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Perceived Clique Definition in Ego-Centered Networks

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Perceived Clique Definition in Ego-Centered Networks PERCEIVED CLIQUE DEFINITION IN EGO -CENTERED NETWORKS BY CHRISTOPHER MCCARTY A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1992 ACKNOWLEDGMENTS This dissertation is dedicated to H. Russell Bernard and Peter D. Killworth who were there for me when I needed them most; to my son Sean who is my pride and joy; and to Gary Toops (a promise is a promise). ii . Dissertation Presented to the Graduate School ot the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy PERCEIVED CLIQUE DEFINITION IN EGO -CENTERED NETWORKS By Christopher McCarty December 1992 Chairman: H. Russell Bernard Major Department: Anthropology Previous research using ego-centered networks is based on the assumption that the explanations for strongly tied cliques, or subgroups, are obvious and can be used as cues to elicit clique membership. Such cues do elicit lists of network alters, but the claim that these are cliques which the informant naturally perceives has been unsubstantiated. This can only be done by allowing informants to freely define their network and measure network ties independently of any specific cues. Forty- seven informants were asked to respond to a computerized interviewing task which lasted from two to four hours. Informants free listed 60 people they knew, where knowing was loosely defined, yet constrained. Informants ranked on a scale of 1 to 5 how well they knew each alter. They then described how they used this 1 to 5 scale. Most time-consuming was the provision of a structured set of information about each alter, including a textual description of how the informant knew the alter. Finally, informants were asked to rank on a scale of 0 to 5 how well each unique pair of alters knew one another, a total of 1,770 pairs The final module resulted in 47 adjacency matrices which were analyzed with an overlapping clustering analysis to form cliques which iii were defined by high interknowing. Using the dossiers from each alter, these were coded into types, where a type explained the interknowing. Cliques were presented to a subset of 10 informants along with several randomly generated cliques to test the viability of the clustering algorithm and the coding scheme. In virtually all cases, true cliques were distinguished from phony cliques and the coding was found to be consistent with the informant's explanation. Attributes of these perceived types were then analyzed with respect to attributes of the informant, alters, network structure and concurrence with other types. In an attempt to estimate the error associated with my small nonprobability sample of 47 informants, a telephone survey was implemented to find the distribution of the types of social relations among Floridians. Some specific differences are noted. IV ! TABLE OF CONTENTS ACKNOWLEDGMENTS . ii ABSTRACT iii CHAPTERS 1 INTRODUCTION 1 2 A THEORY OF SOCIAL RELATIONS 3 Knowing Versus Social Relations Maintenance of 3 Relations !!!.!!! 6 3 SOCIAL NETWORKS 9 Introduction Development 9 of Network Theory. 11 Clique Detection !!!.!! Ego-centered 15 Versus Bounded Networks 20 The Status of Social Networks as a Science 24 4 METHODS 26 Computer Versus Paper Formats 26 The Sample 26 Data Gathering on Informants and Choosing Alters The 28 Autocorrelation Problem 30 Ranking Alters on Levels of Knowing ’ Alter Detail 31 Pair Rankings 37 Network 48 Dynamics 53 Summary of Alters !!!!!!!!.! 54 5 GROUPING ANALYSIS 56 Clustering Procedure 56 Cluster Types 58 Ego/raw Versus Non- ego/binary Verification 62 of Clusters 65 Variance Explained ’ Informant 66 Characteristics and Clusters 67 Within Cluster Similarity Correlations 69 ! 71 Factor Analysis on Cluster Type ' ! Overlap ! 73 75 Free Listing Order Recalculation ! ! 79 of Clusters 82 The Meaning of Clusters Telephone 84 Survey 85 Network Density Network 91 Degree !!!!!! 94 6 CASE STUDIES 97 V Introduction 97 Steve 98 Betty 100 Tony and Mary 104 Jennifer 109 Selected MDS Plots 113 7 DISCUSSION AND CONCLUSIONS 126 Experimental Method 126 Knowing 129 The Social Relation 130 Clique Definition 134 Conclusion 136 APPENDIX 138 REFERENCES 139 BIOGRAPHICAL SKETCH 144 VI . CHAPTER 1 INTRODUCTION Imagine a list that contains all of the people you have known in your life. If it were possible to dredge up such a list, some people on the list would not know others on the list, while some people would know others. Is it likely that these social relations occur randomly, or are there clear explanations which make it possible to predict them? Who you know, and how you know them, is a function of where you are, what you do, your likes and dislikes, and almost certainly, characteristics such as your gender, race and marital status. Therefore, the groupings, or subnetworks, of your global network are probably subject to the same phenomena. Who your relations know among your relations and , how they know them are a function of these same factors Furthermore, your position and relation to these groupings is not static. Time and life changes affect social relations. It is likely that each person has a global network of active relations or relations , which comprise the majority of their interaction and behavioral prediction, as well as a cumulative global network of all relations ever held. For an adult villager in the mountains of China, the list of current network actors may be very similar to his or her list of network actors ever known. People in such villages may grow old maintaining mostly the same set of relations they accumulated by age four. Additions to their network are most likely due to the births of potential members in the village. For mid- level executives in national American companies, where transfers and electronic communication are an ordinary part of life, the list of actors ever known is almost certainly much larger than their currently maintained list of actors. 1 2 In this thesis I will present the results of an experiment into knowing, and the definition of perceived subnetworks based on a given definition. The approach is presented as a return to the substance that early anthropologists studying network phenomena chose to examine, utilizing some of the methodological advancements that are the hallmark of contemporary network research. This work is a contribution to the field of social networks in identifying categories of subnetworks that are meaningful to informants. On a more general level, it is suggestive of the dynamism of personal networks , and the critical roles played by location and other variables in their formation. In the next chapter a theory about social relations serves to views as to how social relations are formed and maintained. Chapter 3 is a review of the history of social networks with , a particular focus on clique finding algorithms. Chapter 4 describes my methods, sample and some results relating to the ways in which informants used the concept of 'knowing'. Chapter 5 is the heart of the thesis, presenting all of the analysis based upon the results of the overlapping clustering analysis using the ADCLUS model, as well as the results of a telephone survey method used to verify the results from extended interviews with 47 informants. The sixth chapter consists of five case studies which help illustrate many of the concepts presented in Chapter 5. In the final chapter are discussions of the experimental procedure and conclusions. , , CHAPTER 2 A THEORY OF SOCIAL RELATIONS Knowing Versus Social Relations Babbie (1989) points out that the ambiguity of concepts in social science lead to an ironical cycle. For example, we observe behaviors, such as people visiting one another or sharing life experiences, and we perceive that these are related behaviors which we describe under the umbrella term 'knowing'. As we talk about these behaviors using the abbreviation 'knowing', we come to think it truly exists, rather than being a summary of many behaviors. Finally, we take to task the study of 'knowing' as a thing that exists, or even worse, use the word as a stimulus to evoke a definitive behavior across informants. Is it any wonder that estimators of network size which use 'knowing' as their stimulus for network tie verification vary wildly (Pool and Kochen, 1978; Burt, 1982; Bernard et al . 1987; Bernard et al . 1989; Freeman and Thompson, 1989)? When people talk about knowing someone, they are actually using an abstraction, or variant, of the concept of social relations. Unfortunately, knowing is a subjective term that is far from a standardized concept in social science. The limits of the concept of knowing are made abundantly clear when other languages and cultures are examined. Excluding the ambiguity of the term in its use among speakers of English, there is not a clear equivalent for 'knowing' in many languages. It is a tenuous term of questionable value as a central concept to network theory. We use the term because our informants have an understanding for it which we assume approximates the relation which interests us. That this definition varies across informants one rationale behind this thesis. 3 . 4 A reasonable alternative to the concept of knowing is the social relation, a term which has been used time and again by social scientists since Emile Durkheim. This concept is descriptive and general enough to include all specific relational concepts such as knowing, closeness or even love. As social network analysts, we are interested in the structure of social relations, their content, and how these phenomena interact in a lawlike manner. What, then, is a social relation? How do we decide a relation exists and how is it best described? It does not take long to realize that this is critical to the size and content of both the global network and any subgroupings.
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