochmair (2017) . At model setup , if the intervention is applied ( i.e., number of player agents > 0), a number of PG - related features will be randomly populated based on the calculated average density within the system boundaries. System boundaries were created using the maximum and minimum XY bounding box coordinate values student agent homes, pl us a 2km buffer around th e box. For each PGABM execution, Pokéstops and Gyms have set locations , while spawnpoints are refreshed only once per simulated day to reduce computational load. 2. Player a To simplify the complex variation of pla yer agent PG behaviors, we designed rules and made assumptions for the agents to follow. These are: 1) Gaming frequency : a player agent plays the game 2 5 times per week (Barkley, Lepp and Glickman 2017) and, for simplicity, only once per day. According to the total number of ticks in a simulated year, a day was calculated proportionally (e.g., if 16732 ticks in a year, a day lasts for 46 ticks, and a week lasts for 322 ticks). 2) Pokémon Collection: Player agents always choose the next closest feature when playing the PG, but a visited location will not be visited again within the same play. The nearest neighbor was searched using a K - Dimensional Tree algorithm. An existing study on college student players indicated an average o f 1.36 hours of play every day (Delello, McWhorter and Goette 2018) . Assuming the walking speed is 5 km/h (about 3.1 mile/h), the total average walking distance amounts to 7 km (1. 36 h * 5km/h). If , on average , there 85 are about 139 Pokémon randomly distribu ted per square kilometer (Table 1 3, Boston spawnpoints), then the expected point spacing would be 84.8 meters ((1/point density) - 2 ). A player would encounter around 83 Pokémon in 7 kilometers. To account for agent heterogeneity, we also introduced variability by drawing different values for player agents from a truncated normal distributio n with the mean set at 83 (sd = 20, min = 20, max = 140 . We arbitrarily set the minimum value to 20, and the standard deviation is then calculated to be about 1/3 of the different between the mean and minimum /maximum so that 97% value will fall in the range if the variable has a normal distribution ). 3) Vising Pokéstops and Gyms : Training Pokémon and competing with other players are important game activities, thus , in the PG ABM, we included visits to Pokéstop and Gym s . This also add s variation s to the route s the player agent s t ake during game journeys. A play er agent would visit a Pokéstop on each game day, and a Gym at least once per week. During a game day within a week, before the player agent finishes collecting a target number of Pokémon, a random step is picked at which the player agent visit s the nearest Pokéstop. Similarly, among all game days within a week, a game day is randomly selected in which the player agent visit s the nearest Gym at a randomly picked step. 4) Converting gameplay to total PA : in the baseline model, Wave 1 total PA was th e sum of three ordinal PA variables from the Add Health survey data . These three variables are times of (1) - (2) (3) in the past 7 days . E ach of th ese th ree PA variable s con tains four values , 0 = none, 1 = 1 or 2 times, 2 = 3 - 4 times, and 3 = 5 or more times. Thus, the total PA ranges between 0 and 9. We converted PA resulting from playing PG to total PA based on the total game walking distance per week and th en classif ied it into three levels: 2.5 7.5 km, 7.5 12.5 km, and over 12.5km, corresponding to 1, 2, and 3 total 86 PA units, respectively. Game PA is added on top of the total PA by assuming that it is independent from other PA. For a player agent , the t otal PA (game PA plus other PA) is used to estimate social network and behavior dynamics, and the game PA is adjusted 5) Game engagement : All enrolled player agent s are assumed to have the same level of game attachment. In a previous research, it was found that PG p game fade d over tim e (Liu and Ligmann - Zielinska 2017) . To implement the game attachment fading process, based on the truncated n ormal distribution of the number of Pokémon to be collected, we assumed that the mean of the truncated normal distribution decrease s by 15% every week. A target number of 5 Pokémon to collect is set as the threshold . O nce the number of the Pokémon to collect drops to 5 or fewer, the player agent is no longer considered an active player agent and quit s the game completely in the following weeks. 6) Model output : every player agent due to playing the ga me are recorded. None - player agent is also exported for analyzing the spillover effect. A flowchart of the ABM with PG intervention is shown in Figure 7 . 87 Figure 7 : Flowchart of PGABM 88 Intervention scenarios To explore the effects of the intervention, we tested three scenarios listed below. In each scenario, we ran the ABM 20 times with different random seeds. This number is a compromise between a sufficient level of randomness introduced in the model and its com putational cost. We focused on the end - of - year average PA of all student agent s , including both player and non - player agents, to evaluate intervention impacts and comparing t hem to the baseline model results. We also inspected changes in average total PA a cross time. All intervention s start on the first day of the simulated year and among all intervention scenarios, randomly enrolling 200 students was set as the baseline - intervention scenario to be compared with other scenarios. 1) Scenario 1 - Effects of diff erent scales of the program : to account for the scope of the intervention, we conducted two separate experiments in which we enroll ed 100 and 300 student agents as player agents , respectively . 2) Scenario 2 - Effect of targeting students with larger BMI as a measure of overweight and obesity : 200 student agent s with BMI over 25 were randomly selected as PG player agent s as the intervention. 3) Scenario 3 - Effect of distance to community center : we performed two experiments by ( 1) randomly selecting 200 st udent agent s who live close to the community center (within 1000m radius to the center point (0,0) , and (2) student agent s who live farther from the center (beyond 3000m radius to the center point (0,0)) , as shown in Figure 8 . 89 Figure 8 : Illustration of scenario 3 ( Note: for demonstration purpose, not all students shown in the figure) Simulation and data analyses platforms The ABM was coded in Python 3.8.3. The r un time per experiment (N = 20) was about - 4460 CPU, 3.2GHz, 8GB RAM). Data analyses were performed in R 3.5.3. Results Baseline model The mean of simulated total PA was slightly higher than the observed mean at Wave 2. After 20 runs, the baseline model yielded an average of 3.400 (SD = 1.759) total PA of all 948 students at the end of the simulated year, whereas the mean of observed total PA at Wave 2 was 3.262 (SD = 1.929). In terms of distribution, the majority of student agent s had a total 90 PA of 4, but , in the observed data, the total PA at Wave 2 peaked at the value of 3. The modeled data fitted well at extreme values (total PA = 0 or total PA > 6). Figure 9 : Distribution of simulated weekly total PA (boxes) and observed value at Wave 2 (solid line) We then examined the structural characteristics of the simulated network s . In general, our simulated networks were sparser than the observed data at Wave 2 . In terms of edge density, i.e. the number of friend - nominates over the total possible number of nominations, the simulated networks (mean = 0.0012, SD = 2.3×10 - 5) had lower values than the observed network at Wave 2 (edge density = 0.0017). Regarding triad census, in the empirical data, there were only one 3 - cycles (type 030C in Holland and Leinhardt (1970) ), which was also rare in simulated data (mean = 0.240, SD = 0.476), thus it was not over - simulated. On the oth er hand, there were 22 complete cliques of size 3 (type 300 in Holland and Leinhardt (1970) ) and 78.880 (SD = 3.788) in simulated networks, indicating that it was not under - simulated. 91 Lastly, we inspected the distribution of in - degrees and out - degrees. As shown in Figure 10 , the model over - simulated the number of isolates (in - degree = 0) and , in turn, the frequencies of other in - degree values were lower than the empirical data. The out - degree distribution is shown in Figure 11 . The model over - simulated low values (0 and 1) and under - simulated higher values (2 to 6). It fitted high out - degrees (> 6) well compared to the empirical data. In general, we think the baseline model is acceptable for exploring the impacts of the intervention s due to serval reasons, which are elaborate d in the discussion se ction . Figure 10 : Distribution of simulated in - degree (boxes) and observed network at Wave 2 (solid line) 92 Figure 11 : Distribution of simulated out - degree (boxes) and observed network at Wave 2 (solid line) S cenario results The average total PA of all student agent s, player agent s, and non - player agent s for each scenario is shown in Table 1 4. Below, we briefly describe the results of all the scenarios we tested. 93 Table 14 : Summary of scenario tests Mean sim ulated school average total PA (SD of total PA) (Number of runs = 20) Timepoint 100 Players 200 Players ( baseline scenario ) 300 Players 200 players with BMI > 25 200 players close to center 200 players far from center All student agent s end of simulation 3.791 (1.763) 3.767 (1.784) 3.773 (1.761) 3.757 (1.785) 3.787 (1.788) 3.780 (1.786) end of 1st Week 4.413 (1.815) 4.659 (1.950) 4.901 (2.039) 4.658 (1.964) 4.660 (1.983) 4.640 (1.876) end of 51st Week 3.793 (1.766) 3.770 (1.784) 3.779 (1.762) 3.763 (1.780) 3.790 (1.788) 3.783 (1.781) Player agent s end of 1st Week 6.478 (1.952) 6.474 (1.978) 6.445 (1.955) 6.502 (2.056) 6.632 (2.010) 6.163 (1.856) end of 51st Week 3.745 (1.752) 3.684 (1.762) 3.707 (1.762) 3.686 (1.808) 3.783 (1.770) 3.591 (1.786) Non - player agent s end of 1st Week 4.169 (1.634) 4.174 (1.630) 4.186 (1.643) 4.165 (1.614) 4.140 (1.615) 4.237 (1.663) end of 51st Week 3.799 (1.767) 3.793 (1.789) 3.812 (1.761) 3.783 (1.771) 3.791 (1.792) 3.833 (1.776) PA: physical activity; BMI: body mass index. 94 1. Scenario 1 - Effects of different scales of the program With 100 randomly selected player agent s , the average total PA of all student agents , henceforth referred to as the school average total PA , 20 model runs at the last tick of the simulation was 3.791 (SD of total PA= 1.763, SD of simulation mean = 0.058), which is 11.5% higher than the average value from the baseline model (3.400 at the end of the year). We also examined the s chool average total PA by the end of each week throughout the year. The highest average value (4.413) was recorded in the first week . This was expected given that the PG intervention took place on day one. The weekly average total PA had a decreasing trend ( as shown in Figure 12 ) since player agent s gradually collected fewer Pokémon creatures over time due to fading interests. According to the simulation data, all players quitted the game completely around the 20 th week. We also separately analyzed player agent s and non - player agent s. Player agents had average total PA at 3.745 at the end of the 51 st week, which is 10.1% higher than the end of simulation mean of the baseline model, indicating that , even though the players quitted the game before the middle of the year, the impact of the intervention prevailed . Interestingly, although non - player agent s did not directly engage in the intervention, their total PA was boosted due to social influence , which is the spillover effect we hypothesize d . In the 51 st week, non - player agent s' average total PA was 3.799, slightly higher than the mean of player agent s (3.684) at the end of the year. When increasing the number of player agent s, we observed a similar decreasing pattern of the school average total PA . With more player agent s, the school average total PA was higher at the beginning of the simulation. However, after 16 weeks, when the majority of player agent s quit the game, the s chool average total PA curves started to merge as shown in Figure 12 . Surprisingly , a higher number of player agent s did not affect the school average total PA at the end of the year . Moreover, w ith more player agent s in the system , t he average 95 total PA of player agent s did not vary much at the end of week one , suggesting that , by enrolling more students in the intervention program, the magnitude of the intervention effect on the average total PA of player agent s would not be greatly influenced. On the other hand, the average total PA of non - player agent s at the end of week one increased along with the higher enroll ment, which suggested that a larger scale of the intervention would cause greater spillover effects on students who did not participat e in the intervention program . This is because with more player agents enrolled in the program , more non - player agents have more friends p laying the PG , which led to greater impact on non - players through social interactions. 96 Figure 12 : Scenario 1 - Effects of different scales of the program (dots: mean of 20 models runs; bars: ± 1 standard deviation of simulation means ) 97 2. Scenario 2 - e ffect s of targeting students with larger BMI The second intervention focused on targeting student agent s with BMI larger than 25 , to see whether the game could exert a n impact on the school average total PA . Results (Figure 13 ) show that , during the simulated year, enrolling 200 student agent s will larger BMI l eads to little change in school average total PA when compar ed to the baseline scenario (i.e., randomly selecting 200 of player agent s ) . This suggest s that , to promote overall PA, ta rgeting large - BMI students does not necessarily lead to a change in the intervention impact. According to Table 4, at the end of the first week, the average total PA of player agent s seemed to be slightly higher and the average total PA of non - players seemed to be slightly lower comparing to the baseline scenario , which might suggest that the intervention effect was slightly stronger among overweighted player agent s but the spillover effect was weaker. 98 Figure 13 : Scenario 2 - E ffects of targeting students with larger BMI (dots: mean of 20 models runs; bars: ± 1 standard deviation of simulation means ) 99 3. Scenario 3 - Effect s of distance to the community center In this scenario, we did two tests: randomly (1) enrolling 200 student agent s who lived within 1km of the community center , and (2) enrolling 200 random students who lived over 3km from the community center. Based on our observation of the Add Health data, the higher residential density was closer to the community center, gradually decreasing with distance . In the baseline model, dista i.e., agents were more likely to be friends with those who lived closer to them. In the test of selecting player agent s living c lose to the community center, we noticed that there was little dif ference in the initial impacts on all student agent s between the test and control groups in terms of the school average total PA at the end of the first week (4.660 and 4.659 , respectively). As shown in Figure 14 , the close - to - community - center group overla pped well with the baseline scenario at the beginning, and towards the end of the year, the close - to - center group showed a slightly higher mean than the control group. This suggest s that the lasting impact of the intervention might be a little stronger in terms of boosting the school average total PA . When we examined player agent s and non - player agent s separately (Table 1 4), the player agent s' average PA was higher whereas non - player agent lower than the baseline scenario group. This pattern was consistent in both week 1 and week 51. Within scenario 3 , at the beginning of the year, player agent larger than non - player agent , during t he intervention, enrolling close - to - community - center student agent s would exert greater impact on player agent s, but such an impact would not last long after player agent s quitted the game. Interestingly, enrolling student agent s living f ar from the community center led to an opposite pattern. While the school average total PA in enrolling close - to - community - center 100 student agents scenario aligned well with the baseline scenario at the beginning of the intervention, the school enrolling far - from - community - center player agent s scenario started with a lower mean on week 1 and then overlapped with the baseline scenario towards the end of the simulated year. As shown in Table 1 4, when applying intervention on p layer agent s who lived on the periphery, the direct impact of the intervention on player agent - player agent s was stronger ( compared to the baseline scenario group ) . The spillover effect was also larger than other test ed groups. 101 Figure 14 : Scenario 3 - Effects of distance to community center (dots: mean of 20 models runs; bars: ± 1 standard deviation of simulation means) 102 Discussion In this study, we presented a modified and extended ABM that integrates : (1) social network dynamics developed from empirical data , (2) spatial components, and (2) a novel PG - based intervention on behavioral change . To the best of our knowledge this is the first study that integrates these three components to address public health problems. In the context of our PG ABM experimentation , we found that 1) an increase in PA of player agent s due to the intervention can in fluence non - player agent more student agent s into the intervention would not lead to more increments in school average total PA, but the spillover effect on non - player agent s was slightly greater with an in tervention o n a larger scale; 3) targeting student agent s with large BMI values was not effective in terms of promoting the school average total PA, but had the greatest impact on player agent during the intervention ; and 4) The spillover effect on non - player agent s was the greatest by enrolling far - from - community - center student agent s, and the weakest by enrolling close - to - community - center student agent s. The spillover effects were expected in the simulation results because o ur baseline ABM and PGABM were built based on a social network model . O ur social network model indicated that in the mean time , an induvial would adjust his or her PA level to be close to the PA level of close friends via an assimilation process. Th ese friend selection and social influence processes were built into the baseline ABM and the PGABM . Through our PG ABM, as expected, w e demonstrated that PA - promoting intervention can not only boost the PA of program participants but also influence non - participants through social interaction. The same mechanism is very likely to stay true for other 103 forms of PA interventions. We also obse rved some variations among scenarios, mainly related to the difference between players and non - players. However, due to the complexity of the system caused by multiple influential factors in both friend selection and behavior change dynamics, the magnitude and the scale of the impacts from the intervention could vary. We hypothesize that the slightly stronger PA - promoting benefits during the intervention among high BMI players and close - to - community - center players are associated with homophily /spat ial effects (BMI similarity / home distance to friends ) and social influence from associated peers. The PA - promoting influence of the intervention was exerted directly on players. For example, the school average total PA was 3.694 at the beginning of the sim ulation, and by the end of week one of the PG intervention simulation of enrolling 200 random player agent s , player agent s' average PA was 6.474 (Table 4), which was a 75.3% increment. Students who had similar BMI or live closer to each other were more likely to be common attribute (i.e., similar BMI or live close to each other) happened to be the intervention participants at the same time. The impact of the in tervention on themselves, as well as the increased PA of their friends, formed a reinforcing feedback. Consequently, while in the intervention program, the PA promotion impact on players was larger. On the contrary, for students who live around the periphe ry of the model environment, the average home distance not in the player groups. As a result, the within - group reinforcing influence was week but the spillover ef fect on non - players became stronger, compared to other scenarios. 104 Strengths and l imitations T h is study has a number of strengths. The ABM we built for exploring PA inte rvention integrated empirical social network data, geographic locations, and a novel mobile - game - based intervention , which few studies ha ve done to the extent of our knowledge . We also lay out a framework f or creating such an intervention exploration platform from a social network analysis, which makes this model eas y to replicat e . It can also be migrated to other study areas with different types of intervention s . The e xploration of the different intervention scenarios demonstrated that the impacts of the intervention on participants and non - participants would vary due to social network and network dynamics. This could shed light on the importance of considering the social interaction s among adolescents in policy making or launching school - based or community - based interventions. Also, when evaluating existing or on - going intervention programs, this study demonstrate s that the spillover effect could be prominent , but its benefits and its underlying social interaction mechanism can be easily overlooked. We recognize some limitations to this study . While ABMs are useful for exploring different intervention scenarios , they are not well - suited for prediction either at the pop ulation level or at the individual level. Moreover, t he limitations of the underlying models were carried over to our ABM ( social network and behavior dynamics are based on a Siena social network model and the ABM baseline model was derived from an existin g study (Zhang et al. 2015b) ) . We also noticed that our baseline model did not fit the observed data as well as the ABM in Zhang et al. (2015b) . There are several possible reasons for that. First of all, our model used a different sample school with a dive rse population and included different social influences and homophily effects. There might be more uncertainty due to the different model inputs from another school context. Secondly, unlike the other model that used BMI ( a continuous variable ) as the outc ome variable, 105 our model simulated total PA, which is an ordinal variable. I n the Zhang et al. (2015b) model the extreme BMI values were treated separately . On the contrary and due to our objective of studying the impact of PG intervention on PA , we did not set upper and lower bounds for total PA values. The total PA value in the observed data ranges from 0 to 9, but our simulated total PA can be as large as 15, thus the average total PA simulated from our baseline model is higher than the observ ed data. With that being said, we still think the baseline model is acceptable to be used for addressing our research questions due to its empirical data - driven background and rooted from well - established computational mod el s . Unlike most ABM s that genera te a social network by randomly selecting agents or used simplified social network model s like small world s , the Siena stochastic actor - based model was calibrated using true and complete social network data . Consequently, using parameters and algorithms ba sed on the Siena model to simulate social interaction in our ABM ensures a more reasonable linkage with reality (Auchincloss and Diez Roux 2008) . Also, in our baseline model validation, the distribution patterns of network characteristics were persevered when compar ed to the observed data. We also recognize other limitations of our ABM. Although we tried to cover the major game features and parameterize the model based on published studies, there are still a lot of simplifications and arbitrary assumpti ons in the intervention component of the model. This again, made the model not suitable for prediction. Also, this model may not be generalizable and applied to other schools, as Siena model parameters were estimated based on data from a specific selected s chool . There are also limitations in the Add Health data , especially the age of the data sets . The first two waves of data were collected between 1994 and 1996 and are now ~ 25 106 years old. Friend selection and social influence processes and as well as influe ntial factors m ost likely changed since then . We need to point out that our PGABM was not designed as a prediction model but created with a goal of explor is hard and resource - consuming to te st all those intervention scenarios in the real world. Among countless possibilities to design and simulate the proposed interventions via an ABM, our PGABM is only one candidate model under a series of assumption s introduced previously in our Method section. We argue that among the infinite number of ways to model this complex system, our PGABM is a good proxy as we made most of our assumptions based on empirical data . On the other hand, a wide range of possibiliti es are open to other scholars to modify our PGABM or employ a completely different model design. Finally, given the number of uncertain inputs in our model, in the future we plan to perform comprehensive uncertainty and sensitivity analyse s to further identify the most influential variables and improve the accuracy of our model . Policy implications change among non - players, which may shed light on poli cymaking or initiatives of PA - promotion interventions on adolescents. In our study, we used PG as an example, but there are innumerable possibilities of taking advantage of mobile games in general to provide health benefits. Studies suggest that self - motiv ation and determination play an important role in long - term weight loss and weight control (Teixeira et al. 2012) . However, interventions targeting overweighed or physically inactive adolescents may not engage participants with less motivation 107 to commit to behavioral change. Mobile game - based intervention may make it easier to engage more adolescents into the program. Previous studies have shown that The same issue of long - term efficacy i s faced by other active video games that have been considered as means of PA promotion (Biddiss and Irwin 2010) . It remains to be seen w hether and how such an intervention could lead to a long - term increase in habitual PA. Retaining the loyalty of users is also a challenge to game developers . Consequently, there are plenty of opportunities for the industry and academia to work together on developing more effective PA promotion apps or mobile games with health benefits as a n added bonus. We were o nly able to explore a limited number of scenarios of intervention. In future work, we are interested in investigating more scenarios if more contexts and spatial data are available. Currently, most of the obesity prevention programs are behavior - oriented . F ewer are focused on environmental community or environment - based prevention (Weihrauch - Blüher et al. 2018) . 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American Journal of Public Health 105 (S2):S236 - S243. 112 Zhang, J., L. Tong, P. J. Lamberson, R. A. Durazo - Arvizu, A. Luke, and D. A. Shoham. 2015. Leveraging social influence to address overweight and obesity using agent - based models: The role of adolescent social networks. Social Science & Medicine 125:203 - 213. 113 CHAPTER 4 : CONCLUSION Revisiting research questions In this dissertation, I investigate the influence of social network and built environment (including research questions. Question One focuses on testing whether the social influence in a school context plays an important role in affecting adolescents to conform to taking Physical Education (PE) classes . I address this question i n Chapter One , where I use two waves of Add Health data and a regression based social infl uence model. Results show that , in both sample schools tested. On the other hand, the model results show that observation of PE enrollment status from all nominated friends in the previous year was not significantly associated nominated friends was weak. Interestingly, I found that the exposure to the PE enrollment behavior of similar others , defined as students of the same gender AND the same grade, , and this influence varied in different school contexts. Th ese results suggest that school culture and norms may be more influential on - taking behaviors compared to the direct impact from nominated friends. Question Two focuses on studying the joint influence of the neighborhood environment and friendship network o n . In Chapter Two , I use two waves of Add Health data from two large sample schools to build two Siena coevolution models. I found that environment of neighborhoods had 114 d ynamics, but their PA could be influenced by friends via an assimilation process. However, space still matters as we discovered that students who lived closer together were more likely to form a friendship tie. Thus, I am not able to draw a certain conclus ion about whether social influential. Question Three studies the effects of PA - promoting interventions on both participants and non - participants , given the joint impa ct of social network and space . In Chapter Three , I replicate an existing ABM derived from a Siena social network model by introducing a Pokémon - Go - to social influence and fri end selection process es , the intervention impact on participat ing students might also influence students who did not enroll in the intervention program, called a spillover effect. By testing different scenarios, I also found that the impact on intervention participants and non - participants could vary, when the intervention target s students with larger body mass indexes or students living close to versus far from the community center. By a ddressing these research questions, this research contributes to the current literature on childhood obesity and health geography in two ways. First, spatial and environmental variables are often overlooked in existing studies on the relationship between obesity an d social network s . E mpirical social network data and social network dynamics are usually missing components in studies on obesity in the field of health geography. This interdisciplinary research integrates social network analysis and spatial thinking to i nvestigate the joint influence of environmental and social space s , facilitat ing a more comprehensive understanding of the complex system related to childhood obesity. Second, this research extend s an existing model and develops a spatial agent - based model as a tool to explore a novel intervention, the Pokémon 115 Go mobile game. In addition to detangl ing social influence, friend selection, neighborhood environment, and location of homes, this study also provides an experimental platform for seeking possible mit igation strategies for the childhood obesity problem. The ABM presented in this research can be used by other scholars and can be calibrated using more up - to - date social network data from different sample schools for the purpose of either exploration or ed ucation. Additional thoughts about the practical implications From the Add Health data, I observed a decreasing enrollment rate when students enter higher grades. Based on the results of the analys es PA throug h PE, it m ay be important to cultivate a habit of participating in PE since the freshman year. In reality, however, promoting PA and preventing obesity among adolescents through PE could be very challenging. PE taking is greatly influenced by policies, rul es, cultures, and many other factors. Oftentimes, for students enter ing the ninth grade , their PE participation suddenly becomes challenging because they have to change clothes in a crowded locker room, which could be an embarrassing and overwhelming exper ience (Kunichoff 2018) . In many schools, PE classes are required for freshman and sophomore students, but after fulfilling the credit requirements, many students stop taking PE and devote time to preparing for college. S ome athletic students and students i n the marching band may apply for waiver to skip PE classes (Fieldman and Chuck 2017) . On the other hand, those senior students who stay in PE feel that they have no friends in the class and they do not want to make friends with students from lower grades (Hwang 2017) , which makes it hard for senior students to stay in PE classes. to understand their needs and challenges instead of simply forcing PE enrollmen t. 116 PA - promoting interventions could be school - based, family - based, or community - based, but many times, the implementation and evaluation are actually multi - scaled. In this study, the intervention can be viewed as a school - based one since participants were all selected from the same school, and the social interaction that contributes to the spillover effect was due to the happened in the neighborhood. As it was discussed in Chapter Three , PA behavior can also be shaped by the environment, which is a neighborhood level factor. T aking the Pokémon Go intervention as an example, if the neighborhood environment is equipped with amenities that encourage mobile gaming , such as more Pokéstops, increased safety, better pedestrian paths, more greenspace and trials in parks, participants will most likely increase the frequency and intensity of playing . At the family level, if parents play the game with their kids, it may enc ourage the student players to stay active longer due to family support, while the spillover effects also extend to their family members. Limitations and future work The limitations of this study have been discussed in Chapter One, Two, and Three , respectively. A common limitation of all these analyses is the age of the data. The Add Health Wave 1 and Wave 2 data used in this study were from 1990s, which is almost 30 y ears ago. The relationship among students, their friends, the school contexts, and the built environment may have dramatically changed. The sedentary and active behaviors that high school students did two to three decades ago were also different from nowad ays. Due to limited resources, I was not able to access or collect more current data to answer my research questions. F uture improvements are limited until new and complete social network data is collected . Such longitudinal data from 117 other countries can a lso be used for comparative analyses , since obesity is a worldwide issues, even in some developing countries (Bhurosy and Jeewon 2014) . A second limitation of the entire research is its generalizability. Since models used in this study were calibrated us ing two selected sample schools, it is hard to apply model parameters and findings to other cases. Additional analyses are needed to test if the significant relationship detected in the selected sample schools stay s true elsewhere. Third, many of the env ironmental and sociodemographic factors have not been fully explored due to the lack of data. To protect participant identities, the actual geographic location of their schools and homes are unknown. This makes it impossible to fully understand the social contexts of the study subjects . For example, the finest resolution of the neighborhood environment variables is 1km. Without knowing the actual network, our estimation of accessibility is most likely biased. For example, if there was a park within 1km Eucl idean D it would make the park not accessible by walking even though it was not far. Another example is that , in our ABM, we spread the game features evenly acro ss space. If local distribution data were available, and we could allocate more features alone the road network and the game environment would closer to reality. I also did not add visualization to our spatial ABM due to its computation al cost . I would lik e to add to this functionality the current ABM in the near future. 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