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Ai— » 0 VJ . u .. m‘mmwA .. . ... s . in.“ 1...... .r .2.) ‘o . .. .L H... \C ....$.,..,...Eu . . . . r . f .1. .7... .’ .- t“ 7 h- at .'__'.“f‘-:§'.‘ {J LIBRARY ' Michigan {State ' University L 'z | . 5 ‘-‘.,.‘._ “It -_ i .1? ‘ l'HE'i-PS This is to certify that the thesis entitled SPATIAL ANALYSIS OF URBAN INTER- RESIDENTIAL SOCIAL TRIP FLOWS presented bg Frederick Paul Stutz has been accepted towards fulfillment of the requirements for Mdegree in G30 I‘a h (9, WM Maior professor Date if 0-169 l ABSTRACT SPATIAL ANALYSIS OF URBAN INTER- RESIDENTIAL SOCIAL TRIP FLOWS BY Frederick Paul Stutz This study concerns the spatial and related dimensions of inter-residential social travel in an urban area. Aggregate cross— sectional transportation data from an origin-destination study provided by the Lansing Tri-County Regional Planning Commission are examined first. These data are supplemented by more detailed longitudinal data on individuals' recurrent social travel behavior gathered from a field interview of a neighborhood in the East Lansing area. The study attempts 1) to provide a basic understanding of the temporal, demographic and socio—economic structure of social trips, 2) to identify desire lines of movement and to delimit, for social interaction comprehension, the socially cohesive neighborhoods of the study area, and 3) to explain, to a degree, why spatial patterns are formed as they are by testing two hypotheses concerning the social and physical distance between social contacts. Social trips, when compared to all trips, diSplay marked differ- ences in both diurnal and weekday distributions. The sequencing and linking of social trips also differs from that of total trips in that social trips are primarily from home to another residence and back home again, but may involve more than one social stop. Definite variations in social trip making are shown to be related to the trip maker's socio—economic and demographic attributes. Income, household Frederick Paul Stutz size, and age are shown to be highly correlated (negatively) with social trip making. The minimum inter-residential separation of occupational classes shows that Lansing's residential structure is at least similar to concepts of classical urban rent theory. But, there is apparently little, if any, relationship of this inter- residential separation to the distance people travel on social trips. More importantly, this study reveals that social trips differ substantially from other types of trips in their spatial patterns. At several levels of analysis, it is demonstrated that the individual is constrained in his social interaction by distance and status barriers. When frequency of interaction between traffic districts is compared with distance separating the districts, strong distance decay effects are observed at short distances. Once the interaction is carried on beyond the immediate neighborhood, an individual's social communications network is the prime determinant of interaction, and the distance decay is much more gentle. Urban social interaction patterns are computer generated and interpreted. Flow maps display several prominent linkages among portions of the study area. Factor analysis of two origin-destination matrices elucidate socially organized areas within the larger study area that are internally similar in their social interaction. The factors are interpreted spatially by mapping factor scores for census tracts and traffic districts. Both flow maps and factor analyses show the decreasing social importance of areas with increasing distance from one another. The decreasing importance is not regular, but distorted by variation in the "status plane." Frederick Paul Stutz A neighborhood analysis permits the exposure of the two components thought to be the essence of social interaction. One is the neighborhood component, which is basically a distance decay factor, and the other is the social network component, which is basically a status factor. These are defined and evaluated to determine the extent to which social trips are affected by these two aspects of inter- personal social relations. Due to the voluntary and substitutional nature of social trips, variations in individuals' personalities and attitudes make social trip frequency and patterns of social ties difficult to predict. A partial explanation of how and why individuals select social trip ends is forwarded through a behavioral model. But until these factors of personality and attitude can be measured, a certain random element must be assumed when analyzing social trips. The random element is based not only on these factors of personality and attitude, but also on the individual's unique social communication network, each of which is not completely determined by distance and status considerations. SPATIAL ANALYSIS OF URBAN INTER-RESIDENTIAL SOCIAL TRIP FLOWS By Frederick Paul Stutz A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Geography 1970 Gr - @5573 /- .LJr ‘7/ ACKNOWLEDGMENTS I wish to thank my thesis advisor, Dr. James 0. Wheeler, for the opportunity to work with and learn from him over the last two years, and for his helpful criticisms of this manuscript. Thanks are also due to Dr. Lawrence M. Sommers, the chairman of the Department of Geography, for giving me the opportunity to attend Michigan State University with financial aid in the form of a teach- ing assistantship and a National Science Foundation Summer Traineeship, and for making available to me the resources of the Department of Geography. The University's Computer Institute for Social Science Research provided a stimulating and helpful intellectual environment for me in the latter stages of the analysis. | wish also to thank Robert Kuehne, Chief Planner of the Tri—County Regional Planning Commission, for making available to me much of the data used in this analysis, and for many informative discussions concerning it. Finally, I wish to express my deep appreciation to my wife, Audrey, who supplied card punching and clerical skills when they were most needed, and without whose encouragement this research would not have been completed. TABLE OF CONTENTS ACKNOWLEDGMENTS . LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . CHAPTER I. INTRODUCTION . . . . . . . . . . . . . . . . . . . Objectives of Study and Methods Employed The Data and Study Area . . . . . . . Related Literature . . . Organization of Study . . . . . . . . . . . . . . . . . II. THE NATURE OF SOCIAL TRIPS . . . . . . . . . . . . . . . Temporal Distribution . . . . . . . . . . . . . . . . Linkage of Social Trips . . . . . . . . . . . . . Linking Trip Purposes . . . . . . . . . . . . . . . . Multi-stop Social Journeys . . Socio—economic and Demographic Structure of Social Trips . . . . . . . . . . . . . . . . Explaining Social Trip Frequency . . . . . . . . Data Interval Method . . . . . . Areal Aggregation Method . . . . . . III. SOCIAL TRIP DISTANCE SENSITIVITY Distance Decay of Social Trips Social Trip Length and OCCUpational Status IV. URBAN SOCIAL INTERACTION PATTERNS . Generating Flow Maps . . . . . . . . . . Social Trip Flows . . . . . . . . . . . . . Identifying Social Areas . . . . . . Factor Analysis of Census Tracts . . Factor Analysis of Traffic Districts Page ii vi 12 2O 23 23 28 29 39 44 50 51 52 61 61 68 76 77 82 86 88 96 Chapter Page V. NEIGHBORHOOD ANALYSIS . . . . . . . . . . . . . . . . . . 110 Distance and Status . . . . . . . . . . . . . . . . . . 110 Origin of Social Ties . . . . . . . . . . . . . . . . . 113 VI. CONCLUSIONS AND SUGGESTIONS FOR FUTURE RESEARCH . . . . . 121 Discussion I I I I I I I I I I I I I I I I I I I I I I 12]- Suggestions for Future Research . . . . . . . . . . . 125 A Model of the Choice of Social Travel . . . . . . . 126 A Predictive Model of Social Interaction Patterns . . 131 BIBLIOGRAPHY I I I I I I I I I I I I I I I I I I I I I I I I I 135 APPENDIX A . . . . . . . . . . . . . . . . . . . . . . . . . . 143 APPENDIX B . . . . . . . . . . . . . . . . . . . . . . . . . . 151 APPENDIX C I I I I I I I I I I I I I I I I I I I I I I I I I I 153 10. 11. 12. 13. LIST OF TABLES Trip Purpose Matrix of Transition Probabilities for Total Trips . . . . . . . . . . . . . . . . . Trip Purpose Matrix of Transition Probabilities for Weekday Trips . . . . . . . . . . . . . . . Trip Purpose Matrix of Transition Probabilities for Weekend Trips . . . . . . . . . . . . . . . . Regression with Stepwise Addition of Variables for Multi-stop Social Journeys . . . . . . . . . Relative Social Trip Frequency by Data Category Distance Decay Analysis for Social Trips . . . . . Average Minimum Separation Distance by Occupational Class . . . . . . . . . . . . . . . . . . . . . . Mean Social Trip Distance by Occupational Class . . Income Standard Deviation Ratios for Social Areas . Matrix of Social Ties by Occupational Class . . . . R-Mode Neighborhood Varimax Rotation Analysis . . . Two-Factor O—Mode Neighborhood Varimax Rotation Analysis . . . . . . . . . . . . . . . Three—Factor O-Mode Neighborhood Varimax Rotation Analysis . . . . . . . . . . . . . . . . Page 31 32 33 42 47 67 73 74 108 112 116 117 119 10A. 108. 11A. 11B. 12. 13. 14. LIST OF FIGURES Five—Township Study Area . . . . . . . . . . . . . Distribution of All Weekday Trips by Hour of Day . Distribution of Social Trips by Hour of Day . Hourly Distribution of Social Trips by Day of Week Social Trip Frequency by Age . . . . . . . . . . . Distribution of Income by Census Tract for the Five-Township Area . . . . . . . . . . . . . . Relative Social Trip Frequency by Census Tract for Lansing-East Lansing . . . . . . . . . . . . . Social Trip Frequency by Distance . . . . . . . . Trip Frequency by Distance with Data Transformed . Social Trip Flow Map for Households with Greater Than Median Income . . . . . . . . . . . . . . Social Trip Flow Map for Households with Less Than Median Income . . . . . . . . . . . . . . Social Trip Flow Map for Non-Whites . . . . . . . Social Trip Flow Map for Michigan State University Lansing-East Lansing Social Areas . . . . . . . Factor I Scores . . . . . . . . . . . . . . . . . SOCial Areas I I I I I I I I I I I I I I I I I I I vi Page 10 24 26 27 45 56 58 63 66 79 79 81 81 91 93 100 CHAPTER I INTRODUCTION Researchers are becoming interested, with increasing intensity, in travel patterns and studies of migration of human populations. Regions with large and growing urban populations have naturally caused interest in travel within and between cities, and these populous regions have served well as the primary study areas for analysis of movement patterns. Closely related to these studies of movement patterns have been studies of urban growth and market structure. This paper deals with the spatial patterns of urban social travel and their relationship to urban social structure. In geography, a relatively large proportion of research has been conducted on two types of trips, the shopping trip and the work trip.1 These two types of trips are similar in that they are both non-discretionary. That is, people must perform work and shopping activities and they must perform them with a certain degree of regularity. The destinations are limited to those commercial and industrial land uses adapted for the particular trip type, and each trip deals with a person to activity connection. The social trip is another type of trip that generates urban patterns, but it has received little attention from researchers. The 1For shopping travel patterns see, for example, Garrison, et al., 1959; Berry, 1962; Garrison and Worrall, 1966; Nystuen, 1967; Marble, 1967, 1968; Horton, 1968; and Yuill, 1968. For work trip travel patterns, see Taaffe, Garner and Yeates, 1963; Lonsdale, 1966; and Wheeler, 1967, 1969. The treatment of these types of trips has been, by no means, limited to geographers (Voorhees, Sharpe, and Stegmaier, 1955; Kain, 1962; Lapin, 1964; Mayer and Goldstein, 1964; Keefer, 1966; and Bucklin, 1967). 2 trip for social interaction is quite different from the work trip or the shopping trip in several ways. First, the social trip is concerned primarily with person to person connections, while the other two trips are not. Second, the social trip is discretionary in nature, and is more personalized than the two previously mentioned trips“ because the trip maker becomes socially involved at the trip destination. Third, he also has a wide degree of choice in where to travel. Many other types of activities can be substituted for the social interaction trip. Among them are recreation, going for a ride, or simply relaxing and watching television. These latter activities may not involve a trip at all. The activity that is chosen, whether social or otherwise, depends basically upon an individual's preferences, income, and his leisure time availability. A trip that is discretionary in nature, rather than a matter of necessity, may exhibit a much wider variability in trip generation from household to household because of these preferences. The volume of research outside geography on urban social interaction patterns is small. Although a number of geographic studies have been done on recreation, another leisure time activity, it is surprising that no research analyzes specifically social trips. A distinction will be made not only between social and recreational trips, but also between certain types of social travel. There are many types of social interaction that may take place at a variety of land uses. In this study, only trips made to residential land uses for the social purpose of visiting friends, neighbors, or relatives are considered. Some theory on social interaction exists in the sociological literature of the neighborhood, and it will be subsequently reviewed where relevant, but this literature often lacks the spatial 3 element of Special interest to geographers, and points up the need for spatial studies. Obiectives of Study_and Methods Employed The general purpose of this study is to examine the Spatial and related dimensions of inter-residential social travel in an urban context. Three primary objectives underlie this analysis. The first is to gain a fundamental understanding of the nature of social trips. A need for this is seen by the shortage of basic knowledge, eSpeciaIIy of the Spatial characteristics, but also of the non-spatial charac- teristics, of urban social interaction. The analysis of social interaction is an underdeveloped area of research compared with the research produced on other types of trips. To meet this first objective the paper will describe the general temporal, demographic, and socio—economic structure of social trips based on aggregate data from a metropolitan area transportation survey. Specifically, graphs of the diurnal distribution of social trips are analyzed. A matrix of transition probabilities is generated and analyzed to study the linking characteristics of social trips. A least squares method with addition of variables is employed in the multi-stop social journey analysis. A relative social trip frequency ratio is constructed to analyze variations in trip making by individuals with various socio-economic and demographic characteristics. .Social trip generation is explained statistically by methods of multiple regression. The patterns of income and social trips are visually examined by the use of computer generated isoline maps. A second objective, involving the Spatial component of interaction, 4 is to identify desire lines of movement and to delimitate, for social interaction comprehension, the socially cohesive neighborhoods of the study area. To accomplish this, the study 1) presents and analyzes computer generated flow maps of social interaction and 2) uses factor analysis to determine the degree to which social interaction is similar among different parts of the city. This objective stems from the need to know how the urban areas function socially, eSpecially in view of the likelihood that social travel may be a basis for the understanding of the areal distribution of urban social structure. Since choice of residence via the market place is eventually reflected in spatial structure, the relationship between social interaction patterns and the choice of a residence is a key consideration. Operationally, this means that this objective is concerned with metropolitan area interaction and social interaction systems of a recurrent nature, exhibiting tendencies to cluster into spatial patterns. This objective is met by not only using factor analysis to identify areal dimensions of social interaction and computer plotting of social trips by categories of income and race, but also by mapping factor scores. The third objective is to explain, at least in part, why Spatial patterns of social interaction are formed as they are. This approach would define aSpects of urban social interaction patterns which have predictive significance for urban social structure in metropolitan areas other than only the present study area. In an effort to explain the patterns, this paper generates two hypotheses and tests them with data from a metropolitan area tranSportation survey, as well as with data gathered from field interviews, and constructs a 5 model to predict social interaction flow systems. The two hypotheses tested deal with 1) the distance decay concept and distance sensi- tivity of different status groups and 2) the social class segregation hypothesis which suggests that interaction will be most frequent among individuals of similar socio-economic status. Methods employed to meet this third objective include constructing a scatter diagram and running a regression analysis with data trans— formations to show the relationship between the frequency of social trips between areal units and the distance between these areal units. The format of the transportation problem of linear programming is employed to compute the inter-residential separation of classes of individuals, as this inter—residential separation is thought to be related to trip length. Further, factor scores are mapped, income standard deviations from areas loading highly on factors are computed, and variables suggestive of class rank are correlated with factor scores. Lastly, the distance decay and social class hypotheses are tested on the neighborhood level of analysis in an effort to examine relationships that are hidden at the city level. Data on a neighborhood were gathered from direct field interviews. The Data and Study Area The extensive work in urban transportation and land use planning during the past decade has been, to a large degree, the source of and stimulus for present work on travel patterns. At the same time, it can be said that much of the current work on urban travel activities is limited to the analytical approach that has evolved in tranSportation studies due to the type of data available from the transportation 6 surveys. The analytical approach might be characterized as cross— sectional, aggregative, phenomonological, and predictive. Metropolitan tranSportation survey data are very welcomed, however, by the individual researcher such as the geographer, and it is these type of data that have been used primarily in this study. The data supplied by the transportation planning studies permit the researcher to process large amounts of information, with the aid of computers, that would otherwise be unattainable to him because of the time and cost constraints of obtaining it. These data then, permit the individual researcher to get a broad picture of the phenomena he studies and also to have sufficient data to produce statistically Significant results. The data for this research endeavor have been obtained from the Tri-County Regional Planning Commission of Lansing, Michigan, and are based on The 1965 Home Interview Survey of over 4500 households, representing a 5 percent sample of the population. The major purpose of the Home Interview Survey was to obtain information necessary to adequately plan for improved or new tranSport facilities to accommodate present and future travel needs in Clinton, Eaton, and lngham counties. In preparation for the Home Interview Survey, the sample households and group quarters to be interviewed were selected. The household portion of the sample consisted of single, two, and multiple family housing units. The group quarters sample consisted of university dormitories, fraternities, sororities, cooperatives, and religious units. The households were chosen by systematically sampling the meter address records of the power companies which supply electrical power to the residents of the five township area of the Tri-County Region. These sources included Michigan State 7 University, Lansing Board of Water and Light, and Consumers Power Company. Five percent of the region's approximately 90,000 households and 2% percent of the group quarters residents were selected as the sample. These percentages yielded approximately 4500 household interviews and 500 group quarters interviews. The basis for these percentages was that, according to the tranSportation consultant, Alan M. Voorhees and Associates, they would yield sufficient data to facilitate the necessary statistical expansions and analyses for the region as a whole. The smaller group quarters percentage was chosen because residents are more similar than those living in households. For example, the residents in group quarters are, in most cases, similar in age, daily schedules, income, and car ownership. These characteristics vary considerably among normal household residents, however. In the selection of a systematic sample such as that used, the sample rate was based on the estimated total universe and the total number of samples desired. In order to obtain a 5 percent household and 2% percent group quarters sampling rate, it was necessary to oversample to allow for such circumstances as vacant houses, refusals, and unusable interviews. Therefore, a household sampling rate of one in every thirteen was used, yielding 6933 samples. A group quarters sampling rate of one in every twenty—six was employed, providing 600 samples. Since travel varies by day of week and by week of year, the interviewing period was spread over as long a period as practicable - the months of April, May, and June, 1965, and over all seven days of 8 the week. Each household interviewed received a letter from the Governor of Michigan, and a brochure explaining the Home Interview Survey. In addition, the various news media were used in informing as many residents in the region as possible about the Home Interview Survey. The three counties of lngham, Clinton, and Eaton, in which data were gathered, contain some 1700 square miles and a population of 356,000 people, with Lansing-East Lansing as the nodal center of the area. The Tri-County region comprises seventy-eight local units of government, but the five townships in which Lansing-East Lansing are located —- Delhi, Delta, DeWitt, Lansing, and Meridian —- contain two—thirds of the region's population, and it is with these five townships that the study will deal (Figure 1). Lansing and East Lansing contain a composite of functions and facilities, among them being automobile manufacturing and related manufacturing plants, the many offices of state government, Michigan State University, and principal Shopping and commercial centers, each of which generates a large amount of traffic. The data for all trip types in the Tri-County were made available to the researcher on magnetic tape and consist of 44,860 records (trips). The data which provide a detailed trip-by—trip account of all auto— driver and passenger trips made by each member of the interviewed household five years of age and older for a selected day include the trip purposes as well as the zones and land uses of the origin and destination of each trip. In addition, each record (trip) contains demographic and socio—economic information on the individual and the household of which he is a member, and additional information on the Figure 1. Five Township Study Area. Base Map Source: Tri-County Regional Planning Commission, Lansing, Michigan. x." f .‘11. _ 7&7? ' :1 I " ' I. I! DlMO-NOAILEla‘ — if, . I," - I,...I..L,/.l-_f AL... pr. €(\ '-./' (’1 t' . :- 3"1“ . , '. . ‘M. v - // 4 ’ ‘ '(fi'; ,1 ' 10 I an. .4 J‘\ ’ 0 ¢ , . [ , 7- . ‘ WIpqson =/ * ._1 1‘ _ I -. ' I ‘- ' p | 0 Lil... v ‘ Ls - - -I _ . 4 1' ‘ ‘ I ‘ . I q, ’1‘ I ’ 1 I I z I. O — ‘5 r.’ H - -- v I . .. 1 \I . (A 31’" j n, gt .......................... -. ' ‘ 1 — |[ I ,, 2- FIGURE 1 r—JLm./ ‘4‘: *A _ Boundary of Five Township Area FPS 11 trip, such as transportation mode and the time of day at which the trip took place. Variables and the format under which they appear on tape are given in Appendix A. The records for each person are arranged sequentially for the 24-hour period, and are further ordered by survey, household, and person number. Portions of the analysis concerning only social trips were undertaken on the computer by first sorting out only social trips. This was accomplished by sorting out all trips with purpose at destination as social-eat meal, as these two activities were combined into one trip purpose in an effort to limit the "purpose" variable to a one-column field. These trips were then further sorted according to land use at the trip destination, which in this case was residential. This sort also eliminated trips made to restaurants to eat, thus omitting commercial eat-meal trips. This subset of total trips yielded approximately 1900 records, or approximately 7 percent of all trips made. These were expanded to 63,000 trips for most of the social trip analyses.1 It should be pointed out that this data set contains only informa- tion on out-of—home activities which required the use of a car, taxi, bus, or truck. The only walking trips included in the data are walking trips to work. No bicycle trips were recorded. These limitations prevent a thorough examination of school children's and teenagers' travel patterns. Also missing were the walking mode social trips which may occur on a visit to the next door neighbors. Nevertheless, vehicular social travel is an important factor of urban interpersonal 1Each trip may be multiplied by an expansion factor which is dependent on sample size and which expands the data to 100 percent. 12 interaction, and research on social ties on a macro-scale should help considerably the understanding of urban functional association. Some information basic to geographical analysis of social interaction patterns can be obtained only through talking to the indi- viduals directly involved in the interaction. Therefore, in addition to the basic data tape, a micro—geographic area within the metropolitan area was surveyed. In preference to using the random sampling method, fifty detailed household interviews were gathered at all of the reSponding households on the streets in this neighborhood. A questionnaire was designed and used to record the home interview data. (See Appendix B.) In most cases, the persons interviewed were pleasant and cooperative. Although some refused to answer certain questions, such as income and location of their friends, very few refused to reSpond to the entire interview. The purpose of the field interview was to secure specific types of information, such as longitudinal data on social decision patterns, not available from the data tape, and to become familiar with different individual attitudes and preferences for social travel. Related Literature Many studies show a distance decay function for most human Spatial interaction. The best summaries of that literature can be found in a review article by Carrothers (1956), in lsard's book on regional methods (1960), and in Olsson's monograph (1965). Diffusion research and the construction of mean information fields (Hagerstrand, 1967) and potential surfaces (Warntz, 1964; Neft, 1966) are based on the effects of distance on interaction. Planners have also shown intra—urban 13 trips to decline in frequency with distance inputs (Schneider, 1959; Harris, 1964; and Boyce, 1965). Much non-travel literature that lies outside geography and regional science treats the effect of distance on friendship and interpersonal relations. The diminuation in the probability of social communication and friendship with increasing distance has received attention from sociologists. For example, Katz and Hill (1958) have shown that, at least at the city scale, the greater the amount of potential courtship interaction, which varies inversely with distance, the greater the probability of marriage. Distance has traditionally (Bossard, 1932) and more recently (Morrill and Pitts, 1967 [geographers]) proven to be a Significant variable in mate selection. Ramsay (1966) found that the probability of marriage varies directly with the degree of similarity of occupational status of the two parties involved, and inversely with the distance between their residences. Several studies have included the concept of social accessibility, or functional distance, as a determinant of social interaction, especially at the micro-level. Functional distance reflects the actual pattern of routes of interaction, and may include barriers to person movement such as permanent laundry lines, or hedges. Similarly, common sidewalks or an apartment location near a staircase have been shown to promote social relations (Festinger, et al., 1950). At this micro-scale, much shorter distances have been shown to be important in the formation of friendships and social relations. Studies by Caplow and Foreman (1950) and by Festinger, et al. (1950) have revealed the importance of distance in personal contacts in college married student housing units. As expected, an individual's acquaintanceship 14 field grew as a function of the duration in the housing complex. At all scales, including the neighborhood scale, results of questions asking individuals to name the person or persons that they interact with most frequently reveal the overwhelming influence of propinquity on social relations (Boult and Janson, 1956). Study of social interaction in a dormitory showed that students are friends with others who are near to them, not only in proximity, but also in college class (peership) (Priest and Sawyer, 1967). By tracing individual pairs through time, it was Shown that, between roommates and others living close to one another, attraction changes less when it is initially high. Between individuals more spatially separated, attraction changes less when it is initially low (Newcomb, 1956). Thus, attraction is more stable when it is in balance with proximity. This study has also shown that the perception of distance by individuals tends to vary much as a matter of intervening distance, so that, Similar to distance decay rates for mean information fields (Marble and Nystuen, 1963), the distance traveled to friends depends on the density of potential acquaintances. Accepted ecological theory suggests that spatial distances between spatial clusters of people of the same occupational class are closely related to their social distances (Duncan and Duncan, 1955). With respect to mate selection, as well as other types of social interaction, the probability of interaction has been generally shown to vary directly with degree of similarity in occupational class. Sophisticated methods for measuring the social distances between social status categories using occupational data exist (Beshers and Laumann, 1967). In Beshers and Laumann's study, the social distance to the highest and lowest 15 occupational classes was the greatest and an overall hierarchal effect of social stratification was Shown. In another study, Laumann (1966) showed that comparable occupational class is the main factor in predicting with whom individuals will engage in social relations. Studies of neighborhood social relations have been performed, and they generally point to urban social distance. The reduction in cost of movement and reduced choice of Contacts in a neighborhood result in greater reciprocation and clique formation than would take place otherwise (Frankenberg, 1966). Nelson (1966) has shown greater geographical immobility of those belonging to well—connected cliques, such as might be found in a stable neighborhood, than of those belonging to less well—connected cliques. A study by Foley (1952) shows that many individuals do not interact l0cally and do not consider the local neighborhood to be a social community. This suggests that urbanites are mobile, anonymous, and lacking identity with their local area. In light of the theory on urban structure, it would seem that residents of predominantly lower socio—economic neighborhoods should be the most tightly knit groups spatially, exhibiting relatively low spatial mobility. The higher socio—economic groups should display spatially dispersed patterns. And yet, Smith, et al. (1954) have shown for Lansing, Michigan, that the degree of local intimacy varies directly with income, and not inversely, as suggested above. The reasons given are that the lower social groups' mobility for social interaction is greater because of greater residential mobility. The wealthier have greater residential tenure, and tend to increase friendships the longer they 16 stay. Somewhat contrary to Smith, et al., Priest and Sawyer (1967) have indicated that a person's quota of friends is filled after a certain time, and that increases in length of time in a neighborhood or on a college campus may not increase one's number of social contacts. However, Festinger, et al., (1950) have documented the increasing spread of an individual's acquaintanceship field as a function of the amount of time spent in a housing development. Greer (1956) pointed out the distorting effects that relatives have on the usual distance decay relationship, showing individuals to travel longer than average distances to interact with relatives. Newcomb (1956), the social psychologist, has argued that the object of Similar attitudes must be valued by both the sender and receiver and of common relevance to them. This is most often accom- plished when both parties are of the same status. AS a result of interaction and communication, individuals tend to become more Similar to each other with respect to important and relevant objects. This increased communication will also be followed by an increase in positive attraction between the two individuals, regardless of the content of the communication. Also, Putnam (1966) has argued that influence on voters is mediated primarily through numerous personal contacts among members of the community, and is not due to the activity of the political party in the area. The extensive literature in the area of personal influence points out the social and psychological processes assumed by this theory (Katz and Lazarsfeld, 1955). Reasons why similarity of status is a predominant condition of friendship have been advanced. Cox (1968, 1969) has argued that 17 social relations are associated with an exchange between the participating individuals. This exchange of payoffs is used by the persons concerned to evaluate the costs and rewards, or the expectancies of cost and rewards, likely to be associated with a renewal of the contact at a future time. Williams (1956) has noted that repeated contacts and sustained friendships must result from a mutual evaluation of high rewards, as opposed to high net costs. Location is seen by Cox (1969) to affect this social interaction in two ways: 1) the distance decay or gravity component —- the process of interacting with a person as a function of distance and intervening distance —- and 2) the network biased or diffusional component -— in a topological sense, the degree to which individuals have connections with each other, independent of least cost considerations. Thibaut and Kelley (1959) have stated that rewards must be maintained above the available alternative contact level in order for social Interaction to be maintained; and Beshers and Laumann (1967) have indicated that this is most easily done if the parties are of the same socio-economic group. The social and psYchological studies reviewed above were performed, in most cases, on a small number of individuals, using their complete social activities over long periods of time. It is surprising that there are few studies of social travel in the urban setting. With the lack of literature on social travel, one must turn to studies of other types of trips for insights into the nature of social travel. 0i and Shuldiner (1962), Shuldiner (1962), and Fisher and Sosslau (1966) have established that the frequency of all trip making varies closely with such aspects as household size and car ownership. Some research has shown, however, that, contrary to widely held ideas, 18 the location of the individual within the spatial system does not have a great effect on the frequency of trip making. Garrison (1956) has shown that the frequency of shopping trips was distributed among households without any relationship to the type of road service locally available, and that the frequency of shopping was independent of distance from the shopping center, although the place visited was a function of distance. Oi and Shuldiner (1962) have also found that if household size and car ownership are controlled, the location effect on trip frequency is negligible. Other studies by Marble (1959) and Stowers (1962) have shown that socio—economic status is positively related to gross trip frequency. This relationship of increased trip making with higher status may, of course, be due primarily to the fact that higher status groups have access to more autos on the average and, therefore, have more of an opportunity to travel. However, Walker (1966) has shown that households in which the head of the household is a professional averaged approximately seven trips per day, whereas households in which the head is a laborer averaged approximately five trips per day, even though the number of people in the family and the number of cars owned per family were held constant. Although most of the above findings have been made for trips without regard for trip type, some guidelines concerning social travel may be extracted from the Chicago Metropolitan Planning Reports. Sato (1966), for example, showed that in Chicago the number of social- recreation trips made by the family varied closely with the income of the family, as measured by the number of autos owned. Weekend trips were not used in the analysis. This represents a severe limitation 19 to the findings, especially with respect to social travel, since it is expected that a high degree of social interaction takes place on the weekends, and that social travel during the week is severely limited because of work, school, and other obligatory activities. In summary, one evident research requirement needed in order to become acquainted with social trips is the eXploration of variations in social trip periodicities and generation rates under differing circumstances. Circumstances may be exogenous to the individual, including factors such as day of week, time of day, or location in the urban setting. They may also include endogenous factors of the individual trip maker. These include his various socio-economic, demographic, and personal characteristics. Next, it would seem that from the literature, two basic factors tend to have a bearing on social relations. One is distance between the two potential social contacts, and the other is the status similarity of the two social contacts. These two factors, then will be principle considerations in this study. Specifically, it is hypothesized that the frequency of social interaction between the two interacting individuals will be inversely related to distance, and directly related to similarity of status. Social trips, as studied here, are a single subset of social interaction as a whole and, therefore, the degree to which social trips can be shown to exhibit similar characteristics of interaction, in general, remains to be seen. In addition, the treatment of these hypotheses will examine an area of transportation research that has not been previously investigated. 20 Organization of Study The remainder of the study is divided into five chapters. In the following chapter, Chapter II, an exploration is made into the general nature of social trips. It is necessary to have a grasp of the nature of social trips in order to undertake later portions of the analysis. In the first section of this rather lengthy chapter, the diurnal and weekly distribution of social trips is compared and contrasted to the distribution of total trips. In the following section, the linkage of social trips is considered. The first part of the trip linkage analysis examines the degree to which various trip purposes are linked to one another on multi—stop trips from home. Social trips, as they are linked to all other trip purposes, are compared to the pattern for all trips. The second part of the trip linkage analysis is concerned with the extent to which individuals with certain household characteristics tend to make multi—stop social journeys. The next section of Chapter II concerns the socio—economic and demographic structure of social trips. The relative frequency of social trips by age, income, household size, sex, and race reveals important variations. Next, social trip generation is explained in a statistical sense by 1) regressing the relative frequency of social trips with socio-economic variables, each of which has been broken into several data intervals, and 2) regressing the relative frequency of social trips with socio—economic variables aggregated on the census tract level. Computer maps are then presented showing the areal distribution of income and relative social trip frequency by census tracts. Areal 21 similarities in the patterns are given. Chapter III is divided into two sections. The first section studies the diminuation of social interaction with increasing distance between pairs of contacts. A scatter diagram is constructed and the frequency of social trips between traffic districts is regressed with distance between traffic districts in the study area. In the second section of this chapter, social trip length by occupational class is computed. An attempt is made to explain mean social trip length for different occupational classes by comparing these with the mean inter-residential separation of the classes. For this analysis the mean inter—residential separation of each occupational class is computed by employing the transportation problem of linear programming. Chapter IV analyzes urban social interaction patterns by constructing and interpreting maps from information on origins and destinations of social trips. An effort is made to elucidate social linkages in the urban area and the degree to which these linkages are related to distance and status effects. The first section of this chapter describes the computer generation of flow maps and the second identifies desire lines of movement. In the third Section discrete cohesive social areas of the larger study area are identified. This is accomplished by factor analyzing an origin—destination matrix of social trips to reveal portions of the study area with similar patterns of social trips. Two factor analyses are presented, one on the census tract level and another on the traffic district level of analysis. In Chapter V, the scale of the study is reduced to a single neighborhood. In this chapter the distance and status hypotheses are tested to provide a keener knowledge of the social interaction process. This is made possible by specific types of information on recurrent 22 visiting patterns of the respondents. This information was gathered from direct field interviews. This rather brief chapter examines the social linkages of the neighborhood in question to other neighborhoods, and shows the status similarity between pairs of social contacts. This chapter also brings to light what the author believes to be a neighborhood component and a social network component of social trips. Ths sixth, and final chapter, summarizes the findings from earlier chapters, and also provides supplementary explanations for the observed distance and status relationships. Two models are then presented. The first model is a behavioral model that formalizes the elements involved in an individual's choice to make a social trip. The second model is a predictive model that gives a method by which patterns of social travel may be simulated and predicted for future periods. Empirical verification of the models is suggested as a problem for future research. CHAPTER II THE NATURE OF SOCIAL TRIPS Temporal Distribution One manner in which social trips differ from trips made for other purposes is in their temporal distribution throughout the day and week. The distribution of all weekday urban travel throughout the twenty-four hour day peaks in the early morning and in the late afternoon. This bimodal distribution is a familiar phenomenon to the commuter and the transportation planner. The hourly distribution of all weekday trips for the study area is shown in Figure 2. Each datum point on the graph represents the percent frequency of all trip starts for that Sixty- minute period interval, compared to all trips for the twenty—four hour period. The first peak, between 7 and 8 a.m. represents the morning rush hour, involving trips to work and to school. After this peak there is a rapid decline in frequency of trip starts. A subsidiary peak is shown between 12 noon and 1 p.m.. At this time there is a large number of trips to eat-meal, some of which are to home from work and back to work. A large proportion of this noon activity consists of people making social st0ps, however. A second depression is seen in the afternoon at approximately 2-3 p.m., followed by a sharp rise to the evening rush hour peak between 4 and 6 p.m.. This peak is not as sharp, even though higher in amplitude than the other peaks, because it extends over a longer period of time, due to people getting off work over a two-hour interval. For this graph, the datum point for trip starts from 4—5 p.m. and 23 24 Va N mm3w_u >m was: ._<_UOm ..._O ZO_._.Dm_~.:w_o Still”. 'IVIDOS INJDUIJ .v. maze. u >> u_O >m wept. ._<_QOw do ZOPDmEHmE >IEDOI 28 There is a sustained high hourly frequency of social trips throughout the day, with only a slight depression in the late afternoon. Between 7 and 8 p.m. there is another peak approximately equal in amplitude to the first, after which there is a rapid decline in frequency of social trips. The basic difference between the two frequency distri— butions is that weekend social trips remain at a high frequency from approximately noon to 8 p.m., whereas the weekday social trips Show two sharp peaks, one at noon and one at 8 p.m.. Another difference in temporal distribution between social trips and total trips is in the number of trips made for each day of the week. Fifty—three percent of total trips in the study area occur on weekdays, but only 37 percent of the social trips occur during the five weekdays. Twenty-eight percent of social trips take place on Saturday, with Sunday having 35 percent of the trips. Therefore, nearly two-thirds of social travel occurs during weekends. The sequencing of social trips throughout the day, as they are linked with other trip purposes on the same journey from home, reveals interesting distinctions. The following section will deal with the linkage of social trips to other trips. Linkaqe of Social Trips Over a twenty—four hour day, most travel by residents of the urban area is home-based. That is, residents typically start from home in the morning, return to and leave from home a number of times, and end up there at night. Each journey is composed of two or more trips in the conventional sense, as used in the origin-destination studies of urban travel. For example, the Tri-County Regional Planning Commission (1965) defines a trip as one—way travel from one point to another, covering 29 two or more blocks, for a particular purpose. Thus, round trips to and from work, to and from Shopping, and to and from a friend's residence represent at least two trips in each case, one to travel to the place of work, shop, or socializing, and one for the return trip home. If there are only two trips in a journey, from home to an activity and back home again, then no activity linkages occur on the journey. Complex journeys of more than two trips obviously involve sequencing or linking of activities. Combining several trips for the same or different purposes on a single journey away from the home is efficient behavior, and has received attention in the literature, primarily with respect to shopping trips (Garrison, et al., 1955; Marble, 1964; and Nystuen, 1967). But the linking of activities occurs actually somewhat infrequently. Usually a person leaves home for a single activity and returns home when it is done. Only about 25 percent of all trips in a metropolitan area recorded in home survey studies are not home—based. This section is divided into two parts. The first part will examine the degree to which various trip purposes are linked to one another. Social trips, as they are linked to all other types of trips and also to social trips, will then be compared to the pattern for all trips. The second stage of the analysis will be concerned with the extent to which individuals in certain household types tend to make multi—purpose social journeys. Linkinq Trip Purposes The first stage of the analysis uses a transition probability matrix to analyze social trips made by residents as linked to all other 3O trip purposes. This approach has been used previously, Specifically for shopping trips (Marble, 1964; Thomas, Horton and Dickey, 1966; and Shuldiner and Horton, 1967). Groups of highly linked trip purposes, as revealed by transition probabilities, are identified. The basic input into the trip linkage analysis is a data matrix giving all trips originating and ending at various trip purposes or activities in the Five-Township area for an average weekday and an average weekend day, yielding a total of 1,151,769 trips. The probability pij of a trip going from any origin activity i, labeled on the rows, to each destination activity j, labeled on the columns, was then computed by the expression pij = ij/( : fij’ where fij is the frequency of the ij’rh cell. pij is the ijIfi—entry of the matrix, and is the probability of a trip maker moving from state i to state j. Row i of this matrix gives the probability vector for a trip starting at activity i ending at all other activities m. Column j of the matrix gives the probability vector for trips from m activities ending at activity j, although for the columns, values must be normalized for probabilities to sum to unity. Thus the transition probabilities of moves between states can be shown. The transition matrix of trip purposes for all trips in the Five— Township Area is shown in Table 1. The first eleven columns and rows show the trip purposes and associated probabilities for all trip purposes in the original data. The next two columns and rows give the probabilities, reSpectively, for total trips, as defined above, and social trips. Similarly, Table 2 and Table 3 display probabilities for trip purposes, respectively, for weekday and weekend trips. For example, in Table 1, the probability that an individual will move to home given 31 TABLE 1 TRIP PURPOSE MATRIX OF TRANSITION PROBABILITIES FOR TOTAL TRIPS* To WOK PER MED SCH SOE CGM SHP REC HOM BUS SEV TOT SOC From 1. WOK .01 .03 .01 .OO .13 .01 .04 .01 .65 .07 .05 .07 .02 2. PER .02 .13 .01 .01 .09 .00 .13 .02 .54 .02 .04 .06 .03 3. MED .01 .08 .01 .01 .08 .00 .18 .02 .57 .02 .02 .01 .00 4. SCH .01 .02 .01 .03 .06 .02 .03 .02 .79 .00 .02 .02 .01 5. SOE .01 .02 .OO .01 .13 .00 .06 .03 .65 .06 .04 .16 .20 6. CGM .11 .06 .00 .21 .12 .01 .06 .06 .34 .00 .03 .OO .00 7. SHP .OO .04 .00 .00 .08 .00 .16 .01 .66 .01 .03 .11 .06 8. REC .00 .01 .00 .00 .09 .00 .02 .04 .80 .01 .03 .07 .05 9. HOM .17 .10 .01 .08 .24 .00 .14 .14 .00 .03 .10 .38 .57 10. BUS .02 .02 .OO .00 .07 .00 .03 .01 .41 .41 .03 .12 .05 11. SEV .07 .06 .00 .01 .08 .00 .07 .03 .51 .02 .14 .00 .00 12. TOT .07 .06 .01 .02 .16 .00 .11 .07 .38 .12 .00 13. SOC .01 .02 .00 .01 .14 .00 .02 .01 .77 .02 .00 %All entries not identical are significantly different at P = .01. DEFINITIONS OF ABBREVIATIONS USED IN TABLES 1, 2, AND 3. 1. WOK . . . Work 8. REC . . . Recreation—Ride 2. PER . . . Personal Business 9. HOM . . . Home 3. MED . . . Medical-Dental 10. BUS . . . Business 4. SCH . . . School 11. SEV . . . Serve Passenger 5. SOE . . . Social-Eat Meal 12. TOT . . . Total 6. CGM . . . Change Mode 13. SOC . . . Social 7. SHP . . . Shop 32 TABLE 2 TRIP PURPOSE MATRIX 0F TRANSITION PROBABILITIES FOR WEEKDAY TRIPS* To WOK PER MED SCH SOE CGM SHP REC HOM 10. BUS 11. SEV 12. TOT 13. SOC From 1. 10. ll. WOK .00 PER .02 SCH .01 SOE .01 CGM .01 SHP .00 REC .01 HOM .21 BUS .02 SEV .09 .03 .13 .07 .02 .02 .07 .04 .01 .10 .02 .05 .01 .00 .14 .00 .04 .01 .65 .01 .01 .08 .OO .12 .00 .56 .01 .01 .08 .OO .16 .02 .59 .01 .03 .06 .02 .03 .02 .79 .00 .01 .11 .00 .06 .03 .59 .00 .24 .08 .01 .07 .07 .32 .00 .00 .07 .00 .16 .01 .65 .OO .01 .07 .00 .02 .04 .79 .01 .11 .16 .00 .14 .12 .00 .00 .OO .07 .00 .03 .01 .41 .00 .01 .08 .00 .07 .02 .50 .07 .03 .02 .00 Ill .00 .01 .Ol .03 .41 .02 .05 I04 .02 .02 .05 .04 .04 .03 .11 .04 .15 .05 .01 .04 Ill .00 .10 .06 .39 I16 .00 .03 .04 .00 .02 .13 .01 .09 .05 12. 13. *All entries not TOT .09 SOC .02 .06 .03 .01 .04 .11 .00 .10 .06 .37 .00 .02 .08 .00 .05 .01 .76 identical are significantly different at P = .01. .16 .03 .OO .00 33 TABLE 3 TRIP PURPOSE MATRIX 0F TRANSITION PROBABILITIES FOR WEEKEND TRIPSv‘f- 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. ToWOK PER MED SCH SOE CGM SHP REC HOM: BUS SEV TOT SOC From 1. WOK .01 .03 .00 .OO .12 .01 .05 .01 .67 .06 .05 .01 2. PER .01 .12 .01 .OO .10 .OO .16 .03 .51 .01 .04 .02 3. MED .00 .16 .00 .OO .05 .OO .37 .00 .41 .00 .00 .00 4. SCH .00 .00 .00 .00 .09 .OO .00 .00 .91 .00 .00 .00 5. SOE .00 .01 .00 .OO .15 .00 .05 .03 .72 .01 .03 .24 6. CGM .14 .00 .OO .00 .35 .00 .00 .OO .51 .00 .00 .00 7. SHP .00 .02 .00 .00 .09 .00 .17 .02 .66 .07 .03 .05 8. REC .OO .01 .OO .00 .10 .00 .02 .04 .80 .OO .02 .06 9. HOM .08 .10 .01 .01 .40 .00 .14 .17 .01 .02 .08 .60 10. BUS .02 .01 .00 .00 .09 .OO .02 .00 .44 .41 .02 .02 11. SEV .02 .07 .OO .00 .12 .00 .09 .04 .54 .01 .11 .00 12. TOT 13. SOC .00 .01 .00 .00 .17 .OO .10 .02 .79 .01 .00 *All entries not identical are significantly different at P = .01. 34 that he is at work is 0.65. Trip purpose categories used in the Tri-County data are, with minor exceptions, typical of metropolitan surveys and have generally accepted interpretations. One exception is that social trips are paired with eat-meal trips in the Tri-County data, while social trips are usually paired with recreational trips. A description of the trip purposes used by the Tri—County and in this section is given in Appendix C. By examining column nine of Table 1 it can be seen that the majority of all trips, regardless of origin, have home as the destination. For trips leaving from home, there is an expected probability of 0.24 that an individual is making a social-eat meal trip. Work trips, shopping trips, and recreation and ride, in that order, are the next most frequently chosen trip purposes as one leaves home. From school, by far the most frequent destination is home. Social- eat meal is the next most frequent trip destination from school. Individuals leaving from work are most often returning home, as shown by a transition probability of p = 0.65. The next most frequent trip destination from work is social-eat meal, with a probability of p = 0.13. This reflects, to a degree, trips made by individuals going to lunch from work. Trip destinations highly linked with personal business, other than home, are personal business, and shopping, and latter of which is essentially a form of personal business. Since a medical or dental trip is also a type of personal business and frequently requires the individual to go to a commercial district of the city (where personal business can also be undertaken), the fact that it is linked to personal business is explainable. The shopping trip is most heavily linked to 35 itself, showing the presence of multi-stop Shopping trips. Medical- dental, personal business, and shopping are highly linked with one another. These three trip purposes are somewhat strongly linked to social-eat meal as well. Apparently, individuals are apt to end their personal business with a meal or snack, therefore, raising the probabilities in the social—eat meal column. Individuals are not as likely to begin personal business after a social-eat meal trip, however. Other than with home, change mode is linked to work and school, meaning that these two purposes have a noticeable share of mass transit users. Serve passenger is highly linked to itself, however. Recreation and ride is overwhelmingly linked to home, as this trip purpose is, along with the social trip, an individualistic type of activity that most often occurs as a single trip from home. The next most highly linked trip purpose with recreation and ride is social-eat meal. The probability of an individual returning home after a business purpose is the second lowest in column nine. Equal to this probability is the business trip linked to itself, showing the presence of individuals who make business their mode of work. Examples are individuals who are traveling salesmen, telephone repairmen, vending machine operators, and parcel postmen. The column entitled "total" in Table 1 shows that individuals,on the whole, travel most often to home, next most often for social-eat meal, and then for shopping, business, work, and recreation and ride, in that order. An examination of the transition probabilities for weekday, as seen in Table 2, shows that work is more highly linked than in Table 1 to social—eat meal, showing the enlarged relative frequency of the trip to eat from work over the lunch break. Social-eat meal for the weekday, as opposed to the entire week, is more highly linked with business, 36 as individuals return to work or to business activity after the lunch period. This table shows, as is expected, that trip linkages from home to work are more frequent on weekdays than on all days. Trips to and from business and work show higher probabilities for weekdays than for all days of the week. For weekend trips alone, as seen in Table 3, the probability of going from social-eat meal to social-eat meal is higher than for weekday trips alone. This is due, in part, to the fact that by far the largest portion of multi—stop social journeys occur on the weekend when individuals have time to make more than one social engagement. Trips from home to social-eat meal in Table 3 show a substantially higher probability, p = 0.40, than trips from home to social—eat meal for weekday, p = 0.16, displaying, as previously shown, that 67 percent of social trips occur on the weekend. The linkage of social trips to trips for other purposes, although generated separately, is also shown in Tables 1, 2, and 3. As can be seen from the last two columns of Table 1, 57 percent of all social trips have residential origins, or home as the purpose at origin. This value is substantially higher than the comparable value for total trips, of which only 38 percent have residential origins. It can be seen that 20 percent of all social trips have a previous social trip occurring just before them, suggesting the importance of multiple-stop social journeys. Only 16 percent of total trips have social-eat meal as the purpose at the origin. Another striking difference between social trips and all trips is the fact that another 10 percent of social trips start from work or business origins, whereas 25 percent of total trips start from these originS. Another 6 percent of social trips start from shopping origins, 37 whereas almost twice this amount of total trips begin from shopping origins. Social trips, as linked to other trip purposes at the latter's destination, differ substantially, therefore, from total trips with respect to basic linkage pattern. Social trips occur primarily from home to another residence and back home again, with a relatively low probability that an individual travels to a social stop on a journey with most other activities. By examining the last two rows of Table 1 one can see the ways in which individuals select trip purposes from social trips, as compared to selecting trip purposes from total trips. Total trips may be considered the same as an average trip in this discussion. The entries in the last two rows of Table 1 indicate the probability of an individual making a stop at the purpose labeled on the columns. The basic difference is that individuals usually go home after a social trip, p = 0.77, whereas after an average trip the probability is 0.38 that an individual will go home. The probability of returning home from all trips (or from an average trip), p = 0.38, is seemingly low. However, it is low because this value also includes trips made from home, constituting well over a third of all trips made, none of which have home as the destination. In every category, except social, the probability of an individual stopping at a particular trip purpose after a social contact has been made is much lower than for total trips. This indicates, once again, the high likelihood that individuals return primarily to home after a social contact has been made, but may also travel to other social contacts, rather than to other types of trip purposes. One of the reasons for this relationship is the fact that the largest number of 38 social trips occur in the evening hours. After their completion, few other types of Spatial opportunities are available to individuals and home is the most logical destination. Columns and rows twelve and thirteen in Table 2 and Table 3 show similar types of information for weekday and weekend trips as Table 1 did for total trips. The basic difference between all trip purposes linked to social trips for weekdays compared to weekend days is the fact that during the week there is a higher probability that an individual will go from a work or business trip purpose to a social trip purpose. These former purposes include not only work and business purposes, but also personal business, medical-dental, and shopping purposes. The probabilities for these activities for weekday, as shown in Table 2, are significantly higher, in general, than are the probabilities for these activities for the weekend, shown in Table 3. Another basic difference is the fact that on a weekday, individuals tend to link their social—eat meal trips with social trips somewhat less often than on the weekend, as shown by a probability of p = 0.13 compared to p = 0.24. Similar relationships are shown by the activities individuals choose after leaving a social contact. These relationships are shown in the last row of Table 2 and Table 3. Comparing these probabilities, one can see that, as expected, after a social stop has been made on a weekday, one is most likely to choose activities charac- teristic of weekdays. Due to the restricted number of hours of leisure time on a weekday for most individuals, social stops are linked to each other only eight times out of one hundred on the weekday, as opposed to seventeen times out of one hundred on the weekend. Similarly, due to the fact that fewer 39 types of activities are available on the weekend, especially on Sunday the probability is higher that an individual will return home after a social stop on the weekend, as shown by a probability of p = 0.79, compared to only p = 0.76 on a weekday. A general relationship for all social trips, including weekday and weekend travel, is that there exists a much higher probability the an individual will go home from a social trip than go from home to a social trip. P = 0.77, in the last row of Table 1, means that, when a social trips are considered, there is a strong probability that an individual will go home after the trip. This approaches the highest probability of homeward travel of the analysis, with only recreation and ride being slightly higher. Multi-stog Social Journeys In the previous section of this chapter, it was shown that social trips are linked to other trip purposes on a journey from home somewha less frequently than the average. If an individual does link a socia‘ trip with another trip purpose, or another social trip, he has made what may be called a multi—stop social journey. This portion of the social trip linkage analysis will examine the extent to which differer individuals tend to make these multi-stop social journeys. The purpos is to determine to what degree people in different income, race, and 2 groups link trips on social journeys, and under what conditions of location and household size this linking occurs. In this analysis, a multi—stop social journey is defined as a journey or series of stops during which there was at least one social stop. The method used to determine if a multi-stop social journey 40 occurred was to isolate individuals in the survey data and examine their sequencing of trips. The sort sequence for the data was by survey number, household number, person number, and trip number. Identification of multi-stop social journeys was accomplished by matching, simultaneously, the person number with the household number. When the household number changed, or when a person number changed, a different person's trips were being recorded, and a break in the sequence of trips occurred. When a sequence of matches occurred between person number and household number, then a person made more than one trip in a sequence. By checking the purpose at origin, one could determine whether a multi- stop trip was made. For example, the purpose at origin of the first trip that a person made for the day in question would be coded as nine, home. The trip was made from home to another purpose. If the purpose at the destination was social, then this was one leg of a social journey from home. If the second trip that was made was from a social stop to another social stop, then this person was regarded as linking social stops on the same journey away from home. In this case, two stops were made. Observations which included other stops linked to social stops at the origin, although few in number, were included in this analysis; yet each destination used in the analysis was a social stop. Frequencies of stops on social journeys were divided into four categories. A frequency of one indicated a single stop on a social journey from home. A frequency of two indicated that an individual made a total of two stops on the same social journey. Similarly, a frequency of three and four indicated that three stops and four stops were made, reSpectively, on the same social journey. The number of stops on a social journey away from home was then 41 considered to be the focus of attention and treated as the dependen variable. It was regressed with variables that were thought by the author to have some bearing on the linking of stops on a social jou These included the individual's income, household size, age, sex, re and location in the urban area. Variables and their associated code used in this analysis are shown in Table 4. For the last variable, location, a simple code was constructed, with a value of one indicat that the individual was a city dweller and a value of two indicating that the individual lived in a suburb outside the city limits. Alth there are seventeen census tracts out of sixty classified as suburba less than one—seventh of the population in the Five-Township Area resides in those tracts. A regression analysis with stepwise addition of variables was performed. The results of the regression with addition of variables although diSplaying generally weak relationships, are shown in Table A minimum significance of P = 0.15, rather than P = 0.05, was origin used in order to exclude only very weak relationships, and thereby g a more complete picture of the role that the independent variables p in explaining the dependent variable. The intention was to later rw the regression with a minimum significance of P = 0.05, but all varh entered into the regression in the initial run with the least signif having P = 0.05. The most significant variable was suburban, with household size, age, income, race and sex explaining lesser amountSl variation. A negative relationship was shown for the suburban varim meaning that people in the city make more stops on social journeys t people in the suburbs. A possible explanation is that people in the live in more dense areas and are closer to a larger portion of peoph 42 TABLE 4 REGRESSION WITH SETPWISE ADDITION OF VARIABLES FOR MULTI-STOP SOCIAL JOURNEYS Variable Name Code Values X (1) TRIPSTOP Number of Stops X (2) INCOME 8 Income Intervals (1 = Low, 8 = High) X (3) HHSIZE Actual Size X (4) AGE Actual Age X (5) SEX 1 = Male, 2 = Female X (6) RACE 1 = White, 2 = NonJWhite X (7) SUBURBAN 1 = City, 2 = Suburb Step Variable R2 Increase Sign P Variables Not Included 1 X (7) 0.243 0.243 - '(.01 X (2), X (3), X (4), X (5), X (6) 2 X (3) 0.268 0.025 - (.01 X (2), X (4), X (5), X (6) 3 X (4) 0.280 0.012 - (.01 X (2), X (5), X (6) 4 x (2) 0.285 0.005 + (.01 x (5), x (6) 5 X (6) 0.289 0.004 + .02 X (5) 6 X (5) 0.291 0.002 + .05 43 and, therefore, must Spend a smaller amount of time and travel cost in stopping in more than one place. The next strongest relationship (the variable which contributes most to the remaining unexplained variation in the dependent variable after the first regression) is between the number of stops on a socia journey and household size, although it adds only 2% percent. It sho a negative relationship. This may be due to the fact that smaller households, consisting of single individuals and couples, are mobile, with the ability to make many trips from home. They, therefore, have capacity to make a larger number of stops on social trips, compared t larger families who have children. The next most important relations again negative, is with age, indicating that younger individuals tenc to link social trips more than older individuals. In a later section it will be shown that age is negatively related to social trips. Thi fact may also be important in explaining why younger individuals make more multi-stop social journeys. Income was the next variable to enter the analysis and it was th last variable to be significant at the P = 0.01 level. The last two variables entering the regression, race and sex, show weak positive relationships, meaning that non-whites and females (white and non-whi are more apt to link social stops than are whites and males. Analysi of variance for overall regression was significant at less than P = C due primarily to the large sample size of 1822 observations. However only 26 percent of the total variation was explained, giving generall weak relationships. If parsimony was a criterion, only the first one or two variables would remain. Another regression was run with the presence of a multi-stop soc 44 journey coded as a value of two and the presence of a single stop on a social journey coded as a value of one. The results of the analysis did not improve the amount of variation explained in the previous analysis, however. These results suggest that the social trip is an individualistic and a complex trip and does not correspond well to linking characteristics of other trips. This may be due to the variability of individuals' preferences for and attitudes concerning social interaction, something on which data do not exist at present. If this is true, socio-economic and demographic variables may not be adequate predictors of social trip generation. The next two sections of this chapter are undertaken in order to determine to what degree variables on which data are available can help explain social trip generation. Socio—Economic and Demographic Structure of Social Trips The distribution of social trips by age presents some important variations. Figure 5 shows the distribution of social trip frequency by fiveayear age intervals. The trip frequency metric on the y-axis is the ratio of an age interval’s percent of social trips to the age interval's percent of total population. A value above +1.0 indicates that an age interval makes more than an average portion of social trips. Those below +1.0 are age groups making less than an average share of social trips. The first three age intervals have a below average amount of social trips. It is expected that a large percentage of social trips made by individuals of these age intervals are not vehicular and, therefore, not included in the data, making the frequencies in Figure 5 for these age categories small. Figure 5 shows that the frequency of social trips peaks at age 45 m mm30_u m¢ 2. u0< +nm leom akink flick ooimo V0-00 omumn Vnion QVIMV VVIOV onimm Valom Quinn VNéN 070— 3.0— 0% I Go.— \//K/ /\/ I on.— / .1 wk.— m0< E 05:85 .5: 2.00m Sdllfl. 46 twenty to twenty-four, and generally declines thereafter, with several smaller peaks occurring in the late thirties and the early fifties. The peak in social trips at age twenty to twenty-four is, perhaps, due to the large emphasis placed on social activities by members of this age group. It is between ages twenty and twenty-four that most indi- viduals pursue a marriage partner, for example. After age twenty—four many individuals are married and total social activity declines. The two previous age categories reflect the presence of many non-drivers and even fewer car owners. These effects help make the twenty to twenty-four age group have the highest relative frequency of social trips. A definite increase in social trip frequency is shown for individuals between sixty-five and sixty-nine, after which there is a rapid decline in number of social trips with age. This latter age group represents recently retired individuals. It is possible that these people use their increased leisure time for social visiting purposes, making trips primarily to visit relatives. In sum, social trips make up a relatively large share of trips for those individuals in the twenty to forty age group. But after the late thirties, the social trip purpose is decreasingly selected, except for the first few years of retirement. The relative frequency of social trips by income, occupation, household size, sex, and race also reveal interesting variations. Table 5 gives the relative social trip frequency for these variables by various data intervals. In this table, each value represents the ratio of the percent of social trips made by persons in a data interval to the percent total trips made by persons in that interval, as computed from the 1,151,769 expanded trips on the tape. This ratio is referred to, henceforth, as the relative social trip frequency. A relative social trip frequency larger than unity indicates that persons in the interval 47 TABLE 5 RELATIVE SOCIAL TRIP FREQUENCY BY DATA CATEGORY Relative Relative Code Income Social Trip Code Occupational Social Trip (dollars) Frequency Class Frequency (RSTF) (RSTF) 1 0 1.46 1 Professionals 0.86 and Technical 2 1- 2,999 1.18 Workers 3 3,000- 4,999 1.15 2 Managers 0.80 4 5,000- 6,999 1.00 3 Sales Workers 0.94 5 7,000— 9,999 1.12 4 Clerical and 1.21 Kindred Workers 6 10,000—14,999 0.94 5 Craftsmen 1.06 7 15,000—24,999 0.76 and Foremen 8 25,000+ 0.62 6 Operatives 1.23 7 Service 0.90 Workers 8 Laborers 0.69 90 Not in Labor 1.10 Force Code Sex RSTF Code Race RSTF 1 Male 0.85 1 White 0.98 2 Female 1.17 2 Non—White 1.26 Table 5 (cont'd.) Code Household RSTF Size 1 1 1.23' 2 2 1.26 3 3 1.14 4 4 1.02 5 5 0.80 6 6 0.62 7 7 0.98 8 8 0.40 9 9 0.97 10 10+ 0.96 Code Mode RSTF 1 Auto Driver 0.91 2 Auto Passenger 1.27 3 Bus Passenger 0.18 4 School Bus 0.16 Passenger 5 Taxi 0.90 6 Truck 0.69 II g 49 made more than an average portion of social trips. In Table 5 values for the eight income intervals tend to decline with inc income. The two middle intervals are the only data units not to this pattern, while the two extreme intervals have, by far, strongest patterns. Apparently low income families make a dis tionately large share of social trips, perhaps substituting tt other leisure time activities which require monetary cost. lr social activity is a cheap method of entertainment, compared 1 natives such as going to a movie or to the country club. The distribution of relative social trip frequency by oc< Stnows extremes of the occupational ranking to have smaller the r"Galative frequencies, while the middle categories, clerical, < and operatives, or about 59 percent of all those in the labor have higher than average relative frequencies. Approximately (3*: all trips are taken by those not in the labor force. Fifty F3€3r"cent of social trips are made by these individuals, includi lJffiemnployed, and housewives, however. No doubt the presence 01 r"umber of females in this latter group, as well as in clerica r‘<3 Ips explain the higher relative social trip frequencies of groups. As can be seen from the variable, sex, females make more an average share of social trips, accounting for approximately percent of all social trips made. Non—whites make more social Q('Drnpared to total trips than do whites, the former correspondi ' all trips than do higher income individuals. This relationship is eaEspecially important because it is contrary to the only previous trip 53‘fudy remotely related to the study here. Findings for Chicago have $3hown, as discussed above, that higher income individuals make more E3<>cial-recreation trips than do lower income individuals (Sato, 1965). ‘£\F>parently lower class people substitute for non—home recreation and £3htertainment the less expensive, in-the—home activities of visiting 12"“iends, as was previously suggested. The data points in the diagram of age and relative social trip f:"€3quency, Figure 5, form a generally negative slope. By omitting all 52 individuals twenty years of age and younger, the majority : non-drivers, age of individuals and vehicular social trip highly correlated (r = -0.87, P<.01, N = 14). Another variable, suggested in the last section as be in predicting the number of social trips made by individua household size. The ten classes of household size used in Interview Survey and shown in Table 5 were correlated with frequency of social trips made for each household size cla: was, as expected, a negative correlation (r = -0.58, P = :Showing that larger families substitute more in—the-home a Social travel than do smaller families. These three regressions were conducted individually 0 <33 d not exist on a small level of aggregation which could I i rIto a common regression problem. The separate regression: 1‘Eint relationships to exist between social trips and incom« h<>usehold size and, therefore, constitute significant find Areal Aggregation Method The second method for explaining social trip frequenc <3<>mmon data base on which all variables can be aggregated. LJhit provided the necessary data unit of analysis. In thi \Iaariables can be entered into the same regression, but res ‘wVEeakened because of the heterogeneity of a large data unit <3€39rees of freedom. Nevertheless, this type of analysis w The only common unit on which data were gathered and! ‘<3C>ntained on each record of data was the census tract. Si +r‘acts were demarcated in the Five—Township Area and these 53 the regression analysis. Since the census tract level of analysis is a rather gross level of data aggregation, with approximately 4000 persons per tract, the population of each is somewhat heterogeneous in socio—economic and demographic characteristics, yielding large sample variability. Nonetheless, the relative frequency of social trips for each census tract was computed by dividing the percent of social trips for a tract by the percent of all trips for that tract. Social trip frequency was considered the dependent variable and it was regressed with median family income, average age, average household size, population density, and automobile ownership for each tract. In this regression, income and social trip frequency had a simple correlation of r = —0.23 (P = .08, N = 60). The other variables entered in the analysis were not significant at the P = .10 level. The multiple correlation coefficient for the regression was R = 0.27, explaining only 7% percent of the total variation. It is surprising that any relationship at this heterogeneous census tract level is significant. This regression points out a definite negative relationship between social trip frequency and income. Frequently, urban planners find that the best estimator of total trip generation in an area is the population of that area. Some form <>f population measurement is almost always present in their trip genera— 1'ion equations, and is highly correlated with the number of trips Prxbduced (Chicago Area Transportation Study, 1960). The frequency of SOCial trips per census tract for the study area was regressed with two measures of population, the tract's household population and the fFact's group quarters population. The equation is Y = 519 + 0.24 HH POP + 0.03 GO POP. 54 The resulting multiple correlation coefficient was R = +0.52 (P = .01, yielding a multiple coefficient of determination of 0.26, with a stands error of the mean of 0.46. Again, the variability and uniqueness of the social trip is shown. The correlations between income and social trip frequency can be shown, to some degree, by mapping the patterns. Figure 6 shows a computer map of the distribution of income by census tract for the Five-Township Area, and Figure 7 shows relative social trip frequency by census tract for Lansing and East Lansing. The computer program SYMAP (1969) was used to construct these maps. For each figure, contour lines emerge from a data plane at selecte levels which are determined from the scale of the map and the range of data. For Figures 6 and 7 the values for data points (census tracts) have been divided into quintiles. Dark shading indicates higher values For both figures the approximate locations of Lansing's and East Lansing's CBD (Central Business District) are shown as reference points Several areas of noticeably low and high income can be seen in Figure 6. The downtown section, near the CBD, lies in the lowest quintile of income. This section comprises the largest portion of Negroes in the city. Michigan State University's campus, south of the East Lansing CBD, also lies in the lowest quintile of income, basically due to the large proportion of student and unemployed individuals livir here. To the southwest of the Lansing CBD is one of the highest income areas of the city. This is the Lansing Country Club—Pleasant Grove neighborhood. The westernmost township, Delta Township, has an area of high income in the western two—thirds, with somewhat less average income in its eastern portion. Some of the residents in the western Figure 6. 55 Distribution of Income by Census Tract for the Five—Township Area. 56 =====§====§=====.====. _:_ 12211.1 11515.2. F|GURE 6 57 Figure 7. Relative Social Trip Frequency by Census Tract for Lansing—East Lansing. 58 OVNKY— N172: 8.7mm. Nuts. 3:0 fifilfll 552:: .5: =53 1.32341. ....... .2. t . ..!$.li...¥.....3.nloilx. I :. 'i.:i§..§§ a. 59 part of Delta Township are well-to-do farmers who raise the median income of the area. Delta Township's data for this map are given by only three census tracts, accounting for the lack of detail in this portion of Figure 6. The easternmost township of the study area is Meridian Township, which includes the communities of Okemos and Haslett. The portion of low income on the map in this township in the extreme northwest corner corresponds to the Towar Gardens suburb (also shown in Figures 12 and 14). The northeast corner of the township includes Lake Lansing and Haslett and is shown to be a low income area also. A continuous area of high income is present in the eastern and central portions of this township, running generally north and south. The northern end begins in eastern Dewitt Township and, moving south, includes the Groesbeck area of Lansing, and the Whitehills and adjacent Strathmore-Avendale neighborhoods. The high income area continues to the southeast, including Okemos and the Indian Hills area. The latter place names are shown on Figures 12 and 14. Figure 7 shows the spatial distribution of relative social trip frequency by census tract for Lansing and East Lansing. Since relative social trip frequency and income, as measured by census tracts, are negatively correlated (r = -0.24), it can be said, in a figurative sense, that Figure 6 and 7 correlate at -0.24. Figure 7 is on a larger scale than Figure 6 and the outline of Figure 7 is shown on Figure 6. For Figure 7, low relative frequencies characterize the East Lansing area. This is true for both the high income residential areas to the north and for the low income student housing areas to the south, the latter being deficient in vehicular trips. In the city of Lansing, no 60 obvious relationship can be seen between relative social trip frequency and income, although in the lower income central portion of Lansing the majority of tracts have above average relative frequencies. CHAPTER III SOCIAL TRIP DISTANCE SENSITIVITY An important consideration in a study of spatial human interaction is the friction of distance experienced by individuals. Although it is presumed that social travel will exhibit a distance decay function similar to that found for most other human spatial interaction, the degree to which this is true remains to be tested. Few studies have examined distance decay changes with occupation (Wheeler, 1969), and none have done it for social travel. This chapter is divided into two parts. The first section will examine the diminuation of social inter— action with increasing distance. The second section will examine social trip length by occupational status. Distance Decay of Social Trips In order to test the distance decay concept and the effect of distance on social interaction, an analysis was performed with social trips between traffic districts. A traffic district is somewhat smaller than a census tract. There are eighty in the study area. Measurement was made on the traffic district level in order to gain a finer discrimi— nation of distance than could be obtained at the census tract level. The first stage of the analysis was to tabulate the frequency of unexpanded trips between and within cell districts. Inter—district airline distances were then computed between each of the eighty traffic districts. Distances were measured from the center of each district and were measured to the nearest one-fifth mile. Trips with their origin and destination in the same traffic district were assigned a value 61 62 according to the distance between traffic zones that they connected.1 If trips remained within a zone, they were assigned a distance of one- fifth mile, or the approximate radius of an average size traffic zone. Forty—four units of distance were used, each unit one-fifth mile larger than the previous one. The frequency of trips between each district was then entered into the appropriate cell of a table, from one to forty-four, depending on the distance between the two districts. An idea of the nature of the distance decay relationship can be gained by plotting the values on a graph, Figure 8. 0n the y-axis is frequency of social trips and on the x—axis is distance. The scatter of points on the graph shows two interesting elements: 1) the decline of points is not smooth, and a somewhat large variation about a least squares line exists; and 2) the least squares line is not linear, but concave outward. In the simple regression with frequency of trips as the dependent variable and distance traveled as the independent variable, a correlation of r = —0.66 (P<.01, N = 44) was found, explaining 43 percent of the total variation in trip frequency. Distance, therefore, has a relatively strong negative effect on social interaction. It was expected that a moving mean transformation to smooth the data may improve the relationship, since the distance units (one—fifth mile), as well as the traffic district level of analysis, are arbitrarily chosen data units. Therefore, it was felt that the use of a moving 1Traffic zones are smaller than traffic districts, and there are approximately 300 traffic zones in the study area. Trip data have been summarized on this basis (traffic zone) for some sections of the analysis, including the next section of this chapter. Traffic zone boundary determinants include major roads, political boundaries, land use homogeneity, census tract boundaries, natural features such as rivers, and minimum and maximum land area limitations. The 300 traffic zones are condensed into eighty traffic districts, using the applicable traffic zone determinants to delineate the districts. 63 m mm30_u mud—E Z. muzm >0Zm50mm¢ n5: (3.50m Sdllll. “"305 $0 ADNII‘IDJI! 64 mean on the trip frequency data would not be harmful on theoretical grounds. Three—point moving means of the original trip frequencies were computed, and the resulting data points were regressed with distance. The correlation of this run was r = -0.78 (P<.01, N = 44); the initial relationship was improved by 28 percent. This correlation is still significant at the P = .01 level, even though the number of degrees of freedom are reduced to one—third the original amount because of the use of the moving mean. The use of the moving mean suggests that if a larger sample was available, local variations in the data may well be reduced, resulting in stronger relationships than can be shoWn here in the simple regression with untransformed frequencies. The concavity of the scatter plot was due primarily to the steep negative sloping of the graph for the short distances, especially for distances less than one mile. Large frequencies at the short distances added an upper tail to the scatter of points. A noticeable flattening out of the graph was observed, beginning approximately one mile from the origin. It was thought that a logarithmic transformation of distance would help straighten the scatter of points, and thus improve the statistical relationship and explained variation. Therefore, the logarithm of the distance was computed and regressed with social trip frequencies. A strong correlation resulted (r = —O.84, P<.01, N = 44), explaining 71 percent of the total variation in the frequency of social trips. By transforming the raw distance units to log distance units, an extra 38 percent of the variation over the initial run was explained, showing the non—linearity of the distance — frequency relationship for this data. A higher correlation with the log transfor— mation suggests that human behavior does not vary linearly with distance, but maybe more closely approximated by raising distance to a power. 65 Next, both transformed variables, the moving mean of frequencies, and the log of distance units, were entered into the same regression. The strength of the relationship rose still further (r = -0.93, B(.01, N = 44), explaining 86 percent of the total variation in the data. This was a total improvement of 43 percent over the original analysis which used raw variables. Figure 9 shows the relationships between the two transformed variables. Results for the four distance decay problems are summarized in Table 6. The negative curvilinear relationship between frequency of social trips and distance is explainable in the light of present theory. The steep upper tail of the scatter of points shows a sharp distance decay, as individuals most often interact with people living very near them. The upper tail could be interpreted as a neighborhood component of social interaction. These social contacts live in the same neighborhood as or very near to the trip maker. After a point, the graph levels off substantially, meaning that after a certain threshold of distance is reached, which is probably dependent on the population density, people interact over longer distances and the frequency of social trips tapers off much more slowly. The contacts several blocks to a mile and more away represent individuals who have come into social contact with people through their unique set of activities. These activities include work, school and clubs, to mention a few. These social contacts might be called a social network component of social interaction. People are not as sensitive to distance for this component, thus causing the distance decay curve to be flatter at longer distances. A possible explanation for the flattening of the scatter, beginning at distances of several blocks to a mile, is that people make a small ” a ,_ ‘l .1 m was? n. uni! 00.. O. — O 740...... _ . w M O _ N I1 0 9 w I. V N ”w m. i I m. ICON n I.- N 3 A 00m QmEmOmmZ/EH $.40 I._._>> mUZ/fimfi >m_ >UZmDOmmn. die 67 TABLE 6 DISTANCE DECAY ANALYSIS FOR SOCIAL TRIPS Distance Logarithm Distance 2 2 2 2 r r r r r r increase increase Frequency of Social Trips -0.66 0.43 0.43 -O.84 0.71 0.38 Moving Mean of Frequency -0.78 0.61 0.28 -0.93 0.86 0.43 All r's significant at P = .01. 68 number of social trips compared to other types of trips and regard social trips as a luxury. Individuals are willing to travel the necessary distance, up to a point, to interact with whom they choose, rather than travel to the nearest person available. This is because individuals become personally involved at the destination, and expect a certain amount of personal, psychological rewards there. They are willing to travel extra distance for larger rewards at the destination, making them less distance sensitive for social trips than they might be for other types of trips. It is thought, therefore, that the upper tail of the scatter of social interaction with distance represents a neighborhood component and that the lower tail represents a social network component of social interaction. Reasons for the shape of each have been forwarded, perhaps lending explanation to the social trip distance decay phenomenon, rather than merely describing rates of decline, as is often done for other distance decay relationships. Arguments have been made for explaining such relationships in science (Kuhn, 1962). These two aSpects of social interaction —- the neighborhood and social interaction components —— will be examined further in Chapter V when the study of a particular neighborhood in the study area is undertaken. Social Trip Lenqth and Occupational Status In this section of Chapter III, mean social trip length is considered. It is hypothesized that the mean social trip length is greater for individuals of high occupational status than it is for those of low occupational status. By considering social trip length for different occupational classes, one is confronted with the questions of 1) whether a difference exists in social interaction distance sensitivity for 69 different classes of people, and 2) whether varying social classes exhibit different inter-residential separation. Either of these two factors could have an influence on the groups' mean social trip lengths. The mean social trip length for social classes gives some answers to the above questions. However, spatial opportunities for social interaction vary from urban area to urban area, depending on the associated urban Spatial distribution of individuals. In order to measure an occupational class's social interaction distance sensitivity, it is necessary to compare the mean length of social trips for the class to a comparable measure of the class's inter-residential separation. An attempt will be made below to explain mean social trip length for different occupational classes by comparing it with the mean inter- residential separation of the class. If the residential structure of the study area approximates classical residential rent theory, then the mean length of social trips should increase with an increase in occupational status, ceteris garibus. Urban rent theory assumes a declining rent gradient away from the CBD. A household with a given preference for Space is seen as attempting to maximize the utility of its income by locating a certain distance from the CBD, trading off tranSport inputs for savings in location rent, thus facilitating the consumption of more Space. Therefore, population density declines with increasing distance from the CBD, and households identical in all reSpects will live at increasing distances from the CBD as a function of their income. The Lansing area is clearly not a model example of urban rent theory, as East Lansing provides a subsidiary nucleus. Nevertheless, it is hypothesized that the minimum inter-residential separation between individuals of an occupational group will rise as the status of the group rises. If this relationship holds, then the 70 mean social trip length may well increase as occupational status increases. The minimum inter—residential separation between individuals of eight occupational classes is computed below. Two basic data inputs were necessary for this analysis. One was a 300 X 300 matrix of inter- traffic zone distances. The other was a 400 X 8 matrix of the frequency of individuals in each of eight occupational classes for each traffic zone. Each data input was computer-generated and punched on cards. The linear programming model used to solve the transportation problem of optimum allocation of tranSported goods from m supply places to n demand points is used to give a measure of minimum inter-residential separation of a given occupation. The output of the model is the shortest possible aggregate distance for all individuals Xk of occupational class k from the residences of k, S? (supply places), to residences of k, D: (demand points), as computed between zones. A unique feature of the application of the linear programming model of transportation to this problem is that every household of a particular social type acts both as a supply and demand unit, so that the total supply of a zone equals the total demand of the same zone. The supply of one zone cannot be used to fill the demand of the same zone, however, or the shipments effectively would be zero. This means that the results will be aggregated on the zone level, which is a small enough unit of analysis to give comparable results, but more important, it is the same data unit on which trip length was computed. Associated with the movement of individuals between zones is a cost, Cij’ of travel from i to j, which is considered to be a linear function of distance in this analysis. In the objective function of the linear programming model, total 71 cost, Zk, of moving all individuals of occupational class k is minimized. The objective function is expressed as k m n k Z =: Z Xi'ci" where (m=n) i-1 j-1 J J subject to the constraints that total supply from residences and total demand at residences equal the number of individuals shipped. This is written ” k 2: xi. = s. (i = 1,2,...m), J-l J J and m k 2: x.. = 0. (j = 1,2,...n), i-l 'J J respectively. 0r, total individuals moving from residences is the same as the total amount demanded at residences, i—1 j-l Finally, movements cannot be zero or negative, or the solution would be mathematically trivial: The average minimum inter—residential separation, MIS, for occupational class k is U The data described above were organized into eight matrices, using the Tucker Format. Row one of a matrix gives the destinations and row n of the matrix gives the demands for each destination. Column one of the matrix gives the origins and column n of the matrix gives the supply at each origin. The cells of the remaining n-2 X m-2 square matrix contained costs (inter-zone distances) between each pair 72 of supply and demand points. Each of the eight matrices was then used as input into the eight linear programming problems. MIS values for each occupation are shown in Table 7. High values of MIS for the highly ranked occupational groups indicate that these groups have greater mean separation of residences between individuals of that group. Low values for low occupational status groups suggest residential concentration of these groups. AS can be observed, however, the relationship is not a perfect one. Nevertheless, the assumption of residential location of urban land rent theory, as measured by MIS for individuals of occupational classes, at least, generally seems to hold for the Lansing area. The mean social trip distance by occupational class is shown in Table 8. An examination of the distances for the occupational ranking shows a general decrease in distance with an increase in status. The two extreme classes, the lower being laborers, (a mean social trip distance of only 1.70 miles), and the upper being professionals (a mean social trip distance of 2.49 miles), are the only exceptions to the general relationship. If these two extreme cases are omitted, a perfect negative relationship exists between the occupational status and associated mean distance traveled for social contacts. Whether or not the two extreme cases are omitted, no support can be given to the hypothesis that lower status individuals make shorter average social trips. Lower status individuals are apparently not more distance sensitive than other individuals, and may even be less sensitive. In fact, the findings lend support to the Smith (1956) hypothesis that lower income individuals travel farther for social contacts due to the presence of generally Shorter residential tenure. Individuals at the 73 TABLE 7 AVERAGE MINIMUM SEPARATION DISTANCE BY OCCUPATIONAL CLASS Occupational Class Distance (miles) Laborers 1.03 Service Workers 1.35 Operatives 1.63 Craftsmen and Foremen 1.40 Clerical and Kindred Workers 1.53 Sales Workers 1.68 Managers 2.11 Professionals and Technical Workers 2.01 74 TABLE 8 MEAN SOCIAL TRIP DISTANCE BY OCCUPATIONAL CLASS Occupational Class Distance (miles) Laborers 1.70 Service Workers 3.05 Operatives 2.93 Craftsmen and Foremen 2.85 Clerical and Kindred Workers 2.61 Sales Workers 2.43 Managers 2.29 Professionals and Technical Workers 2.49 75 upper end of the occupational ranking may well live in more stable neighborhoods, a factor which would promote more friendships in the local area. Apparently there is little relationship between the MIS of a class and the class's mean distance of vehicular social trips. This may be different for non-vehicular social trips, which are, obviously, more important in densely populated areas. These findings Show that inter- residential distances between people of the same occupation are rather small compared to home—work distances (Wheeler, 1967, 1968). Yet, because social interaction is so personal, individuals prefer to travel the necessary distance, whatever it might be, to see a good friend, rather than going to the closest person. Therefore, because individuals expect rewards from a person or group that they become personally involved with at the destination, they are willing to travel to the individual's location, and the MIS seems to have little relevance. This idea, discussed in the previous section of this chapter, is discussed further in Chapter VI. CHAPTER IV URBAN SOCIAL INTERACTION PATTERNS This stage of the analysis will attempt to answer the question of the extent to which urban social interaction patterns exist and can be identified in the study area. This question is actually part of a larger question of whether there is a direct connection between social structure and social interaction within an urban area. If social trips among residents in the Lansing area are plotted, with a straight line linking the origin and destination of each trip, one can identify portions of the study area that are functionally related, socially. This mapping will Show if "social areas" do indeed exist, and also if different neighborhoods are linked to one another. If this linkage occurs, the channels (desire lines) of interaction between neighborhoods will be shown. This chapter is divided into three sections. The first deals with the method of constructing flow maps of social trips. The second uses these flow maps to help determine the extent to which parts of the study area are functionally tied to one another. The constructed flow maps of social trips are examined in this section. In the third section, an attempt is made to identify discrete cohesive social areas in the larger study area. To accomplish this, an origin-destination matrix of social trips is factor analyzed to reveal portions of the study area with similar patterns of social trip origins and destinations. 76 77 Generating Flow Mags Social trips are displayed graphically in Figures 10A, 108, 11A, and 118. These maps were constructed by the calcomp plotter, using the program, MAPIT (Kern, 1969). There were two basic data inputs involved in the program. One was the "individual's" deck which consisted of cards, each representing one social trip made by an individual. Each card contained coordinates of the trip—maker's residence, or the origin of the trip, and the identification number of the traffic zone of destination. Therefore, origin and destination information necessary for mapping trips was available. The individual's deck was punched directly from the tape. The second data input was the city deck, which consisted of cards, each of which included the identification number of the zone, as well as the zone's associated coordinates and its size. Therefore, the individual's deck supplied the points of origin of trips and the identification number of the points of destination. The program then located the destinations by finding coordinates in the city deck corresponding to the identification numbers. The coordinates for the traffic zones of destination for the study area that were necessary for the city deck were coded and punched with the geodigitizer. The process requires the use of a base map with the locations of data points on it. In this case, data points were considered to be centers of traffic zones. A map such as this, with the locations of all traffic zones, did not exist because of the large variation in the Size of traffic zones in the Tri—County area. Such a map was constructed for the Five—Township area, however, by manually transferring the locat’ions of the traffic zones from a series of smaller size maps of 78 Figure 10B. Social Trip Flow Map for Households with Less Than Median Income. Figure 10A. Social Trip Flow Map for Households with Greater Than Median Income. 79 I‘MIlE E o SOCIAL TRIP IN LANSING- EAST LANSING IANn Virtmttv AND VIFINITY 80 Figure 118. Social Trip Flow Map for Michigan State University Students. Figure 11A. Social Trip Flow Map for NonJWhites. 81 mHH mm30_u Qz< :2 <_ Z O yHHzHuH> ©z< ozflmz<4 em