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J This is to certify that the dissertation entitled Inequality and Heterogeneity in lnterorganizational Networks presented by Gaston J. Labadie has been accepted towards fulfillment of the requirements for /4 y degree in / M 3101- professor /\ Date; / /g%/ MS U is an Affirmative Action/Equal Opportunity Institution 0-12771 Msu LIBRARIES RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. 3 a") 3;: s. INEQUALITY AND HETEROGENEITY IN INTERORGANIZATIONAL NETWORKS BY Gaston J. Labadie A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Sociology 1986 Copyright by GASTON J. LABADIE 1986 ABSTRACT INEQUALITY AND HETEROGENEITY IN INTERORGANIZATIONAL NETWORKS by Gaston J. Labadie Blau's macro-structural theory on the effects that ine- quality and heterogeneity have on rates and patterns of interaction is extended and tested at the interorganizatio- nal level. Major limitations of theoretical approaches to interorganizational relations, as well as the network tech- niques and approaches employed to analyze them, are re- viewed. Blau‘s theory and some of its major limitations are introduced and discussed. On the basis of the organizational literature, nominal and graduated parameters of organiza- tions are distinguished. The nominal parameters employed are whether the organization is public or private and what type of activity is practiced. Graduated parameters are consi- dered to be size, as measured by number of employees, budget size, power, influence and prestige. Hypotheses as to the effects of heterogeneity and ine- quality on the rates of out—group relations and the status distance among associates are tested in twelve interorgani- zational networks from twelve Midwestern cities. Measures of power, influence and prestige are performed, for substantive. reasons with different algorithms, and a relational inequa- lity measure is extended so as to account for the possibili- ty of multiple ties for each actor. Two regression models that establish curviliner relationships between heterogenei- ty and inequality and their respective dependent variables, are estimated by OLS. The dependent variables are indexes calculated on two different exchange dimensions: information exchange and cooperation among organizations. Major findings fail to confirm the expected relation- ships for heterogeneity but confirm the positive relation- ship between inequality and the status distance among asso- ciates. This "paradox of inequality" is interpreted in terms of systems' theory statements on the relationship between complexity in the environment and complexity in the interorganizational network. The consequences of the find- ings for Blau's theory and for interorganizational relations and cooperation are discussed. In the conclusion the main limitations and difficulties encountered in this research are reviewed and suggestions for further theoretical and empirical work are offered. ACKNOWLEDGEMENTS I wish these pages came closer to the masterpiece I had in mind when I dreamt about writing my doctoral disserta- tion. I wish they even came close to what I had in mind when I wrote my proposal. On one hand, however, I do not suppose I am the first to run short of his expectations. On the other hand, I suppose every student faces the reality of limited resources, whatever these may be. Time was among those I was the most keenly aware of. The above notwith- standing, this dissertation is the culmination of my gra- duate studies in the US. A learning experience that was extremely rewarding, and not only in its intellectual as- pects. Many people enriched my experience while in the U.S. and helped, whether knowingly or unknowingly, at different stages of my personal and professional development. In particular, with respect to the dissertation, all the members of my committee provided helpful comments. Philip Marcus, the chair of my dissertation committee, III "made" me work for him with the kind of social network data that is used in this resaearch. Something that I would not have done just for myself. In so doing, he provided much needed financial support. Besides, and foremost, he informa— lly oriented me and encouraged my study of the social net- works literature (as well as many others) in a department where there is not one course taught on the topic. J. A. Beegle, my advisor during my graduate studies, not only provided useful suggestions but he was also a most patient and helpful editor. He has also provided support of all kinds and in all amounts during the course of my stu- dies. In fact, the Beegles have played a major role in my own and my wife's social support network. This is, of cour- se, a sociologically alienated way of saying that they are very dear to us. Tom Conner and Craig Harris have substantially improved the quality of the final version of this dissertation with their comments. Contact with them during my studies was always instructive and gratifying. Frank Camilleri was not a member of my comittee but he might as well have been. He provided, as usual, very helpful critical comments. He has also been my preferred "methodolo- gical foil" (if there can be such a thing), as well as a IV constant example of critical analytical thought. Time was indeed a constraint in this dissertation. Its completion would have been impossible without the support that Pat Terry, a colleague and friend, provided, in parti- cular with respect to the assistance in computer-related matters, but in many conceptual issues as well. Professors R. Burt, J. Skvoretz, and L. Freeman were kind enough to send helpful materials and computer programs from other Universities. Intelectual and affective support was also provided in a general sense by countless other people, at different stages, from different professions, from different nationa- lities, all of whom cannot possibly be mentioned but who have all enlightened my perception and appreciation of this world and have enriched this experience. Ines, our Colombian friend for all these years, played a particular role, but she was certainly not the only one. I am sure some of the friendships I have developed here are among the most en- during I will have. When one belongs to two worlds, support is needed from the two of them. It was provided, as usual, by my parents and brother - my family as a whole -; and by Ana —who shared both of my worlds-, first as my girlfriend in Uru- guay, and more recently in the U.S., as my wife. Word of mouth has it in my family that my grandmother used to say that books were the gems that intellectuals gave (or dedicated ) as presents. While a dissertation is not a book, and this one in particular may not be a gem, I would like to dedicate this work to Ulises Graceras. Many things have passed by since he was my professor, then my mentor and, finally, in so doing, became my friend. We may agree or disagree on many issues - and indeed we do - but the fact is that it was his model as a sociologist and his way of thin- king that were instrumental in motivating me to become one. VI TABLE OF CONTENTS Page LIST OF TABLES OOOOOOOOOOOOOOOOOIOOOOOOOOOOOOOOOOOOOO x INTRODUCTION 0.000000000000000000000000000000000000 1 CHAPTER 1 " SITUATING THE PROBLEM 00000000000000... 7 Organizations as Actors: Interorgani- zational Networks ..................... 7 Blau's Conceptual Framework ........... 16 CHAPTER 2 - INEQUALITY AND HETEROGENEITY IN INTER- ORGANIZATIONAL NETWORKS O O O O O O C O O O O O O O 25 Difficulties and Limitations of the Theory 0.0.0.000...OOOOOOOOOOOOOOOOOOOO 25 Nominal Parameters in Organizations ... 38 Graduated Parameters in Organizations .. 42 VII CHAPTER 3 - STATEMENT OF THE PROBLEM AND HYPOTHESES . 48V ResearCh PIOblem 00000000000000.0000... 48 Hypotheses 0000.000000.00.00.0000000000 49 CHAPTER 4 - METHODOLOGICAL PROCEDURES ............. 54 Data 000000000000000000000000.000000000 S4 Operationalization and Measurement .... 56 StatiStical AnaIYSiS 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 65 CHAPTER 5 - FINDINGS AND DISCUSSION ooooooooooooooo 68 Findings 00.0....000000.000000000000000 68 DiSCUSSion 00.0.0000...000.000.0000.... 84 SUMMARY AND CONCLUSIONS 0.00000000000000000000000000 92 NOTES 00.00.00.00000000000.00000000000000.0000000000 1““ APPENDIX 1 - PERCENTAGE NON-RESPONSE oooooooooooooooooo 105 VIII APPENDIX Z-QUESTIONS 00.00000000000000000000000000000 106 APPENDIX 3 -COMPUTER PROGRAM 0.0.0.0...000000000...... 107 APPENDIX 4 - COMPONENTS OF INTERSECTION AND CONSOLIDA- TION INDEXES AND THEIR RELIABILITY .... 119 REFERENCES 0000.00.00.0000000.000.0000...0000.00.00... 12“ IX TABLE LIST OF TABLES Effects of Heterogeneity Along Nominal Para- meters Public/Private and Type of Activity on Two Exchange Dimensions ....................... Ratio of Out to In Ties for the Groups Along the Nominal Parameters for Two Exchange Di- meDSions OOOOOOOOOOOOOOO0.000000...0.00.0000... Effects of Status-Diversity Along All Gradua- ted Parameters on Two Exchange Dimensions ..... Effects of Inequality Along Graduated Parame- ters on Two Exchange Dimensions ............... Effects of Multiple Consolidation of Gradua- ted Parameters, With Intersection of Nominal Parameters Controlled, on Two Exchange Dimen- sions Page 68 72 74 77 81 INTRODUCTION The concept of social structure is used in different ways by different authors and it is by no means an unequi- vocal concept in sociology. 0n the one hand, its ambiguity stems from the now classical distinction between two ap- proaches: the "linguistic or French structuralism" (e.g., Saussure, 1959; Levi-Strauss, 1963; 1969)1 and the structu- ralism of the British social anthropologists (e.g., Radcli- ffe-Brown, 1957; Nadel, 1957), to which the Marxist version could be added (e.g. Althusser, 197G; Althusser and Balibar, 1970; Poulantzas, 1975). On the other hand, the ambiguity of the concept is generated because there seems to be little consensus with respect to the concept even in each of the various traditions (Blau, 1975; Merton, 1975; Leach, 1981; Rossi, 1981; 1983; Heydebrand, 1981). A few convergences can be found, however. Whatever the epistemological orientation of the author, most writers agree that social structure refers to emergent properties that do not characterize the separate elements that compose the aggregate (Blau, 1981). Most agree also, in that social structure is a system with a hierarchy of levels (Miller, 1965; Harary and Batell, 1981). Those that can be included within the epistemological orientation of the British anthropologists,2 would loosely adhere to a concept of social structure as a "regular arrangement of social rela- tions that result from laws operating over time in a per- sistent though, not necessarily unchanging fashion" (Hol- land and Leinhardt, 1977: 386). Among them, there is also an increasing consensus for the idea that social' networks should play a major role in whatever structural concep- tualization is proposed (Blau, 1975; Goode, 1975; Coleman, 1975; Homans, 1975; Holland and Leinhardt, 1977). To the extent that for some structural analysis is identical to network analysis (Berkowitz, 1982; Wellman, 1983). While the latter assimilation may be considered an exageration, the concept of social network does provide a formalization of most interactional systems that uses an explicit mathe- matical representation: a set of relationships shown in a matrix (Freeman, 1980), which in turn can be the object of multiple algebras. Consequently, the least ambitious claim that can be made with respect to the relationship between social networks and social structure is that the former provides a representation, formalization, and calculus for the latter. Burt is even more radical: "At once a connection between micro and macro level social theory as well as an epistemic link between abstract concepts and empirical research, network models offer a powerful framework for describing so- cial differentiation among actors in a system"(1980:79) While there are different ways of conceptualizing social networks (see review in Burt, 1980), few substantive theo- ries of the structure of networks are available. According to Berkowitz, "The relationships between the constituent parts or elements of this paradigm itself have yet to be arti- culated in detail" (1982:154). All these aspects of the notion of social structure are present in the literature on interorganizational net- works, to the extent that an interorganizational concept of social structure and a new actor have been introduced. As Warriner suggests: "The organization is the acting unit , and‘ its activity systems are the acts that are observed. This implies that societal structure at this level is no longer conceived in terms of persons or of actors in positions, but rather in positions embedded in orga- nized acting units" (1981: 187) In fact, these organized acting units or corporate actors interact with each other and are able to draw signi- ficantly larger amounts of resources than would be possible for individual actors (Coleman, 1974; 1982). Research on interorganizational relations (IOR), howe- ver, has rarely treated interorganizational behavior as subject to social structural opportunities and constraints similar to individual behavior. One recent and notable theoretical attempt to explain how social structure influences the extent of interrela- tions and associations among individuals has been proposed by Blau (1977). The theory does not explicitly address the dynamics of social networks, but to the extent that it addresses any behavior that symmetrically involves two or more actors, its application to them should be most fruit- ful. In fact, some attempts have already been made ( Rytina and Morgan, 1982). Although Blau's theory is deductive, with a quantita- tive conception of social structure and suggested operatio- nalization of the main concepts, there have been very few attempts to test it empirically. The work has been cited in a host of different publications but the only serious attempts to test some propositions of the theory have been those of Blau et al., (1982); Blau et al., (1984); Blum, (1984); Blau and Blau (1982) and Sampson (1984). The former three tests used data on intermarriages, while the latter two used data on criminal victimization. More recently Blau and Schwartz (1984) have published further tests and some restatements of the theory using the same types of data. The present dissertation tests and extends Blau's theory as applied to interorganizational networks. In com- parison with the tests mentioned, interaction among organi- zations offers the advantage that its process is not appa- rently influenced to any great extent by spatial propinqui- ty as in the case of marriage or crime, and hence its 3 effects can be ruled out. Another improvement of the present study is that actual social networks are employed and that for the first time the theory is tested with multiple ties and not just one to one ties, as is the case with marriages. Using organizations as the unit of analysis, however, poses a series of problems since the theory is consistently concerned with predicting the behavior of groups or popu- lations of individuals and not groups or populations of organizations. Hence, the present work is not, stricto sensu, a test of Blau's theory. It is an attempt ,instead, to extend Blau's theory, increasing its scope andgenerali- ty. The present research uses data on twelve interorganiza- tional networks to perform this test. While new procedures and techniques are introduced and, for the first time, tables of tie-accounts are used, the study is preliminary in its nature. That is, sophisticated quantitative techni- ques are used to obtain qualitative evaluations of the effects of variables. This, of course, is not strange in structural analysis. Further, sometimes the number of cases precludes any definitive conclusion. The dissertation is organized in five chapters and a conclusion. The literature on interorganizational networks is reviewed in Chapter 1 and an attempt is made to show some limitations of the most commonly accepted approaches to interorganizational relations (IOR). It is also shown that organizations can be conceived as actors at a hierar- chical level different from that of individuals. Blau's theory is also introduced in that chapter. In Chapter 2 the main shortcomings of Blau's theory are reviewed in the context of its application to interorgani- zational behavior. Nominal and graduated parameters are determined on the basis of the existing literature. Main propositions and hypotheses to be tested are pre- sented in Chapter 3, followed by a discussion of their operationalization and measurement in Chapter 4. Chapter 5 presents and discusses the findings. In the conclusion the main advantages and limitations of the pre- sent research are discussed and suggestions are made for further research. CHAPTER 1 SITUATING THE PROBLEM The present chapter situates the problem of this dis- sertation within the context of two different kinds of literature. First, a review of the literature on interorga- nizational networks is done in order to show some limita- tions of the most commonly accepted theoretical and metho- dological approaches to interorganizational relations (IOR). An effort is made to show that complex organizations can be conceived as actors at a hierarchical level diffe- rent from that of individuals. Second, Blau's theoretical framework is introduced and reviewed, in an attempt to show that it should be applicable to any level of social organi- zation. ORGANIZATIONS AS ACTORS: INTERORGANIZATIONAL NETWORKS The fragmented and non cumulative IOR research (White and Vlasek, 1973), has yet to provide a consensus on theo- retical perspectives or levels of analysis (Aldrich, 1979; Laumann and Marsden, 1982). Granted, a network is usually used as the metaphor, with the organizations acting as nodes and their interrelationships as the links in the network. Most of the studies, however, have examined a focal organization, that is, one specific organization treated as the node of concern (an "ego"), and characteris- tics of that organization that are related to its in- terorganizational network are identified. Hence, the unit of analysis has been the organization and not the relation- ship. Three main types of studies can be distinguished in this tradition (Marcus and Smith, 1980): 1- Studies of the linkage patterns of a few organiza- tions (e.g., Aiken and Hage, 1968; Levine and White, 1963; Hall, 1977; Aldrich, 1976: Schmidt and Kochan, 1977). 2- Investigations of the interorganizational relation- ships of particular kinds of organizations, that deal with a single type of client (e.g., Lehman, 1975; Adamek and Lavin, 1974). 3- Investigations of portions of organizations' "role- sets" (Evan, 1966), with the focus on the respondent organizations (Aldrich, 1976; Hall, 1977). Other aproaches have included the effect of community va- riables on interorganizational relations (Turk, 1970; 1973; 1977) and some relational analysis of dyads (Paulson, 1976; Rogers, 1974). At a more global level, that is, taking into account systemic interrelations among organizations, models have been proposed to explain patterns in networks of interorga- nizational transfer of political information (Galaskiewicz, 1979); exchange among industrial sectors (Burt, 1982); in- ter-locking directorates of major corporations (Pennings, 1980; Mizruchi, 1982); and transactions in and among volun- tary associations (Knoke and Wood, 1981). Many alternative techniques have been used to analyze these networks (Burt, 1982; Burt and Minor, 1983; Berko- witz, 1982). Most of these techniques try to establish "socially homogeneous" subgroups, differing in the way they explicitly or implicitly conceive and create the groups. Two main traditions have been distinguished (Burt, 1983; Friedkin, 1984). One tradition, a relational one, attempts to analyse networks on the basis of the concept of cohesion or social proximity. On this basis cliques are established using graph theoretic models (Harary Norman and Cartwright, 1965, Alba, 1973; Alba and Kadushin, 1976; Alba and Moore, 1983; Seidman and Foster, 1978; Seidman, 1983) or using small space analysis and related distance based and multidimensional scaling measures (Laumann and Pappi, 1976; Galaskiewicz, 1979); with the potential for an ana- lytical integration of these two techniques (Freeman, 1983). Another tradition, a positional one, tries to establish the similarity among the patterns of interrela- tions that a series of actors have among themselves in order to determine if they are "structurally equivalent" (Lorrain and White, 1971; White et al., 1976; Burt, 1976; 1977).3 This approach employs procedures such as blockmode— 1ling ( Breiger et al.,l975; Arabie et al.,l978; Knoke and Wood, 1981) and related techniques ( Bonacich, 1980; Boyd, 1983; Carring-ton and Heil, 1981; Everett, 1983; 1984; White and Reitz, 1983; Wu, 1984). A few other techniques that try to accomplish the same purpose might prove to be useful but they have not been used in large networks. Examples are techniques based on informa- tion theory (Phillips and Conviser, 1972 ) or those based on algebraic topology and Q analysis (Atkin, 1977; Doreian, 1982). None of these techniques, however, provides "much in the way of even informal guidelines based on experience (to say nothing of formally justified standards) to guide an investigator in deciding whe- ther the structure resulting from a given analysis reflects anything more than random processes" (Lau- mann and Marsden, 1982: 330). It is probably too soon to determine if the actual application of log-linear models to multivariate directed Graphs (Fienberg and Wasserman, 1980; 1981; Fienberg, Meyer and Wasserman, 1981; Galaskiewicz and Marsden, 1978; Galas- kiewicz and Krohn, 1984; Holland and Leinhardt, 1981) will provide guidance in this respect. They do provide, by way of 10 using contingency table-like counts of types of relation- ships, a way of determining whether the structure is a result of random processes or not. A counting procedure of this sort is used in the present work too. The theoretical aspects are not much more promising. On one hand there seems to be some convergence among the global models in terms of using an exchange framework (White et al., 1971; Adamek and Lavin, 1974; Cook, 1977) or a resource dependence or a political economy approach (Zald, 1970; Ben- son, 1975; Aldrich, 1976; Pfeffer and Salancik, 1978; Lau- mann, Galaskiewicz and Marsden, 1978). As Knoke and Wood put it: "These various writers seem to have reached a con- sensus that an organization's ability to continue functioning in a competitive, resource-scarce envi- ronment depends on its ability to select an appro- priate internal structure and to establish interor- ganizational relations that sustain a steady flow of resources" (1981: 17) On the other hand, the population ecology approach also shows promise (Hannan and Freeman, 1977; Brittain and Free- man, 1980; Freeman and Hannan, 1983; Freeman et al.,l983; McPherson, 1983; Carroll,1984). While organizational ecology cannot be equated with the population ecology approach (Ca- rroll, 1984), most of the analytical developments as well as research have taken place in the latter area (see review in Carroll, 1984). The approach basically incorporates the 11 ecological models usually applied to animal populations into the study of populations of organizations with the conse- quent use of concepts such as organizational births, deaths, niches, that call attention to such processes as competition and mutualism. Hence, the diversity of organizational forms and their survival is accounted for in terms of the relative fit of the organizational form (species) and its environ- ment. No actual research on interorganizational networks has been performed with the population ecology approach, but the compatibility exists and the potential usefulness of the population ecology model for the study of IOR has already been noted (Aldrich, 1979; McKelvey, 1982). If nothing else this possibility should have sensitized researchers as to the importance of general parameters of the populations of organizations. All these approaches, however, provide only very general orientations for the researcher. The current state of the field is such, then, that "we lack a theoretical basis of comparable generality to that provided for networks of in- terpersonal relations by theories of balance (Heider, 1958) or cognitive consistency (Heise, 1979)" (Laumann and Mars— den, 1982:331). Since Blau's Inequality and Heterogeneity (1977) addre— sses the behavior of groups of individuals and not of orga- 12 nizations, the relevant issue to be determined here is whe- ther, on theoretical grounds, his theory should be appli- cable to the social structure conceived in interorganizatio— nal terms. Heydebrand (1973) has argued that conceptualiza- tions developed for intra-organizational phenomena to ex- plain individual behavior are not applicable for interorga- nizational behavior. White (1974), on the other hand has argued that decision making approaches could be used at both levels of analysis. In point of fact, the resource-dependen- ce and the population ecology approaches imply more or less explicitly that organizations are purposive eniities, trying to maximize or optimize some kind of utility (the ulti- mate one being survivability). A structural theory with a sufficient level of generali- ty should be applicable to both levels of analysis. Logical support for such a theory can be drawn from system concep- tualizations and the existence of hierarchies in social sys- tems. There is no apparent alpriori reason to assume that the general principles of organization of social systems should be different from those of any other system (Miller, 1965; 1976). Hierarchical organization of different levels seems to be a common principle of organization in biological systems, in languages and in ecosystems (Dawkins, 1976b; 13 Miller, 1976; Webster, 1979; Whyte, Wilson and Wilson, 1969; Pattee, 1973; Allen and Starr, 1982). It is, in fact, a definitional characteristic of the concept of system (Harary and Batell, 1981). Simon (1973; 1981) has argued that social systems tend to organize in a hierarchical way. Partial or near decompo- sability, that is, a relative independence of the compo- nents, would characterize the different levels. In fact, this hierarchical organization implies that the different levels act as filters and the environment of the units at one level is constituted by those units or Holons (Koes- tler, 1967) that are peers at the same level, or by units at a higher level. The notion of environment then is not a static one but is related to different "rythms", and it entails that some units (upper level) can await others and appear to be "fixed" since their change is perceived by lower level units as if it were not taking place. Upper levels, then, have different thresholds of information processing and input reception. In essence, this accounts for the fact that the social system can be considered to evolve with a series of nested hierarchical levels and that the behavior of the different levels can be analytically treated as partially independent. In fact, utility maximization of information approaches 5 could be considered to operate at each level (Kaniss, 1981) 14 Organizations, then, while composed of individuals, would constitute a different hierarchical level of social organization. Their interrelations, while clearly handled by individuals occupying positions, would be performed by those individuals insofar as they are acting for the orga- nization. Recent research has once again shown that the same individuals, while acting as representatives (agents) of the organization will report opinions different from their personal ones (Namenwirth et al., l981)6. This argument is somewhat suggested by Blau (1977) when he implicitly refers to two "hierarchical levels of entities which can perform ...work: individuals... and collectivities ('organizations')"(Wallace, 1981:217) and when he discusses the notion of substructures (l977:174ff.). Recent work pays more attention to the issue of different hierarchical le- vels, at least from a theoretical point of view. According to Blau and Schwartz: " ...society's structure entails variations and relations among, as well as within, its subunits. There are emergent properties on every level of so- cial structure, and the combinations and interrela- tions of subunits are what produces these emergent properties. The analysis of society's structure must take the differentiation and connections both among and within communities (or other subunits) into ac- count." (1984: 153) In conclusion, there is no a priori reason to believe that Blau's theory and its predictions are not applicable to patterns of association among organizations. 15 3 1293 10808 2565 IIIHIHNIHIMINIMUM!”IIIIHHIIIHHIIIUHUIIIH Even if this work were not stricto sensu a test of Blau's theory, just the metaphorical application of it provides a very much needed theoretical framework to under- stand: 1) the effects of different structural opportunities and constraints as they affect interorganizational rela- tionships and 2) the effects of vertical differentiation among organizations, an issue hardly researched in the IOR literature (Whetten, 1981). BLAU'S CONCEPTUAL FRAMEWORK The aim of Blau's theory "is to explain how the structure of opportunities and constraints resulting from variations in population compositions and distributions affect peo- ple's relations, independently of their psychological pre- ferences and cultural norms ..." (Blau and Schwartz, 1984:193). Social structure is defined, according to Blau (1977), as the distribution of people among social positions. Diffe- rent proportions and frequencies of persons located in different positions have major consequences for the pat- terning of social relations. The issue of the emergence of social structure then, is treated by Blau as the result of the differing numbers and proportions of different positions as they affect interac- 16 tion, something that cannot be accounted for by the des- cription of the individual units involved. Blau's concept of social structure could lead one to interpret the emergent properties of social structure as the mere result of an aggregation process in which intere- lations among parts are taken into account. But then the issue of emergence of social structure would be true but trivial (Nagel, 1961). While the issue is not straight forward, I tend to consi- der that Blau's structuralism is trivial in the above sense but not trivial in the conclusions that it leads to. Al— though proportions have an effect on the constituent parts and appear to be the sum of their interrelations only because of their relationship to the whole, they are ob- tained by performing operations on the component parts. This is what constitutes Blau's ”trivial" structuralism. Further, Blau's structuralism, despite appearances, cannot be classified with the one that "tends to see structural and morphological characte- ristics as ...mechanisms capable of defining their own teleology and imposing it on their agents" (Bourdieu, 1981: 312). Quite on the contrary, from an analytical point of view, Blau's treatment of collective phenomena corresponds (at least his independent variables) to the properties classi- fied by Lazarsfeld and Menzel (1961) as analytical and not 17 global, that is, properties of collectives which are ob— tained by performing some mathematical operation upon some property of each single member. Hence, his conception of macro—phenomena seems to be in accord with what reknown pro-"methodological individualism" authors, such as Col- lins (1981) and Harre'(l981) would admit to be pure macro- concepts (see also Knorr-Cetina, 1981 and Wallace, 1983). Further, Blau's interactionist structuralism (Bourdieu, 1981) makes possible a "methodological individualistic" interpretation, at least at the explanatory level (Brod— beck, 1973), of some of his theoretical predictions. For example, the unintended consequences of an agent seeking to interact with his socially homogeneous co-actors are, none- theless, due to the aggregation of many heterogeneous indi- Viduals, higher rates of interaction with his socially "non-homogeneous" co-actors. This way of framing the problem could provide Blau's theory a sense of process that the current version lacks, locating many of the processes studied in the tradition of a prisoner's dilemma-type situations of the kind Schel- ling (1978) and Boudon (1981; 1982) exemplify 7. Social structure then, reflects the differences in so- cial position that different numbers of people have. Social positions "are indicated by attributes or affiliations that distinguish people and that they themselves take into ac- 18 count ...and use as criteria for making social distinctions in their social intercourse" (Blau and Schwartz, 1984: 9). Consequently, they are defined quantitatively and empirical- ly as ”any attribute that influences people's role rela- tions" (1977:277). Hence, they are defined in terms of parameters of differentiation or characteristics for which people tend to differentially associate among themselves, in particular choosing as associates those like themselves. " (I)f no differences in social relations can be discovered, positions cannot be considered to be socially distinct" 8 (1977:4) . Parameters, which are "the axes that delineate social space" (Messner, 1980:398; Blau, l977:6), can be nominal or graduated. Nominal parameters or characteristics divide populations into groups with no inherent rank ordering; they establish horizontal differentiation. Groups are "all nomi- nal categories of persons who share a social position that influences their role relations" (Blau, 1977:276). Graduated parameters entail a vertical differentiation, establishing rank orders among people in the population on the basis of the quantity of social resources in their possession or available to them. That is, they determine their status. These two kinds of parameters generate, respectively, two different kinds of differentiation in society: heteroge- nity and inequality . Actually, graduated parameters, given 19 the existence of a rank order, establish two forms of diffe- rentiation. Inequality, which is “the average difference in distribution of the population among many groups, defined by the relative status" and status diversity, which "refers to the great number of different statuses among which a popula- tion is distributed (and) is the graduated-parameter equi- valent of heterogeneity" (Blau,l977 276-7). Heterogeneity, which refers to people's distribution along a nominal para- meter, that is, among groups with no inherent rank order, is quantitatively defined as "the probability that two randomly chosen persons do not belong to the same group" (1977:276). Parameters can be more or less salient. They are salient when ingroup relations are more frequent than chance expec- tations would dictate. That is, the sheer numbers of people in different categories would determine a random distribu- tion of ties within and accross categories. The larger is the number of ingroup ties in relation to the expected number of ties determined by chance, the more salient is the parameter. A complex structure is characterized by the consolida- tion and intersection of its parameters. The latter are consolidatgd when they are correlated (for graduated: "posi- tively") . Nominal parameters are maximally intersected when they are orthogonal, that is, not correlated. Graduated parameters are maximally intersected when they have a nega- 20 tive correlation of minus one. In complex structures individuals tend to have role relations with others in a large number of different social positions, which Blau denotes (using a combination of Merto- nian terminology) as cosmopolitan role sets. Structures can be more or less integrated. Integration "refers to the extensive social associations among different groups and strata, either in terms of a specific parameter or, as a theoretical concept, in terms of all parameters" (Blau, 1977:277). The theoretical strategy employed by Blau is to make a series of assumptions and then to deduce a series of theorems. In the following section I will list the assump- tions and the propositons relevant to those to be tested, with their number in parenthesis , as used by Blau (1977). Single parameter statements It is assumed that the members of a society associate with others not only in their own but also in different groups (A-0) and hence, for any dichotomy of society, the small group has more extensive intergroup relations than the large group (T-l). Also, the probability of extensive in- tergroup relations increases as the size of groups, distin— guished by a given nominal parameter, decreases (T-l.5)(for a constant salience - cf.Blau and Schwartz, 1984:31). 21 It is further assumed that social associations are more prevalent among persons in proximate rather than between those in distant social positions (A-l) , that ingroup associations are more prevalent than outgroup associations (A-l.l) , that the prevalence of associations declines with increasing status distance (A-l.2) and that superior status is manifest in superordinate roles in social association (PA-6). As consequence, and because elites are small, for any division of status above the median, the upper stratum has more extensive relations with the lower than the lower has with the upper (T-S). Since social associations depend on opportunities for social contacts (A-9), increasing heterogeneity increases the probability of intergroup relations (T-ll) and increa- sing status diversity increases the probabilities of asso- ciations among persons whose status differs (T-11.3). These two final theorems are readily testable and are the most important ones with respect to predictions concerning only one parameter of differentiation. With the latest revision (Blau and Schwartz, 1984), predictions with respect to relative inequality are similar: the greater the inequality, the greater the probability of status distant associations (1984: 15). This prediction, 22 however, is one of the most important ones so as to distin- guish the effects of inequality and heterogeneity. If the latest revision is correct,‘ that is, if the greater is the relative inequality, the greater is the probability of sta- tus distant associations, predictions with respect to ine- quality and heterogeneity are identical on everything except as to some of the effects of consolidation—intersection 10. Furthermore, this statement on the effects of inequality is one of the most perplexing ones in Blau's theory because of its apparently paradoxical effects. Since integration is defined by extensive social associations among groups and strata, the greater is the relative inequality, the greater is the probability of integration in society . Multiple parameter statements. When more than one parameter is involved, their interre- lations depend on the type of parameter at issue. The in- fluences of various parameters on social associations are partly additive, not entirely contingent on one another (A- 11). Hence, the lower the positive correlations between parameters, the more extensive are intergroup relations (T- 12). When nominal parameters are intersecting they improve the integration of various groups by raising the rates of association between their members (T-12.l). When they are consolidated, ingroup bonds are stregthened and the inter- 23 group relations that integrate various groups are attenuated (T-12.1l). Size, again, plays a role in the process: as group size, in terms of one nominal parameter, declines, the probability of intergroup relations in terms of other inter- secting parameters increases (T-l4). Graduated parameters are those that determine status differences, which are differences in comparable social resources of generally acknowledged validity in social ex- change (A-12). Hence, the less that graduated parameters intersect, the greater is the inequality (T-15.3). When there is multiform inequality, intersecting gra- duated parameters attenuate the rates of social association among different strata and thus weaken their integratiOn (T- 12.2) and the intersection of nominal by graduated para- meters integrates groups and strata by raising the rates of social association among them (T-12.3). In turn, the more consolidated group differences are with correlated status differences , the less frequent are integrative social asso- ciations among groups and strata (T-12.31). These final theorems (T12.2, 12.3 and 12.31) are also readily testable. 24 CHAPTER 2 INEQUALITY AND HETEROGENEITY I! 'INT'_ERO"_RGAN'I'—ZAT_Io'N—_AL NE Tw'O'R—Ks In the present chapter Blau's theory is translated from the inter-individual level to the inter-organizational 1e- vel. Before doing so, however, a series of problems that the theory presents are introduced and reviewed. In order to improve the understanding of some of these problems a "biased net" formalization of the theory is reviewed in very general terms. Then, parameters of differentiation among Organizations are distinguished based on the organizational literature. DIFFICULTIES AND LIMITATIONS 2: THE THEORY As Bell (1978:695) has noted, one of the main problems with the theory is that Blau takes as a fundamental axiom that people prefer associates with whom they share social attributes and that ingroup associations are more prevalent than outgroup associations (A-l). 25 This presents problems for individual behavior (Bell, 1978; Fararo, 1981, Skvoretz, 1983) but there is evidence that mutuality (reciprocity) and transitivity play a major role in networks of interpersonal attraction and affect (e.g. Davis, 1967; 1979) 12. There is no equivalent principle for organizations. Indeed, the resource-dependence approach would suggest that the opposite is the case: organizations tend to develop asymmetric flows of resources (Laumann and Marsden, 1982) and try to relate to those that are not in the ingroup (Galaskiewicz and Wasserman, 1981), especially when exchan- ges of only one type of resource are considered (Knoke and Rogers, 1979). However, as Laumann and Marsden (1982) argue, principles of autonomy ( Cook, 1977; Schmidt and Kochan, 1977) and plurality (Kochen and Deutch, 1980) or redundancy (so as to mantain organizational security or stability), may act against an all-asymmetrically tied network. These argu- ments would suggest that there is in fact reciprocity and mutuality even among organizations, a view that is supported by some empirical evidence (Knoke and Rogers, 1979; Galas- kiewicz and Wasserman, 1981). Two other problems arise when trying to apply Blau's theory. What types of parameters will be of the "inbreeding" (with an ingroup bias) type and what kind will be of the "outbreeding" (outgroup bias) type ? (Skvoretz, 1983). At 26 the empirical level, although not at a theoretical level, this problem has a relatively easy solution. It can be determined statistically. A theoretical difficulty remains, however, namely, what are the consequences of heterogeneity and inequality with respect to "outbreeding" types of relations ? (such as marriage at the individual level, if the parameter is sex). The answer to this problem is not such a simple one and a proper understanding of it is very much related to the concept of salience . Indeed, this concept of salience may also be related to the solution of yet another limitation of Blau's theory. This limitation is that it does not state how structural conditions interact with or mediate each other. That is, at the individual level, does income weigh the same as race in a person's choice, or is one more important than the other?. Also, how does the prior opportunities and constraints created along one parameter determine the oppor- tunities and constraints along others that come later ?. Salience seems to be a critical concept in this respect but Blau does not "formalize his predictions to the same degree as in his other theorems" (Blum, 1984:609). These relationships have been shown better by a biased net forma- lization developed by Fararo (1981) and Skvoretz (1982; 1983) and Fararo and Skvoretz (1984). Biased net theory, or a theory of random networks, was 27 first developed by Rapoport and clleagues (Rapoport and Horvath, 1961; Foster, Rapoport and Orwant, 1963). They originally argued that biased networks could be characte- rized by a series of parameters . Fararo and Sunshine (1964) introduced a new parameter, and consequently a biased net could be characterized by a reciprocity or parent bias, a cofriend or sibling bias (in recent work related to the notion of weak ties) and a popularity bias. Fararo (1981) and in particular Skvoretz (1983), making a few assumptions, develop a model in which Blau's theory is embedded and formalized in a biased net model. I will not develop the model in detail, but an introduction of some of the termi- nology and formuli will facilitate a proper understanding of the complexities involved. The reader should assume two bias events. A first event is "inbreeding", meaning that if it occurs, there is a probability one (1) that a co-actor will be selected and will belong to the same category as that of the actor ini- tiating the action. The second event is "outbreeding", where the opposite situation takes place. Assuming that the bias, or preference strengths if the reader prefers, is constant accross categories, Fararo (1981) proved that (in the ex- tended form of Skvoretz, 1983:361), the probability of an ingroup association is: P = in+(1-in-out)(l-H), where H is Blau's heterogeneity. This formula is applicable in the 28 general case when there is an inbreeding bias (in) or an outbreeding bias (out) or a mixed situation. Salience, as already mentioned, refers to the degree to which observed ingroup associations deviate from those theoretically expec- ted on the assumption of independence. Independence means that there is no bias or no particulare preference. Hence, if (in) and (out) are set to zero in the previous equation, the probability of ingroup relations becomes: P = 1-H. Notice that the probability of outgroup relations is the complement, that is, Q = H; where, again, H is Blau's hete- rOgeneity. This, of course, is consistent with Blau's theo- ry. A refinement of the theory is introduced with a proper definition of salience, as the difference between the ob- served associations, that is the first P, and the expected under the assumption of independence, the second formula for P. As a result, salience becomes, if the situation is an exclusively inbreeding one, S = (in)H, and if it is an outbreeding one, S = (out)(l-H) (Skvoretz, 1983). From these formuli Skvoretz (1983) extends and corrects Blau's predictions in the sense that "even though increasing heterogeneity produces more outgroup and less ingroup asso- ciation, it also makes the characteristic more salient ...(and correcting B1au)...there is absolutely less but relatively more ingroup association...,heterogeneity may 29 exacerbate the tendency to discriminate against outgroup members" (Skvoretz, 1983:362), when there is a pure inbree- ding bias. When there is a pure outbreeding bias, as in the case of marriage, in which gender is the parameter, with increasing heterogeneity there is absolutely more but rela- tively less outgroup association. These conclusions are certainly clarifying with respect to the relationships among heterogeneity, salience and rates of inter-group association. The assumptions of the model are somewhat problematic for some sets of data, because real data sets usually show, as is the case in the data used in this work, that there is not a uniform bias accross categories. Further, biases are mixed, not uniform and different for different networks. The model sensitizes, however, with respect to the importance of the relationship between in-group ties and out-group ties, since this is an indicator of the bias. The biased net model is only one possible formalization of Blau's theory. Rytina (1980), in a less elegant but useful formalization of topics related to the theory, ob- tained very rich and insightfull results (see also Rytina and Morgan, 1982). Among them, it is worth noting the fact that the effects of heterogeneity on the diversity of con- tacts are relatively minor (an increase in number of catego- ries from 5 to 100 only leads to an increase of 24% in 30 diversity of contacts). Salience, again, seems to be the most important concept in this respect. Another major problem with Blau's theory is the dis- tinction between nominal and graduated parameters. In the summary of the theory outlined earlier, the issue was presented as non problematic. However, Blau's notion of these types of parameters is not quite consistent accross his publications (see Blau, 1974; 1975; 1977). Blau defines a nominal parameter as a variable that "divides the population into subgroups with explicit bounda- ries", while a graduated parameter is one that "differe- ntiates people in terms of a status rank order" (Blau, 1974:617). Marsden, in his interpretation of the difference between these types of parameters, has drawn the distinction that the "defining criterion of a nominal parameter from a relational standpoint might be that persons in a particular category of it do not discriminate among outsiders, beyond the fact that insiders are in general to be preferred to outsiders", For a graduated parameter, instead, 'sociable intercourse is expected to be inversely related to the status distance between persons'(Blau, 1974:617)" (Mars-den, 1981: 3). From there Marsden considers that the parameters should be distinguished "in terms of the characteristic patterns of association that they generate" and assimilates 31 Blau's notions of status distance and social distance with Bogardus' (1925; 1933) and Laumann's (1966; 1967) notions of social distance. ‘ Marsden's interpretation, however, seems inappropriate and would make all of Blau's work totally tautological. If parameters are defined in terms of relational distance (so- cial distance) based on the amount of interaction among individuals, how enlightening would it be to make predic- tions with respect to rates of interaction among groups? The problem is not absent in Blau's conceptualization and it is related to what Messner (1980) has typified as the "dual nature“ of structural analysis (Blau's). That is, in order to know if a parameter exists it is necessary to empirically determine if it affects social relations. Once it has been established that it exists, predictions are made as to the types of effects that it will have. The problem is not so serious because in the second step the researcher is concer—ned with the distribution of individuals along those parameters but it is still somewhat "bootstrapping". Further confusion is introduced for Marsden by Blau's use of the notions of social distance and status distance. Marsden interprets them in the sense referred to above, a la Laumann or Bogardus. However, as McFarland and Brown (1973) remarked, two notions of social distance have been distin- guished in sociology: l) a concept that is based on interac- 32 tion, determined by the intensity or the type of social interaction likely to take place between two individuals (Bogardus, 1933) or by the amount of interaction (Laumann, 1966; 1967), and 2) a concept based on similarity, identi- fied with Sorokin (1927), and typified by the following quotation: "The greater the resemblance of the positions of the different men, the nearer they are toward each other in social space" Blau's notion, in my Opinion, is that of Sorokin, and in fact is that of Simmel when he refers to social types (Le- vine, 1971), as suggested in an earlier note. Further, Blau's suggestion of measuring intersection and consolida- tion of parameters by correlations indicates that social distance refers to the fact that individuals share charac- teristics (although they may not actually interact, namely be distant according to the interactional concept). This concept of distance can be generalized to the notion of local distance and or similarity employed by Feld (1982) and also by Fararo and Skvoretz (1984). This diffe- rent interpretation has, of course, empirical consequences, precluding, among other things, the use of Marsden's logli- near techniques for characterizing the structural parameters 13 of groups (1981) . The concept of social distance and Blau's eventual in- consistency are not the only causes of problems with the 33 distinction between nominal and graduated parameters. As I see it, the distinction between nominal and graduated para- meters hinges on issues of classification, nomothetic vs. ideographic issues, measurement, and theoretical problems. Let me begin with the issue of classification. The problem in sociology, as usual, is as old as Durkheim (Durk- heim and Mauss, 1963). It was argued there that the classi- fication of things reproduce the classification of men. The point of concern here being that of men (or organizations, for that matter). When the classification of men is addressed, the problem of logical and social classes is at stake. In this respect it is important to distinguish between those classifications in which the classes distinguished are defined by attributes or where the classes are defined by internal relations, an issue that has been remarked by many authors (Bourdieu, 1966; Naville, 1961) and which is at the core of the dis- tinction between the categorical and structural approaches to social structure that White et al.(l976) draw and, of course, related to the Marxian problem of "class by itself" and "class for itself" (see, as a classic, Ossowski, 1963). The reader may have guessed already that my treatment of the problem of classification is extremely cursory and, having been a major problem for these authors, will hardly be solved here. 34 A nominal parameter, as was stated above, is a "crite- rion of group membership underlying social distinctions people make in their role relations" and groups are "all nominal categories of persons who share a social position (social attribute) that influences their role relations ...They have boundaries and no rank order" (Blau, 1977:276- 77). Hence, the "dual nature" of Blau's structuralism is given by the fact that distinctions and consequent classes based on attributes are tested to see if, in fact they are classes based on positions. But then, do these attributes establish a natural or an artificial classification ?. Blau seems to suggest in the way he compares heterogeneity to status diversity, that an artificial classification would be, let us say, appropriate enough. But if it is an artificial classification, why would this have a positional effect ?. Why would people draw significant distinctions (Bourdieu, 1966) so as to derive the condition or situation of class ? This, then, is related to the nomothetic and ideographic issue, well addressed on these matters of class by Naville (1961) and Carlsson (1958). Not only are attributions and distinctions problematic. What does it mean that groups have no rank order ? As Bell 35 (1978) notes, some of those parameters that Blau considers nominal, such as occupation, sex and race carry a rank order. Indeed, the whole literature on occupational com- plexity and hierarchies of skill is based on these "non- vertical dimensions of stratification" (e.g. Kohn and Schoo- ler, 1978; Kohn, 1981; Spaeth, 1979) (where non-vertical may be a tribute to tradition). Further, the literature on status characteristics has clearly shown the effects of sex and race as such status characteristics. That is, attributes or ”characteristics of actors around which evaluations of and beliefs about them come to be organized" along dimen- sions of power and prestige (see Berger, Conner and Fisek, 1974; Berger, Rosenholtz and Zelditch, 1980). Social differentiation among units usually implies two kinds of processes: differentiation of subpopulations and ranking of them (Turner, 1984). The process of differentia— tion of subpopulations usually supposes, in turn, the pro- cesses Kochen and Deutsch (1980) call pluralization and functional specialization. Pluralization, with spatial dispersion or not, implies a process that essentially generates redundancy in a system (for whatever reasons). This process is sometimes called segmentation (Luhmann, 1982) and consists of a process in which all the parts generated are esentially identical ac- tors, or if the reader wishes, structurally equivalent from 36 a functional and relational point of view. When organizations are concerned and their activities are considered, segmentation is the situation described by Thompson (1967) as parallel technology, and discussed in graph theoretic terms in the context of the division of labor by Kemper (1972). Pluralization cannot constitute what Blau considers to be heterogeneity because all plural actors share one common attribute that constitutes the "mark of distinction" between them and the rest. Functional specialization could instead lead to the dis- tinctions that Blau wants to make. But again, most litera- ture, including earlier writing by Blau (1972) tends to argue and show that functional differentiation is usually accompanied by a ranking process (or a re-ranking one). The famous (or infamous) ”structural mobility" is generated by these processes (see, for example, Mayhew, 1975; Turner, 1984). Theoretically, then, one has to conclude that situations where heterogeneous groups co-exist without some kind of ranking, cannot occur. What can occur, instead, as Marsden (1981) would argue, is that differential distinctions are drawn. For nominal categories the distinction only involves the out-group and the in-group distinction, without discriminating among out- 37 siders. These kinds of situations in which dychotomies are involved, have long been described by anthropologists, and it is a favourite among the French structuralist tradition ( e.g. left vs. right, white vs. black). For graduated parame- ters, the distinction is based on a finer discrimination of social distance (again, not in Marsden's sense). Measurement of these local distances (Feld, 1982) is not yet developed and we certainly do not have an empirically based list of those variables that fit that situation at the individual level, much the less at the organizational level. A proxy to these situations, however, may be the inter- pretation that Bell (1978) gives to the distinction between nominal and graduated parameters. Graduated parameters would be based on a resource that can be exchanged. The interpre- tation is, of course, based on Blau and it was the defini- tion of a graduated parameter that was emphasized in the outline of the theory presented in the preceding chapter. NOMINAL PARAMETERS .I_N_ ORGANIZATIONS Blau (1977) does not provide any way to determine what categories are relevant criteria of distinction for social interaction and which are not ( i.e. which ones are parame- ters). He suggests that the concept of salience of a para- meter is the one that establishes that distinction. 38 Skvoretz (1982), however, has shown that Blau's predic- tions with respect to the effects of heterogeneity are valid for any categorical distinction, whether it is salient or not. He has further shown that categories that may not be relevant as parameters of differentiation from a theoretical viewpoint, ( e.g. the brand of tooth brush that individuals use) will be relevant with respect to the individulas'pat- terns of association if they are significantly associated with a salient parameter. This then, introduces a dis- tinction similar to Rytina's, between salience and signifi- cance of a parameter (Rytina, 1980) or between primary and derivative salient parameters (Skvoretz, 1983:371). The literature on organizations has traditionally stu- died structural characteristics of organizations that have been shown to be relevant in order to determine organiza- tional types. These variables then should eventually cons- titute primary salient parameters of differentiation among organizations. Typologies of Organizations have emphasized different elements in determining the main criteria to classify orga- nizations, such as fuctional categories, societal function performed, prime beneficiaries, type of authority, type of compliance of members, major structural factors, technologi- cal and environmental complexity and uncertainty, and type of relationship to clients and participants (see review in 39 Scott, 1981). When considering nominal or graduated parame- ters of differentiation among organizations then, all these characteristics seem to be relevant. For the present purposes, and given the data on social service agencies described below, many nominal parameters have been controlled, such as whether the organizations are work organizations or not (Blau and Scott, 1963), whether they use remunerative power and calculative participant involvement or not (Etzioni, 1975), whether they use ratio- nal-legal types of authority or not (Weber, 1947), and who are the prime beneficiaries of the profit (Blau and Scott, 1963). The issue then,for present purposes, is to establish relevant parameters of differentiation among non-profit social service organizations. Whether or not the organization is public should be a relevant parameter of differentiation. Public organizations do not have the same competitive constraints that some pri- vate organizations have (Aldrich, 1979; Downs, 1967; Jack- son, 1983) and their birth, growth and death processes tend to suggest an absence of predators but no significant shor— tage of sustenance (Casstevens, 1980). They also differ in that public organizations often have an externally imposed legally mandated network ( Hall et al., 1977). That is, they are organized in a hierarchy (in Williamson's (1975) sense - 40 a relational hierarchy-), while private organizations are more prone to be organized in a "market" (also in William- son's sense). Among those structural factors that are relevant, tech— nology, defined as the characteristics of inputs, through— puts, and outputs as related to materials, operations and knowledge (Scott, 1981), seems to be a most important one (Perrow, 1967; 1970). The technical core has been used as the main criterion to establish a concept of organizational Species (McKelvey, 1982). Greater technological complexity is associated with greater structural complexity; greater technological uncertainty is negatively associated with formalization and centralization (Scott, 1981). It has also been shown that technological organization is related to systems of control (Woodward, 1965; Hrebiniak, 1974), as a function of the type of interdependence generated by the technology in use ( March and Simon, 1958; Thompson, 1967; Baumley, 1971) 14. Hence, type of technology should be a main parameter of differentiation. Unfortunately the percentage of non-respon— se in the present set of data precludes the use of a complex measure of technology. However, the functional category of the organization, namely the type of service provided should be related to the type of technology employed and it will be used as in this work as a proxy variable. 41 GRADUATED PARAMETERS _I_N_ ORGANIZATIONS Whether it is understood as a dimension of organizatio— nal structure (Hall and Tittle, 1966) or as a contextual variable (Blau and Schoenherr, 1971; Pugh et al., 1969), size has generally been conceived as a relevant chara- cteristic of organizations (Scott, 1981). As measured in the most common way, by number of employees (Scott, 1981), size is, however, related to a scarce resource, manpower (Niel- sen, 1978; McPherson, 1983). Another common measure of size for service organizations is the number of clients served which clearly refers to an important resource for service organizations. Consequently, given that a graduated parameter is based on the possession or availability of a scarce resource, size should be considered as such. Another measure of size is the budget available to the organization (Kimberly, 1976). This variable is clearly the equivalent of income at the individual level, in particular for non-profit organizations. Hence budget size should also be a graduated parameter of differentiation. Inequality refers to the distribution of people in terms of a status dimension. Power, influence, and prestige are sources of social status for individuals. The same should be 42 the case for organizations. The concept of power is another of those significant concepts in the social sciences upon which there is no agreement, to the extent that it has been considered an "essentially contested concept" ( see Lukes, 1974). The lack of agreement as to how power should be defined and the indistinct use of related terms as influence and control (Rogers, 1974) have increased with the relatively recent resurgence of interest in the concept within sociolo- gical theory, in general, ( e.g. Burns and Buckley, 1976; Chazel, 1974; Crozier and Friedberg, 1980; Foucalt, 1980; Goetschy, 1981; Liebert and Imershein, 1977; Lukes, 1974; Martin, 1975; Poulantzas, 1974; Wrong, 1979) and organiza- tion theory in particular (e.g. Clegg, 1979; Pfeffer, 1982). The only uncontested aspect of power is that by its nature it is a dispositional concept, namely, that power is not an observable construct and that it implies a potentiality. Further, under some circumstances it is a multidimensional concept (Kadushin, 1968). Among those notions of power that are relational and that can be conceptually applied to exchange and social networks, Coleman (1977) has distinguished two forms of power. A "perfect (competition) market" form, where "the power of an actor is the control he has over events, weigh- ted by the value of these events" and an "imperfect (compe- 43 tition) market" form, where power is to gain the outcome one prefers in opposition to the other party's interest in gaining the outcome he prefers" (1977: 184-5). Extended models of the former type have been developed for social networks (Burt, 1977; Marsden and Laumann, 1977; Marsden, 1981; Marsden, 1983). The concept of power that has been the most researched, however, is Emerson's bilateral conception of power-depen- dence relations (1972; Cook and Emerson, 1978). This con- cept of power makes it a direct function of the dependence of A upon B, which in turn is "a direct function of the value to A of B's resources" and "an inverse function of the number of A's alternative exchange relations with ...parties with resources similar in kind to B's" (Stolte and Emerson, 1977: 120). Unfortunately this notion is based on a bilate- ral conception of power and must be reformulated in order to be properly applied in large networks (Cook et. al., 1983). That organizations exercise power is hardly a revelation (Warwick, 1975; Rourke, 1976; Coleman, 1984; 1982). Few stu- dies, however, have addressed the issue of power at the in- terorganizational level (Beniger, 1983; Burt, 1980; Galas- kiewicz, 1979; Miller, 1980; Mizruchi and Bunting, 1981; Ro- gers, 1974). The concept has been operationalized as centrality in a network of relations. Centrality has been considered a 44 source of structural power (see Hickson et. al, 1971). Centrality also links the notion of status as power, which is typically represented "vertically" (as in an organiza- tion chart), with a "structural positional meaning, a la 'status in the Linton sense' " (Stolte and Emerson, 1977: 126). As Freeman (1977; 1979) makes clear, there are three general types of centrality measures that have been used: those of point centrality; those based on betweenness; and 15 those based on closeness . The second type of measure, those based on betweeness, index the potential of a node for control of exchange (Free- man, 1977; 1979). This measure has been given a game theore- tical interpretation (and hence some substantive "sense") (Grofman and Owen, 1982) and it is then, clearly related to brokerage as a source of power in controlling exchange networks. While the most recent empirical evidence with respect to its equation with power is mixed, at least in "negatively connected" networks (Cook et al., 1983) 16, it is still the best operationalization of the concept availa- ble, and it has been shown to be relevant in empirical research (Beniger, 1983; Burt, 1982; Galaskiewicz and Krohn, 1984). Clientele support, as an exchange dimension, is impor- tant in determining the power of social service agencies 45 (Beniger, 1983; Rourke, 1976) and clients are a significant resource for these agencies. Hence, those organizations that are central (in the betweeness sense) with respect to the distribution of clients should be more powerful. The concept of influence is also used in a vague way, sometimes it is understood as the genre, being power the species (Wrong, 1979); sometimes it is used interchangeably with power or with prestige. However, in everyday speech it is not the same to describe a person as powerful as to call him/her influential. To be influential (for a person or an organization) seems to be related to the ability of affec- ting B's actions in the absence of a sanction ,a contingency of reinforcement if the reader prefers it, ( Bell, 1975), and much related to what Wrong (1979) calls anticipatory influence. Influence then, as compared to power, clearly entails an attribution process, probably best captured at the measure- ment level by the reputational techniques ( see Bonjean and Olson, 1964). Prestige is another dimension of organizations that has hardly been dealt with. The relevance of prestige as a scarce resource and its importance for social interaction is extensively shown by Goode, who defines the concept as "the esteem, respect, approval that is granted by an individual or a collectivity for performances or qualities they consi- 46 der above the average" (1978: 7). The issue of prestige in organizational networks has been singularly argued by Perrow (1961), who identifies it with a favorable public image, and Caplow (1964). Prestige affects the distribution of resources, at- tracting personnel, clients, donors, investors and the dis- tribution of credibility and influence with respect to rele- vant legislation, and in setting the standards of achie- vement in its organizational set. The differences between concepts such as prestige and power or centrality have been recently discussed by Knoke and Burt (1983) in dealing with the concept of "prominence". In the latter concept, the prominent actor, i.e. prestige- ful, is the object of many relations, while the actor may not directly participate in those relations. The distribution of organizations along these three graduated parameters of differentiation should have similar effects to those predicted by Blau for groups of indivi- duals. In the next section, specific hypotheses involving these variables are presented, following Blau's theoretical state- ments. 47 CHAPTER 3 STATEMENT 9: THE PROBLEM AND HYPOTHESES RESEARCH PROBLEM The problem addressed in the present work can be stated as a test of a theory that predicts how the structure of opportunities and constraints, as generated by the diffe- rent proportions and frequencies of complex organizations along parameters of differentiation, affects the degree of interrelations among them. More specifically, the predic- tions are made with respect to the rates of out-group asso- ciations and the degree of status distance among actual associates that occur in a previously defined interorgani- zational network. Nominal parameters that determine groups of organiza- tions were determined on the basis of the existing litera- ture and are: public vs. private organizations and type of activity of the organization. The graduated parameters that will determine the status groups are size, budget size, power, influence and prestige of the organizations. These 48 same parameters determine degrees of inequality which are used to make predictions with respect ot the status distance among interacting organizations. For the sake of clarity, it should be noted again that Blau's notion of group is a categorical one, where the standard introductory textbook distinctions between an ag- gregate (a mass), a category (an age group) and a group (with the classical Mertonian characteristics) do not hold. Theoretical predictions with respect to the dependent variable, instead, refer to an actually relational variable: degree of association among organizations. Namely, interre- lations in an actual symmetric social network, that is, a set of links in which A has, for example, named B and B has named A and so on, (from here on, called ties) are predic- ted. In what follows, the main hypotheses, as deduced from the relevant theorems of the theory, are elaborated. HYPOTHESES From the theorem that increasing heterogeneity increases the probability of intergroup relations (T-ll), it is ex- pected that: H-l. Those networks with higher heterogeneity with respect to the nominal parameter public-private will have a higher average number of ties to the outgroup than those with 49 lower heterogeneity in that parameter. H-2. Those networks with higher heterogeneity with respect to the nominal parameter type of activity performed will have a higher average number of ties to the outgroup than those with lower heterogeneity in that parameter. From the theorem that increasing status diversity in- creases the probability of associations among persons whose status differs (T-ll.3), it is expected that: H-3. Those networks with higher status diversity with res- pect to size will have higher average number of ties to the outgroup than those networks with lower status diversity along that parameter. H-4. Those networks with higher status diversity with respect to budget size will have higher average number of ties to the outgroup than those networks with lower status diversity along that parameter. H-5. Those networks with higher power status diversity will have higher average number of ties to the outgroup than those networks with lower status diversity along that parameter. H-6. Those networks with higher status diversity with res- 50 pect to influence will have higher average number of ties to the outgroup than those networks with lower status diversity along that parameter. H-7. Those networks with higher status diversity with res- pect to prestige will have higher average number of ties to the outgroup than those networks with lower status diversity along that parameter. From the theorem that intersected nominal parameters im- prove the integration of various groups by raising the rates of association between their members (T-12.l), it is hypo- thesized that: 8—8. Those networks with higher intersection (lower corre- lations) among type of activity and public-private dis- _tinction , will have higher average number of ties to the outgroup than those networks with lower intersection (hi- gher correlations) of these parameters, when controlling for the degree of intersection between graduated and nominal parameters. From the theorem that intersecting (less consolidated) graduated parameters increase the rates of association among different strata and thus weaken their integration (T-12.2), it is hypothesized that: 51 H-9. Those networks with higher intersection (higher nega- tive correlations) among size, budget size, power, influen- ce, and prestige will have higher average number of ties to the outgroup than those networks that do not have such high level of intersection ( such high negative correlations), when controlling for the degree of intersection between graduated and nominal parameters. From the theorem that the greater the relative inequali- ty , the greater is the probability of status distant associations, it is hypothesized that: H-10. Those networks with greater relative inequality with respect to the parameter size, will have a greater rela- tive inequality among those organizations that are linked by one or more ties. H-ll. Those networks with greater relative inequality with respect to the parameter budget size, will have a greater relative inequality among those organizations that are lin- ked by one or more ties. H-12. Those networks with greater relative inequality with respect to the parameter power, will have a greater rela- tive inequality among those organizations that are linked 52 by one or more ties. H-13. Those networks with greater relative inequality with respect to the parameter influence, will have a greater relative inequality among those organizations that are lin- ked by one or more ties. H-14. Those networks with greater relative inequality with respect to the parameter prestige, will have a greater relative inequality among those organizations that are lin- ked by one or more ties. As mentioned earlier the last hypotheses (10 to 14) are particularly relevant for their paradoxical effects on the integration or connectedness of a network. 53 CHAPTER 4 METHODOLOGICAL PROCEDURES Data The data used in this research was collected by survey interviews with the heads of social service organizations that participated in the delivery of mental health services to the aged. The services were located in twelve midwestern Cities (six in Michigan and six in Ohio), whose population ranged between 100,000 and 600,000 inhabitants. The data were collected by P. Marcus and A. Sheldon under grant # 31898-02 from NIMH in 1978. Sample frames were built on the basis of United Way listings, telephone directories and information obtained from interviews with informants invol- ved in the cities' social service delivery systems. The organizations included in the sample were actual providers of services and had more than five permanent members on their staff. Three questionnaires were used. In the first, directly administered by a professional interviewer, the directors of the agencies were asked to determine, (on the basis of a 54 list provided) the agencies with which their agencies inte- racted on 21 different types of dimensions. Actually, some of these dimensions did not refer to exchange dimensions but rather provided, by means of a sociometric technique, data that were not available otherwise (i.e. prestige of diffe- rent organizations). The second and third questionnaires were self administered and sought information on structural characteristics of the organization. The interorganizatio- nal networks that resulted from these data ranged in size from 37 to 47 organizations. The response rate for these questionnaires, ranging from 65% to 75%, was not as high as the response rate for the first questionnaire (about 95%). Consequently, technological charac-teristics as well as some other variables for some cities cannot be used without seriously biasing the analysis. Response rates for each city are provided in Appendix I. Details regarding data collection and descriptive cha- racteristics of the data can be found in Marcus and Sheldon (1983). The three main criteria for defining a boundary are spa- tial, functional and analytical (Kuhn, 1974). Analytically, the boundaries of the netwoks in the present study are defined nominally, according to their geographic (spatial) location and to the type of service delivered by the organi- zation (function performed). 55 Operationalization and Measurement Dependent variables Two types of dependent variables are used in this study. For those predictions based on hetero- geneity (hypotheses l to 9), the dependent variable is always the number of ties to the outgroup. However, since the effects of heterogeneity are contingent on the salience of the parameter and the relative number of in-ties, the dependent variable was operationalized as the ratio of the number of ties to the outgroup over the number of ties to the ingroup. Two different dependent variables are used to obtain different outgroup counts. The variables measured are infor- mation and informal exchanges of cooperation. Data on these variables were collected through the following questions: With which agencies do you exchange opinions, information and ideas?, and ...please identify any agencies with which your agency works on any sort of informal cooperative basis. ( For precise wording of the questions, see Appendix II, where the relevant questions are reproduced). The nature of these exchanges is substantively symmetri- cal, satisfying in this sense the requirements Blau (1977) imposes on the type of social relations with which he is concerned. It is the case, however, that acknowledged reciprocation 56 is also dependent on dimensions such as prestige (people tend to choose peers or "superiors" -Davis, 1967; Davis and Leinhardt, 1972 ; Laumann, 1966; Laumann and Senter, 1976) It should also be clearly dependent on the volumes of the resource that are exchanged, relative to the total amount of that resource that is received or given by a specific organization. Hence, each choice made by a member of catego- ry X1 to X2, is considered to be symmetrical, namely it implies that there is a tie from X2 to X1, as well. The reciprocity issue, however, implies that actual choices from X1 to X2 and from X2 to X1, may differ. Conse- quently, both choices for both categories have to be counted and the actual reciprocated choices discounted. To state it another way, reciprocation is imposed for each of those choices from X1 to X2 and from X2 to X1 that were not actually reciprocated. The counting procedure is relatively simple. Since the ties are symmetrical, ( Ties OUT + Ties OUT - Reciprocated OUT Ties ) / N1 + N2 = Ties OUT + Ties OUT / N = Average number of ties to outgroup. For the poly- tomous case and for the multivariate case, the general counting formula is: ( Total # of Ties - E Ties IN - Reci- procated Ties ) / N = Average number of ties to outgroup. The computer program employed for this counting was written by Patterson Terry and it is reproduced in Appendix III. For those predictions that concern inequality, the de- 57 pendent variable is always status distance among associates. For these purposes, a special rate, similar to the one used by Blau and Schwartz (1984) for marriages, is developed. The purpose of such a rate is to determine the average status distance among organizations that actually interact, expres- sed in terms of a unit which is the mean status in the population or social network of concern (see Skvoretz and Fararo, 1983). Hence, for the present purpOses a relational Gini index would be: n k .21 l ( Z lsm - S(j)l )/k1 rel - Where k is the number of associates j that an actor i has, n is the total number of actors in the network, S(i) is the status of actor i, S(j) is the status of the asso- ciate, and S is the mean status in the population. A relational Gini coefficient was calculated for each of the two dimensions of exchange mentioned in each of the twelve cities, using the same computer program shown in Appendix III. The choice of two dimensions of exchange was made for several reasons. On one hand, it provides a way of testing 58 Blau's theory with two kinds of relation and not just one. On the other hand, it is a way of improving the validity of the results. Evidently the a priori probability of finding sig-nificant statistical relations with twelve cases is vor small. Besides, the statistical validity of the findings. based on twelve cases could be argued. If the statistical analysis is performed for two different kinds of ties, a replication of the test of the theory is carried out and the findings may not be statistically significant but they will be more robust. For those readers who still remain critical after this rationale, it should be noted that there is no published study that uses network variables and uses twelve cases. By current standards in the discipline then, using twelve di- fferent networks seems to be an improvement on previous work. Independent variables.The independent variables are pu- blic-private distinction, type of activity, heterogeneities and size, budget, power, influence,and prestige status diversities, when hypotheses concerning heterogeneity and status diversity are concerned (H-l to H-9). Type of activity is measured by the reported main acti- vity of the organization and a subsequent classification performed by Marcus and Sheldon (see list, 1983: 201), 59 generating the following categories: Primary Mental health organizations, Secondary Mental health organizations and No Mental health. Whether the organization is public or not was determined on the bases of self reports of the main source of funding plus the reports of selected informants, Blau (l977:9) suggests as a measure of heterogeneity the following formula: H = 1 - Z:(Pi2 ), where H is heterogeneity and Pi is the proportion of organizations in each nominal category. For the case of sampling without replacement this formula is not appropriate, however. Blau correctly notes that these would not be a problem for large samples. For the present data the same measure developed for the case of sampling without replacement is used, as suggested by Skvoretz (1983: 360n). H=1- it Hi) (fm -1)1 / nun-1) Where f is the number of organizations in each nominal i category, and n is the size of the population. Size of the organization is determined by the reported number of employees in the organization . Size of the budget is measured by the reported total income or revenue of the agency from any source, except clients' income maintenance funds, circa 1978. Power and influence were extensively discussed in the 60 preceding sections. Following conceptual and traditional principles, power was considered to be a positional concept, while influence was a reputational one (Bonjean and Olson, 1964). Consequently, and for present purposes, a distinction is drawn between informal power acquired through the strate- gic (central) structural location in the network of scarce resources —and influence, based on the reputation (or per- ceived power) of the organization. Informal power is measured by the centrality index, based on betweeness (Freeman, 1977; 1979) in the network of exchange of the resource "clients", namely, in the referral network. In order to establish control over the flow of clients, a sociometric matrix was built based on the ques- tion "Which agencies send people to your agency?" The trans- pose of this matrix (where the rows become columns and viceversa) has senders as headings of rows and receivers as headings of columns. The centrality index, based on be- tweeness, was calculated for this matrix, according to the following formula (Freeman, 1977): 17 n C [p(k)] = 2: b(ij) [p(k)] , where n is the numb r b — i LLM :5 < of nodes in the network and b(ij) [p(k)] = g(ij) [p(k)] / g(ij): where g is the number of geodesics linking p and p and g (p ) is the number of geodesics linking ij k 18 p and p that contain p (Freeman, 1977; 1979) . i j k 61 To facilitate the comparison accross networks a normalizing factor of N2-3N + 2 is used 19. The measure of centrality was calculated with the computer program Center that belongs to the library of UCINET from the University of California at Irvine. In order to make this measure usable for the indicator of status diversity, five 20th percentiles are established. Influence, established by a reputational technique, is measured by the answer to the question: Which agencies have the most influence over decisions about human services in this community? Harary (1959), when suggesting the only measure of status based on graph thery (Roberts, 1979 ), introduced the concept of contra-status. This concept takes into account that status is determined not only by the subordinates but also by the superordinates that an actor has. His measure of status, however, gives a higher weight to those that have more subordinates. That is, the more “distance an actor can put between himself anf his subordi- nates, the higher is his status (Taylor, 1969). This is in conflict with the concept of influence which implies that higher levels in a relational hierarchy should have relatively less influence over an actor than those that are directly over the actor (Simon, 1981)."Popularity" mea- sures of status, that is ,the sum of the direct and indirect links to an actor, do not capture these different weights. 62 The most appropriate measure of influence then, would seem to be Taylor's (1969) reformulation of Katz's (1960) measure. This measure uses a matrix (M) in which the ones represent "influences to". Hence, since the question col- lects information on who has influence over another, its transpose is the desired matrix M. The measure is the follo- wing: Inf(i) =r(i) - c(i) / Z r(i) 3' Where, r and c are the ith row and columns sums of P, and —1 P = [ ( I - wM ) - I ] / w Where I is the identity matrix, w is a weig en ng cons- tant such that 0 < w < l and M is the influence matrix above described. The measure ranges from -1 to 1 but a constant of 0.5 was empirically determined so as to have all positive values. In order to standardize the results, the weighting constant was 1 / n; where n is the number of organizations in the network. Prestige, instead, is a typical example of prominence, that is, "an actor's prestige is higher to the extent that it receives many ties directed to it by many prestigious actors who are themselves the recipient of directed ties from many other actors" (Knoke and Kuklinsky, 1982: 55). The measure is the following: 63 Prest(i) = nil p(j) 2(jik) j=l where each element in the column vector of an actor i is multiplied by the prestige scores ( p ) of the n-l j ac- tors. Since prestige is on both sides of the equation, a simultaneous solution is required and is described in Knoke and Burt (1982) and Burt ( 1982). The computer program employed for the calculation of prominence or prestige was a variation of Burt's Structure (version 2) 20. All these graduated parameters were divided in five percentiles and the formula for heterogeneity was applied so as to measure status diversity. Relative inequality is the other independent variable, employed in hypotheses 10 to 14. While there are many measures of inequality (Allison, 1978; Schwartz and Win- ship, 1979), Blau's suggestion is followed and the Gini index is employed in this work. For practical reasons the formula applied is not identical with the one Blau (1977; Blau and Schwartz, 1984) suggests, but is the equivalent one proposed by Allison (1978), which is equivalent. The formula employed is the following: n n I: (f. lsm -s.05 and P (.1, which for the number of cases is considered here to be a fairly acceptable level, those that are between P >.l and P <.3 and those that are plainly not significant, above P > .3. Those results that are only significant at the latter level are not always 68 presented. As a visual aid, the more asterisks used, the less significant is the value of the coefficient. The reader should also be reminded that both statistical models used and introduced in the previous chapter are non- linear (or curvilinear) when the relationship is stated in the original units (before the logarithmic transformations). Results for the regressions that test the effects of heterogeneity on the rate of out-ties are shown in Table 1. As can be seen there are two possible interpretations of the results. If no attention whatsoever is paid to levels of signifi- cance, the effects of heterogeneity along the nominal para- meters are contrary to the effects expected from hypotheses l and 2. That is, in those interorganizational networks where there is higher heterogeneity of groups of organiza- tions based on whether they are public or private or based on the kind of activity practiced or social service deli- vered (Primary mental health, secondary mental health or no mental health), the rate of intergroup association is lower than in those less heterogeneous networks. The alternative interpretation, a more logical and co- rrect one, is that there is no effect whatsoever of hetero- geneity on the rate of outgroup associations. Indeed, not only the significance levels but the null or very low adjus- 69 ted R squares support this interpretation. TABLE 1 EFFECTS OF HETEROGENEITY ALONG NOMINAL PARAMETERS PUBLIC- /PRIVATB AND TYPE OF ACTIVITY ON TWO EXCHANGE DIMENSIONS HYPOTHE- HETEROGENEITY EXCHANGE DIMENSION SIS ALONG INFORMATION COOPERATION “ 2 2 A 2 2 NUM. PARAMETER b R AdR b R AdR *** *** *** *** 2 Type Of Activity -.78 .07 .0 -.46 .37 .09 2 2 AdR = Adjusted R *** b value is not significant even at P<= .30 Many alternative 3d hog explanations could be attempted in view of these unexpected results. A first explanation could be that, given the fact that the theory is being applied to complex organizations and not to associations among people, the predictions of the theory are not applicable. Two sets of reasons seem to counterba- lance the validity of this argument in the present context. 70 First, similar findings (and lower R squares) have been reported for individual level data, as is the case with extremely salient characteristics, such as race (Blau and Schwartz, 1984). Second, and more important, the two discus- sions of the relationships between salience, heterogeneity and outgroup relations that were previously reported (Ryti- na, 1980; Skvoretz, 1983) suggest that the effects of hete- rogeneity are more complex than those Blau suggests. Indeed, Rytina (1980) shows formally in a model that the effects of heterogeneity are practically unimportant in comparison with those of salience. As already mentioned, in his bias net model Skvoretz (1983) has shown the complex paradoxes that can be created depending on the type of bias that exists. Indeed, the reason the dependent variable was operationa- lized the way it was (as the ratio of outgroup to ingroup relations) was precisely to control for the relative vs. the absolute effects of outgroup associations vis a vis ingroup associations. This distinction, as remarked earlier, seems to be at the core of these complex effects. The results shown in Table 1, in the context of the results to be shown subse- quently, tend to support in an informal way the argument that heterogeneity is relatively unimportant in comparison with salience (Rytina, 1980) in the determination of the rates of association. 71 They also tend to show that the type of bias is critical in the determination of the effects of heterogeneity, as Skvoretz (1983) has shown. As a mere example, the mean ratio out-ties/in-ties is shown for the two dimensions of exchan- ge, for the two parameters in Table 2. TABLE _2_ RATIO OF OUT TO IN TIES FOR THE GROUPS ALONG THE NOMINAL PARAMETERS FOR TWO EXCHANGE DIMENSIONS NOMINAL EXCHANGE DIMENSION MEAN --------------------------------- and S.D. INFORMATION COOPERATION for N in PARAMETER Ratio Out/In Ratio Out/In Subcategory 31 (5.57) Public/Private .75 .83 { 24 (4.89) Type of 11 (4.19) Activity .68 .75 { 12 (3.40) 17 (4.05) It is suggestive that the dimension with the highest R square in Table l, cooperation along the parameter public- private, is the one that presents a clearer bias in favor of in-ties. Inspection of the individual cases would show that this is true, however, in only 9 out of 12 cases. It is also suggestive that when these cases are sorted out, the effects of heterogeneity become positive (results 72 not shown). Clearly everything is suggestive but not con- clusive because of significance levels and the number of cases. The problems raised by the complex relationships between heterogeneity and salience are increased as a result of tes- ting predictions that are dynamic or longitudinal with syn- chronic or cross-sectional data. This problem is not only due to the doubtless possibility of determining an equibili- brium state -a priori- but also due to the fact that diffe- rent trajectories of the relationship among variables may not be properly reflected in a cross-section. Specifically in relation to the issue of heterogeneity and salience, Rytina (1980) argues that: "in diachronic comparisons of the state of a single population, to the extent that increases in hetero- geneity are not accompanied by increases in salien- ce, cross category contact should increase. But in synchronic comparisons of different populations, the key issue is probably the initial salience, and not the degree to which differentiation has progressed" And one should add: if, in fact, the parameter is signifi- cantly salient 22. The results of the tests for hypotheses 3 through 7, are shown in Table 3. Inspection of the signs of the b's shows that for both dimensions of exchange, along every parameter (with the exception of budget size), the effects of status diversity are the predicted ones. One b coefficient for 73 power status diversity (for cooperation) poses some TABLE .1 EFFECTS OF STATUS DIVERSITY ALONG ALL GRADUATED PARAMETERS ON TWO EXCHANGE DIMENSIONS HYPOTHE- STATUS DIVER- EXCHANGE DIMENSION SIS SITY ALONG INFORMATION COOPERATION A 2 2 A 2 2 NUM. PARAMETER b R AdR b R AdR 3 Size .90 .56 .46 1.33 .71 .64 *** *** * ** 5 Power 1.33 .35 .20 1.48 .44 .32 6 Influence 1.61 .42 .30 1.96 .67 .60 * 7 prestige .96 .75 .69 .80 .64 .56 2 2 AdR = Adjusted R * Significance between P=.05 and P=.l0 ** Significance between P=.ll and P=.3 *** Value is not significant even at P<= .3 significance level problems and both coefficients for budget size status diversity are simply not significant. Hence, those coefficients that show a sign contrary to 74 the expected one, are not significantly different from zero (or a positive value, for that matter). Further, and in logical relationship to this, the R squares are the lowest, in comparison with the other ones along the same dimension of exchange. The positive and expected results for status diversity, while not necessarily contradicting the previous interpreta- tion of the findings, call for a comparison. Heterogeneity and status diversity are not identical concepts in Blau's conceptualization but their predicted effects are the same. These findings would tend to support the argument that the effects of heterogeneity and status diversity are different. In fact, there are theoretical reasons to expect this to be the case. In their most recent work on inequality Fararo and Skvoretz (1984), while primarily concerned with other issues, show that for the case of graduated parameters the effects of inequality on the status distance among asso- ciates are independent of whether there is an inbreeding bias or an outbreeding bias. This is also the case when strata are distinguished, and these strata are equal-inter- val strata, as is the case in the present research. The re- sults shown in Table 3 tend to analogously extend these re- sults, as one would expect, to the rates of outgroup asso- ciation. This conclusion appears, after the fact, as logical, to 75 the extent that the categories or strata, (status groups as Blau calls them), are based on equal intervals and conse- quently reproduce, albeit in an aggregate way, the distribu- tion of the graduated parameter that underlies them. None- theless, this point has not been noted in the theoretical literature. As to empirical findings, the results are simi- lar to those reported by Rytina (1982) at the individual level. Before proceeding to show the results of the tests of hypotheses 8 and 9, results for hypotheses 10 to 14 will be shown. As table 4 shows, the tests of the effects of overall relative inequality on the status distance of associates are, in general, the paradoxical ones predicted in hypo- theses 10 to 14. That is, the greater the relative inequa- lity in each of the networks considered along all graduated parameters (except for budget), the greater is the relative inequality in each exchange dimension in terms of the status distance along graduated parameters among those organizations that actually interact with each other. The findings are generally consistent and significant, with the exception of the results for budget. 76 TABLE .1 EFFECTS OF INEQUALITY ALONG GRADUATED PARAMETERS ON TWO EXCHANGE DIMENSIONS HYPOTHE- INEQUALITY EXCHANGE DIMENSION SIS ALONG INFORMATION COOPERATION ‘ 2 “ 2 NUM. PARAMETER b R AdR b R AdR 10 Size 2.37 .67 .55 2.17 .49 .30 ** ** 11 Budget Size -3.16 .46 .26 -2.39 .49 .29 12 Power 5.27 .55 .38 4.54 .63 .49 ** 13 Influence .96 .96 .94 .60 .42 .27 * l4 Prestige .70 .71 .61 .56 .40 .18 2 AdR = Adjusted R * Significance between P=.05 and P=.10 ** Significance between P=.ll and P=.3 These coefficients with negative signs, however, are the least significant among all the regression models listed in table 4. monly accepted levels of significance, Indeed, 77 if one is to be faithful to the most com- the findings are not significant ( P=.ll and P=.24, repectively). The R squares are also the lowest, in comparison to the other regressions within the respective exchange dimension. On the other hand, given the number of cases (12), standard levels could be left aside, and the results would be contradictory with hypothesis 11. An empirical reason may account for this. The rate of non-response is significantly higher for the variable budget in comparison with the other ones (see Appendix I ). If this is not the case and, consequently, in the sheer realm of Speculation, it could be that the processes that lead to the positive results on the other parameters (size, power, pres- tige) do not take place when budget is considered. I will return.to this issue later. The other rather unexpected result shown in Table 4 is the extremely high R square for the effects of inequality of influence on the status distance along influence among asso- ciates. There is no peculiarity either on the original survey data or in the results from the indexes calculated that could account for this. Notice that the differences in R squares and significance levels of the coefficients be- tween the model for cooperation and the model for infor- mation is inconsistent with the overall picture of relative consistency among R squares and b values for the other parameters. 78 Hypothesis 8, which states that the effects of the low consolidation or high intersection of nominal parameters would increase the rate of associations among groups, was tested, as already shown, in the same regression model whose R squares were shown in Table 1. Notice that the test of this hypothesis is not identical to those reported up to now. The hypothesis, when operationalized, states that the lower the correlation between the nominal parameters pu- blic/private and type of activity, the higher will be the rate of out to in group associations, with the correlation of the nominal and the graduated parameters controlled. Notice, however, that the test must control also for the heterogeneities of the respective parameters. Again, with 12 cases, the test that was chosen for this hypothesis, as well as for hypothesis 9, was a convergent one. Since no two heterogeneities (much the less more) could be controlled at the same time and only one relevant rate of out to in group ties could be a dependent variable in a regression model. Results of the four regressions for the two nominal parameters -public/private and type of activity- and the two exchange dimensions -information and cooperation-, would at least indicate the direction of the relationship. The re- sults of these regressions all present the expected signs but they are not at all significant (only at levels such as 79 P=.668 or more). Consequently the values are not shown. The results of a similar type of test for hypothesis 9 are shown in Table 5. Hypothesis 9, in its operational form, states that the higher the negative correlations between graduated parame- ters the higher the rates of out to in group ties, or other- wise stated, the higher the relative distance among asso- ciates. The hypothesis refers to negative correlations, which conceptually is the concept of intersection. This concept is, in turn, the opposite of consolidation, which is measured by positive correlations. Since there was no ave- rage negative correlation, that is, all graduated parameters tend to be consolidated in the present data set, the hypo- thesis was reformulated as follows: the higher the positive correlations among graduated parameters, the lower the sta- tus distance among associates. While not all coefficients are significant, all (except for those for budget), show a positive sign, contrary to the prediction. In fact, all those that have a higher sta- tistical significance fail to confirm the hypothesis. These findings are contrary to what Blau and colleagues (Blau et al., 1984; Blau and Schwartz, 1984) have found at the individual level. None of the previous tests has actua 80 PARAMETERS, TABLE .2 EFFECTS OF MULTIPLE CONSOLIDATION OF GRADUATED WITH INTERSECTION OF NOMINAL PARAMETERS CONTROLLED, ON TWO EXCHANGE DIMENSIONS HYPOTHE- CONSOLIDATION EXCHANGE DIMENSION SIS ALONG INFORMATION COOPERATION ‘ 2 “ 2 NUM. PARAMETER b R AdR b R AdR *** *** 9 Size .37 .67 .55 .15 .49 .30 *** *** 9 Budget Size -.53 .46 .26 -.49 .49 .29 ** * 9 Power 1.96 .55 .38 1.93 .63 .49 *** *** 9 Influence .17 .96 .94 1.20 .42 .27 *** ** 9 Prestige .35 .71 .61 .98 .40 .18 2 2 AdR = Adjusted R * Significance between P=.05 and ** Significance between P=.ll and *** Not even significant at P<=.3 lly controlled for the different effects of intersection of nominal and graduated parameters and consolidation of gra- 81 duated parameters. But this does not seem to be an explana— tion because those coefficients also show a positive effect (not shown). Hence, the more consolidated the graduated parameters are with nominal parameters, the higher the relational inequality. However, these findings, irrespec- tive of significance levels, are all logically consistent among themselves. They may suggest, in light of the findings by Blau and collaborators that the effects of consolidation of parame- ters are different for negatively connected networks, and for positively connected networks or for mixed types (Cook, 1977; Cook et al., 1983). Marriage networks, as those em- ployed by Blau, are "typically negatively connected net- works throughout" (Cook et al., 1983: 278). That is, if someone is involved in a marriage exchange relationship, at least in the Western culture, he or she does not have ano- ther. The interorganizational networks employed in the pre- sent work are not of that kind. To summarize the findings, then, it was shown in Table 1 that the expected results for heterogeneity, (that is, an increase in the degree of out-ties to other organizations) were not supported. Hypotheses 3 to 7, instead, were su- pported by the results shown in Table 3. Consequently, it was suugested that status diversity and heterogeneity have, 82 contrary to what is suggested by Blau (1977) different effects. Increasing status diversity generates, indeed, an in- crease in the degree of out-ties to other organizations. A suggested interpretation of the differential effect is based on the different effects that the concept of salience and those of in or outbreeding biases have with respect to heterogeneity and status diversity and inequality. In the case of status diversity whether there is an inbreeding or an outbreeding bias is irrelevant, while this is not the case for heterogeneity. A similar process, albeit not that clear, occurs with respect to the effects of salience. Inequality was the object of hypotheses 10 to 14. The results, shown in Table 4, with the exception of those for budget, support the expected relationship, at least follo- wing the most recent version (Blau and Schwartz, 1984). Hypothesis 8, that predicts the effects of intersecting nominal parameters, was rejected or, at best, not confirmed. Hypothesis 9, that predicts the effects of consolidation among graduated parameters was tentatively not confirmed. The validity of this last test, however, is not high due to the statistical significance of the findings and the conver- gent way in which the hypothesis was tested. 83 Discussion How, if in any way, are these findings related to the literature on interorganizational networks ? The results for heterogeneity show that its change does not seem to have the expected effects. Hence, when heterogeneity along the para- meters public/private and type of activity increases, the rate of out-group associations does not increase. This is true, at least, with the present cross-sectional data. No- tice that the increase in heterogeneity is exclusively due, given the measure and the distinctions employed, to a "ba- lancing" of the sizes of sub-groups. The number of catego— ries in this test (and all others up till now, for that matter) remains constant. It is always Public/Private or Primary Mental Health, Secondary Mental Health and No Mental Health. The real process of differentiation among organiza- tions, as that for individuals evolves in a way in which not only the relative proportions get balanced or umbalanced, but in which the number of categories increases or is decreases. The most important finding of the preceding section, however, is the one that confirms the hypotheses that the greater the relative inequality along a graduated parameter, the greater is the average status distance among the inte- racting organizations (along that parameter). The findings 84 are startling and counter-intuitive, i.e. to the extent that the relationship has been denominated by Blau and Schwartz (1984) the "paradox of inequality". In what follows I will show that this paradox is not only relevant for - understan- ding interorganizational relations but also not new, if seen from another point of view. In order to do so, however, some of the properties and characteristics of the Gini index have to be considered. The formula presented in the previous chapter for the Gini coefficient is the one presented by Allison (1978): n n 23 ( I: | S(i) - S(j)| ) i=1 j=l The formula introduced in this work to measure relatio- nal inequality was an extension to multiple ties of the formula employed by Blau and Schwartz (1984) to measure relational inequality in marriages (one tie): n k i: I < 22 ] S(i) — S(j) | ) / k 1 i=1 j=l rel 85 The only significant difference between this formula and the one used by the above mentioned authors (and also by Fararo and Skvoretz, 1984) is that n, that is, the number of actors and not the number of ties (marriages) is in the formula. Actually this difference has no consequence what- soever in the present context because both are constants and the following arguments are totally applicable. The second formula, if applied to a totally connected network, that is a network where everybody is tied with everybody else, becomes identical to the first formula 23. A totally connected network, as the one described, is what could be called the maximum potential network that can occur 24. Consequently, the above noted equality, indicates that Blau's paradox of inequality can be phrased in a different way. That is, the greater the relative inequality of the potential network, the grater the actual inequality of the network. Or otherwise, the greater the potential relational inequality that the.system can have, the greater the actual relational inequality attained. Phrased this way, some of the paradoxical properties are washed away. This, of cour- se, implies seeing a community or a population in a rela- tional way. Expanding even further this relational interpretation of the Gini coefficient, it can be shown ( Ray and Singer, 86 1973) that the Gini coefficient can be expressed in terms of proportions as: 1- (2/N £iP(i))-1/N Where N is the number of actors, i is the rank and P(i)' is the proportion in rank (i). Hence, the Gini index is a function of the rank share products ( iP(i) ). All of which implies that the Gini is extremely similar to any other index of concentration (Taagepera and Ray, 1977; Allison, 1978; Theil, 1967). Indexes of concentration are all inter-related in one way or another (Taagepera and Ray, 1977) and they are in the last resort, always measures of complexity. The Gini coefficient measures what one could call a ranked complexity. However, as argued in Chapter 2, all complexity, if it is not redundancy, is ranked, whether in a more diffuse or a clearer way. Hence, the paradox of inequality can now be stated as: the greater the complexity of the potential network, the greater the complexity of the actual network. Or if the reader wishes, in a way that is well known in many areas related to systems theory and particularly in the field of interorganizational networks, the greater the complexity of the environment, the greater the complexity of the interor- ganizational network. I hope I have shown through this lengthy chain the con- nection that there exists between Blau's paradox of inequa- 87 lity and some of the earliest formulations of the open systems approach to organizations ( e.g. Emery and Trist, 1965). Granted, the units and levels of analysis are diffe- rent but paraphrasing Emery and Trist, one could state the paradox of inequality as the more turbulent the potential network, or the environment, the more turbulent is the actual network or the interorganizational field (Warren, 1967). The difference is that Blau's approach provides a more formalized and systemic approach than these other some- what typological frameworks. In fact, if seen in this context, the present research is the only study that has tested this sort of proposition in a systemic or global way, at a macro level. Consequen- tly, it is extremely difficult to compare results. Besides, the majority of those other studies that have looked at the interorganizational level in a global way, as whole net- works, usually have been descriptive (Galaskiewicz, 1979; Whetten, 1981). The earlier findings, however, have not been necessarily contradictory. It was found, for example, that corporate interlock networks may evolve recruiting relatively more or less popular organizations to new boards (Galaskiewicz and Wasserman, 1981). No measure of the overall inequality in the network was performed but it could well have been the case that it increased. Indeed, at the interorganizational 88 level, the paradox of inequality does not seem to be as counter-intuitive, to judge from the theoretical literature on exchange relations among organizations (Benson, 1975; Levine and White, 1971) as it seems to be for individual level interaction. Indeed, the notion that in order to secure their boundaries and ensure their own survival in a competitive environment organizations will use their re- sources to establish exchange relationships with other orga- nizations (Levine and White, 1961; Galaskiewicz, 1979) is akin to the fact that graduated parameters are based on resources. Besides, as shown when the propositions on status diver- sity were confirmed, the predictions do not imply that out- group or more distant associations predominate over in-group or less distant associations. The more inequality, the high- er is the distance among associates, relative to the pre- vious inequality. This does not mean that social heterophily predominates over social homophily. Hence, the findings are also consistent with the systems theory literature on loose- ly coupled systems. Indeed, in a very general sense, the argument that systems respond to the complexity of their environments by increasing their complexity while at the same time they are loosely coupled and hierarchically orga- nized, is what is expressed in the relationship between social homophily with its in-ties and social heterophily 89 25 with its out-ties . Integration and cooperation among organizations have been obsessive preoccupations in all kinds of interorganiza- tional literature (Tuite et al., 1972; Turk, 1970; Whetten, 1981). To the extent that the present findings confirm the hypothesis that increasing inequality increases the relative relational inequality, increasing inequality along graduated parameters would increase the probability of integration. I only say the probability of integration because a proper concept of integration should be based on density (Rytina and Morgan, 1982) and not just the distance among asso- ciates. Notwithstanding this, as a matter of fact, inequality along graduated parameters increases the status distance among organizations that cooperate and exchange information with one another (although not necessarily reciprocate since it was forced in the data). If voluntary cooperation among different organizations depends on structural opportunities (Whetten, 1981), then inequality should promote the probabi- lity of voluntary cooperation. But it could also promote conflict, since it provides the structural opportunity for conflict to occur. Cooperation and conflict would not constitute in this case a "zero sum game". More complexity could increase at the same time, the amount of cooperation and the amount of 90 conflict. This would be consistent with earlier studies that have suggested that more complexity leads to more conflict that, in turn, would be solved by this same complexity (Coleman, 1957). In any event, the findings are generally supportive of an extension of Blau‘s theory to the interorganizational le- vel, showing that some structural process are similar at different levels of social organization. In particular, the structure of opportunity and constraints affects organiza- tions as well as individuals. This is a truism for structu- ral analysis, but all too often forgotten by researchers and theorists. If nothing else, this dissertation should sensitize those who study interorganizational relations, as to the effects of the structure of opportunities and constraints that have a substantial effect on the characteristics of the actual pattern of connectedness in the network, and that has to be taken into account together with other variables. 91 SUMMARY AND CONCLUSIONS Social organization presents different hierarchical levels. One of these levels of social structure is the interorganizational level. The purpose of the present dissertation was to extend and test Blau's macro-structural theory at the interorgani- zational level. There is no agreement in the literature as to what theory should be employed to explain interorganiza— tional behavior. The main theoretical approaches are: the political economy, the resource dependence, and the popula- tion ecology. In Chapter I it was shown that they all respond to at least a vague logic of conceptualizing orga- nizations as purposive actors. Network models and techni- ques employed for their analysis were also reviewed, ar- guing that, in general, they do not allow the researcher to determine whether the observed relationships are random or not. At the theoretical level, the notion of the organization as a purposive actor is an extension of the way much of sociology has seen individual action. There is no reason then, to assume -a priori- that Blau's theory is not appli- 92 cable at the interoganizational level. Further, in so doing, a testable macro theory of interorganizational networks is available. Blau's theory was introduced with its major axioms and theorems. The effects of heterogeneity, or the distribution of a population among many groups along a nominal parameter, were reviewed. The similar effects of inequality, or the distribution of a population along a graduated parameter, were also reviewed; as well as the effects of the intersec- tion and consolidation among nominal and graduated parame- ters. Some of the major limitations of the theory were introduced in Chapter 2, in the context of its application to the organizational level of analysis. Major findings tended to generally support Blau's theory with respect to the predictions on inequality but failed to confirm predictions with respect to heterogeneity. Conse- quently, in this cross-section of twelve Midwestern inter- organizational networks, an increase in heterogeneity does not have a positive effect on the rate of out-group asso- ciations but an increase in relative inequality does in- crease the relative status distance among associates. The lack of an effect of heterogeneity was interpreted to be the result of the complex relationships that exist between heterogeneity and salience of a parameter. The para- doxical effects of inequality were shown to be less parado- 93 xical if the Gini coefficient is interpreted in a structural or relational way. In fact, these effects were shown to be very similar to the effects of well known statements from systems theory: the higher the complexity of the environ- ment, the higher the complexity of a system. In so doing Blau's theory was again related to theories of interorgani- zational relations and open system theories of organizatio- nal behavior, as well as to the typical preoccupations of those theories: coordination and conflict. The present research presents advantages and limita- tions. It probably raises more issues than it settles. For the first time Blau's theory is tested at the interor- ganizational level. For the first time, multiple ties in actual social networks are used as the dependent variables. In order to do so, a new technique that determines the randomness of the ties is used (in this way) for the first time with actual data. Also, for the first time, structural measurement of va- riables such as power, influence and prestige is introduced. In fact, for the first time those variables that are men- tioned in Blau's theory as typical cases of graduated para- meters, are introduced as such in a test. For the first time also, a macro-structural theory is tested and offered as an explanation of interorganizational behavior and tested using twelve interorganizational networks. 94 Pioneering has its costs, however. Cross-sectional data is used to test propositions that refer to dynamic processes or dyachronic relationships. There are neither logical nor methodological reasons to expect that the results from a cross-section are generalizable to a longitudinal rela- tionship. However, it is not the first time that this is done in sociology and it constitutes, anyway, a first appro- ximation to a more valid test. The fact that major findings show the expected relationships calls then, for better tests. In my opinion, the most significant problem encountered in this research, from an empirical point of view, relates to the number of cases. There are no studies in the litera- ture that have 12 interorganizational networks as data but, Still, the number of cases is very small. An attempt was made to solve that problem by means of offering a replica- tion, using two different exchange dimensions as dependent variables. This practice somewhat improved the robustness of the findings but not the validity, as measured by sta- tistical significance. Nonetheless some very relevant find- ings, such as those related to the effects of inequality were found to be statistically significant at standard le- vels of acceptance. Besides, the limited number of cases allowed a careful examination of the data. The number of cases was crucial, however, in the limita- 95 tions imposed on the number of variables that could be included in the regressions performed to test the results. In this respect the tautologies involved in Blau's theo- ry compel the researcher to be extremely careful with the Statistical specification, so as not to end regressing two different mathematical (linear) transformations of the same variable. The task is even more difficult because the rela- tionship between salience and heterogenity is not formally specified. Some formalizations that have been attempted were reviewed but they are still preliminary, and have not been tested. Unfortunately, given the data limitations mentioned above, these formalizations could not be tested here. They provided guidance but could not even offer much help in measurement issues because their assumptions, such as the equal bias in the biased net formalization, are not met in the present data. Further, proper measurement of concepts of salience or even average out-ties involves complexities that have not been dealt with in this research, nor in any empi- rical research performed until now for that matter (e.g. Blau and Schwartz, 1984). At the theoretical level then, this calls for further work on the specification of relationships between the con- Cepts of salience, heterogeneity and bias. Some other findings in the present research, while not always statistically significant, call for further research 96 and suggest theoretical elaboration. Budget size was a para- meter whose effects were systematically different from all the other graduated parameters. Future research should exa- mine this issue in more detail, as well as a related one,namely, what are the relationships of precedence among parameters ? Contradictory findings between the present research and previous one as to the effects of the consolidation of parameters, call for further tests on the type of connecti- vity that predominates in the network. Networks with multi- ple ties tend not to be negatively connected, as marriage or dating networks are and this fact may have significant consequences. Unfortunately, the present findings are not conclusive because it is not only the case that different types of exchange connections are considered here but alos different levels of social organization. Network theorists and researchers could explore these differences, whether at the individual level or at the interorganizational level. Mergers between organizations are very much like marriages. The findings provide general support for the statement that similar structural processes take place at different levels of social organization. This should call the atten- tion of researchers in the field of interorganizational relations. And even of those working in the applied field. For researchers, this study should act as a reminder that 97 structural processes take place in the interorganizational structure. While the differences between different structu- ral approaches, such as the purposive actor orientation and the more teleological system oriented approaches have not been solved, research on interorganizational relations has predominantly paid attention to the purposive actor pers- pective. Blau's theory, as was argued in Chapter 2, is not teleologically oriented and offers a good opportunity for theoretical work trying to explain the processes that lead to the differential effects of parameters and other proces- ses. At the empirical level these findings call for more multi-level research to explain interorganizational rela- tions. Research of that kind should be able to determine if, in fact, the structural processes found in the present work take place when other contexts are taken into account. For those in the applied areas of interorganizational relations, the present findings call attention to the pos- sible importance of ranked differentiation in the generation of opportunities for cooperation. These opportunities could also promote conflict, and more research is needed on the topic, but if structural opportunities are not provided ties will not develop. Mandated legal networks and budget networks sometimes tend to create structurally equivalent organizational actors. They may actually be increasing the 98 tendency of similar organizations to interact with one ano- ther, generating some kind of local social closure, instead of promoting integration or cooperation. Huxley wrote somewhere that what an individual becomes depends on what he inherits, what his circumstance has done to him, and what he chooses to do with his inheritance and his circumstance. As sociologists we should know that Hux- ley's "circumstance“ is constituted by the set of socially structured alternatives. These alternatives, be it for indi- viduals or for organizations, are dependent, among other things, on the distribution of attributes and resources in their populations and, in turn, how these populations are distributed along the parameters created by these resources. 99 NOTES (1) But see Eisenstadt's argument that Weber anticipated and went beyond Levi-Strauss (1981). (2) I am using the dichotomy British social anthropology vs. French structuralism to characterize the epistemologi- cal distinction as to whether social structure is assumed to be real ( referring to actual social relations in socie- ty), or whether social structure is a system of logical relations imposed externally and a priori by the resear- cher. The latter is Levi-Strauss' notion (1963). (3) Although not even service organizations in urban cen- ters are totally exempt of the effects of spatial proximity as facilitator of interorganizational relations; see Boje and Whetten (1981). (4)In sociology there have been some attempts to merge population ecology models with decision making models such as Olson's (1965) (Nielsen, 1978); more relevant to the point in case, however, seems to be the tradition led by J. Maynard Smith (1982) that explains evolution in terms of the theory of games. This approach has been considered by Dawkins (1976) to be one of the most important advances in evolutionary theory since Darwin. (5) Which do not have to be partitions as Simon (1981) suggests-see Atkin (1981). (6) This is not, of course, a simple issue and is very much related to the agency problem in microeconomics and con- tractual law and,in particular, to the "theory of the organ" in public and constitutional law, in which Jellinek - an intelectual father of Weber- has played a major role. However, "corporate actors" can be defined as a formally constituted and recognized grouping of individual actors, which may be treated as possessing superordinate goals, Objectives, or purposesthat organize the contributions of persons to the corporate enterprise and direct the inte- rests of the corporate actor vis-a-vis other corporate actors and persons (cf. Coleman, 1974; Laumann et al.; 1978). 100 (7) Blau's "emergence" is very similar to Boudon's: "an emergent effect is ...an effect which is not expli- citly sought by the agents of a system and which re- sults of their position of interdependence ...the in- terdependent system creates here an effect of 'over- shooting ' " (1979: 59) (8) Notice that these notions of position and role are related to Simmel's notions of human types (Levine, 1971). Blau's notion of position is such that the relational nature of positions and not exclusively the normative as- pects are taken into account. In this sense the notion is similar to Nadel's (1957). His notion, however, is signifi- cantly different from an attempt to operationalize Nadel's concept, namely the structural equivalence approach (Lor- raine and White, 1971; White, Boorman, and Breiger, 1976) because the latter considers useless the categorical ap- proaches (normative?) to the notion of role (White et. a1, 1976). This approach, however, establishes positions but not roles and it is population-specific (Winship and Man- del, 1984). (9) Notice that the sign of the correlation is not relevant for nominal parameters because there is no meaningful orde- ring. (10) Originally Blau (1977) had stated the opposite effect, that is that inequality reduces the likelihood of associa- tion between status-distant persons. Blau explains himself: ?The original reasoning was that because status distance Inhbibits associations-by assumption (which is empirically supported)- and because inequality is defined in terms of average status-distance, a plausible inference is that mean status-distance, just as status distance, has the effect of discouraging associations. But this argument looks at asso— ciations completely from the stand point of the individual and ignores the constraints the social structure imposes on the individual's choices of associates. Just as an increase in heterogeneity makes it more likely that chance encoun- ters involve persons of different groups, an increase in inequality makes it more likely that chance encounters involves persons whose status is further apart" (Blau and Schwartz, 1984:15). Actually I must say that the original statement had to be very unclear, as Blau himself admits, because I had inter- preted it to say what the current phrasing says; and Skvo- retz and Fararo (n/d) did too. (11) Actually integration should be measured by density and 101 not by the mere relation of out-ties to in-ties (see Ryti- na, 1980) (12) As Skvoretz (1983) notes, the absence of the treatment of this type of orientation towards outgroup relations may be due to the fact that Blau is concerned in explaining integration of a differentiated society. With outgroup or- ientations or "outbreeding" the issue does not pose major problems. (13) Actually Marsden introduces an interesting distinction between nominal and graduated parameters that basically implies that there is an equal bias for all the outgroups in the case of nominal parameters and a differential one (based on social distance) for graduated parameters. His empirical example for occupation as a graduated parameter is faulty, however, since occupational correlates, i.e. income, prestige, etc., should be controlled in order to determine appropriately if occupation should be conceptua- lized as a graduated parameter. (14) Mohr (1971) and the Aston group (Pugh et al.,l968; 1969; Ikson et al., 1971: Child, 1972) seem to be the only studies that contradict the assertion on the relevance of technology. Mohr, however, seems to confound systems of control with participativeness in decision making. Aldrich (1972) has persuasively argued on the questionable validity of the findings of the Aston group on technology. For a recent study on the effects of size and technology, see, for example, Marsh and Mammari (1981). (15) These are types of measures. Many other actual measures exist. For reviews and examples see Burt (1982); Knoke and Burt (1983); Freeman (1977; 1979) and Mizruchi and Bunting (1981). (16) A connection is negative if exchange in one relation is contingent on nonexchange in the other (Cook et al., 1983) (17) This measure is not only appropriate because it deter— mines the potential for control but because it can be calculated on sparse networks as opopssed to the distance based measures (Freeman, 1979) (18) A geodesic from i to j is a path from i to j of minimum length, where length is the number of lines (see Harary, Norman and Cartwright (1965) (19) Freeman (1977) has shown that this is the maximum 102 value that the central node can attain (see also Knoke and Kuklinski, 1982). (20) The original version of Structure (version 2) calcu- lates prominence only for symmetric matrices. Structure (version 3) attempts to calculate it for asymmetric ma- trices too. Structure (version 3) could not be implemented in the system, but the algorithms were implemented in Version 2. The program uses at the same time, the mathema- tical routines EISPACK and IMSL. The changes to Structure are available upon request. (21) White's test is based on aregression that fits the residuals and the product of nR square. However, since the number of cases is small, visual inspection was also em- ployed. (22) The salience of the parameters in this study is con- sistently shown by a host of rates that relate densities that are produced as output of the computer program in- cluded in Appendix III; and as the result of earlier compu- ter runs performed by Patterson A. Terry that looked at segregation indexes in the vein of Freeman (1978). The reason not one single straight forward index of salience could be used was that as Rytina (1980) has already noted, real data is very different from models. In this set of data there is practically always a different salience for each subcategory, for each dimension of exchange, for each city. But, to increase the problem, each subcategory has different saliences for the respective subcategories. This means that there are about N(N-l) saliences, with N being the number of subcategories, for each dimension along each parameter, in each city. (23) If the reader requires assistance in the algebraic manipulation, notice that when every body is tied with everybody, the k in the formula for the relational Gini becomes n (or n-1) and becomes a constant that can be "taken out" of the sum. Since it is dividing, the denomina- tor has now an n square term and becomes identical to the general formula for the Gini coefficient. (24) I am using here by analogy terminology from Willer and Anderson (1982). (25) At a merely speculative level it is worhtwhile to mention the unexpected findings with respect to budget. The results were not always statistically significant but they were consistent. Galaskiewicz (1979) in one of those few pieces of research somewhat relevant for the present 103 discussion, found that the network of exchange that dealt with money was the most important one. Further, he also showed that four blocks of organizations could be distin- guished in the community under study. One of them was the block of social services. What has been called the poten- tial network here is at best a subset of this block. Bud- gets, though, among public social service organizations (and those private based on grants) are generally allocated by processes that are partially external to what is consi- dered to be the potential network in the present research. It could well be that the processes of inequality along the parameter budget that determine the structure of opportuni- ties and constraints for these organizations are to be searched in a broader network. Of course, in the context of the present research none of this speculation is a "fact" nor can it be proven but I consider it worthwhile to engage in such speculations until new research findings become available. 104 City 10 11 12 37 47 38 38 42 44 44 32 41 31 41 APPENDIX I PERCENTAGE NONRESPONSE 6.8 14.6 9.8 105 Variable 14.5 15.0 18.8 13.2 11.9 13.7 22.7 12.4 12.2 6.8 12.2 APPENDIX II QUESTIONS Which agencies have the most influence over decisions about human services in this community? (WRITE IN ID NUMBER, RECORD ONLY THOSE SPONTANEOUSLY MENTIONED) Which agencies send people to your agency for services? (WRITE IN ID NUMBER, RECORD ONLY THOSE SPONTANEOUSLY MEN- TIONED) Which agencies have the most prestige? (WRITE IN ID NUMBER, RECORD ONLY THOSE SPONTANEOUSLY MENTIONED) With which agencies do you exchange opinions, information and ideas? (WRITE IN ID NUMBER, RECORD ONLY THOSE SPONTA- NEOUSLY MENTIONED) Which agencies does your agency rely on to deliver your own services/programs to clients? (WRITE IN ID NUMBER, RECORD ONLY THOSE SPONTANEOUSLY MENTIONED) We are interested in knowing about any informal cooperative relationships your agency has with other agencies in this community (HAND YELLOW CARD). This card lists some of the common types of cooperative relationships social services agencies develop on an informal basis. By informal rela- tionships we mean relationships that have no formal ba- sis...that is, there isn't a written agreement or contract, probably very little, if any, money changes hands and most of the problems that arise or changes that are made are worked out by mutual adjustment. Using the list on the yellow card as examples of inter-agency cooperation, please identify any agencies with which your agency works on any sort of informal cooperative basis. (AFTER RESPONDENT IDENTIFIES AGENCIES, PROBE TO REVIEW COMPREHENSIVENESS OF LIST USING TYPES OF RELATIONSHIPS IDENTIFIED ON YELLOW CARD. RECORD ID NUMBERS) 106 APPENDIX III COMPUTER PROGRAM EMPLOYED FOR PART OF THE ANALYSIS The program produces choice and tie-account tables, calcu- lates densities, ratios of densities, segregation indexes different categories, on the basis of the number of choices and the number of ties (ties have forced reciproca- tion). A relational Gini coefficient is also calculated. It was written and developed by Patterson A. Terry. PROGRAM BINOM(OUTPUT,TAPE1,TAPE2,TAPE3,TAPE4) IMPLICIT INTEGER(A-Z) REAL CHMAT(19,19,2),CHMATX(5,18,2),DMAT(19,19,2), 1DMATX(5,18,2),PCHMAT(19,19,2),PCHMATX(5,18,2),PMAT 2(6,19,19,2),RMAT(6,19,19,2),STATUS(48),PRESTAT(48) DIMENSION CHRMAT(48),CMAT(18),IMAT(47,47),IRMAT(99), lUID(48) RESTART=ENDFLG1=ENDFLGZ=NCITIES=NSETS=0 NCHAR=5 NCHP=NCHAR+1 CALL READl(CITYIDI,NCITYID,OCITYID,NCITIES,NCHAR,NCHP, 1NUID,UID,CHRMAT,CMAT,IRMAT,ENDFLG1,PRESTAT) CALL READZ(CITYIDl,NCITYID,OCITYID,NSETS,NCHAR,NCHP,UID,NUID, IENDFLGl,ENDFLGZ,IRMAT,CMAT,CHRMAT) DO 2 Z=1,NSETS CALL CHSET(CHMAT,CHRMAT,NCHAR,NCHP,NUID,PRESTAT,STATUS, lUID) CALL PCHDSET(CHMAT,CMAT,DMAT,NCHAR,NCHP,NSETS,NUID, 1PCHMAT) CALL RPSETI(CHMAT,DMAT,NCHAR,NCHP,PCHMAT,PMAT,RMAT) CALL RPSETZ(CHMAT,CHMATX,DMAT,DMATX,NCHAR,NCHP,PCHMAT, 1PCHMATX,RMAT) CALL RPSET3(CHMAT,CHMATX,DMAT,DMATX,NCHAR,NCHP,PCHMAT, 1PCHMATX,PMAT) CALL WRITEl(CHMAT,CHMATX,CMAT,DMAT,DMATX,NCHAR,NCHP,NUID, 1 OCITYID,PCHMAT,PCHMATX,STATUS,UID,Z) CALL WRITEZ(NCHAR,NCHP,PMAT,RMAT) IF(ENDFLG2.EQ.1)GO TO 999 107 NSETS=0 REWIND 3 GO TO 1 999 STOP END SUBROUTINE READl(CITYIDl,NCITYID,OCITYID,NCITIES,NCHAR, lNCHP,NUID,UID,CHRMAT,CMAT,IRMAT,ENDFLGl,PRESTAT) IMPLICIT INTEGER(A-Z) DIMENSION CHRMAT(48),CMAT(NCHAR),IRMAT(99),UID(48) REAL PRESTAT(48) Do 1 I=1,NCHAR 1 CMAT(I)=0 LASTID=I=1 l0 READ(l,l0l,END=51)CITYIDl,UID(I),CHRMAT(I),PRESTAT(I) 101 FORMAT(2I2,3X,12,5X,F9.3) IF(UID(I).LT.LASTID)THEN BACKSPACE 1 NCITYID=CITYIDI CITYID1=OCITYID GO TO 52 ENDIF IRMAT(UID(I))=I CMAT(CHRMAT(I))=CMAT(CHRMAT(I))+l OCITYID=CITYID1 LASTID=UID(I) I=I+1 GO TO 10 51 ENDFLGl=l 52 NUID=I-1 NCITIES=NCITIES+1 RETURN END SUBROUTINE READ2(CITYIDl,NCITYID,OCITYID,NSETS,NCHAR, 1NCHP,UID,NUID,ENDFLG1,ENDFLG2,IRMAT,CMAT,CHRMAT) IMPLICIT INTEGER(A-Z) DIMENSION CMAT(NCHAR),IMAT(47,47),IRMAT(99),LINE(8), lUID(48),CHRMAT(NUID),FMT1(3) NCID=RESTART=0 ENCODE(30,1001,FMT1)NUID 1001 FORMAT('(',12,'I1)') 3 DO 4 I=1,NUID DO 4 J=1,NUID 4 IMAT(I,J)=0 LASTID=0 NSETS=NSETS+1 10 READ(2,101,END=28)CITYID2,ID,(LINE(I),I=1,8) 108 101 12 l3 14 28 29 31 99 11 FORMAT(2X,ZIZ,5X,8(12,5X)) IF(ID.LT.LASTID)THEN BACKSPACE 2 IF(CITYID2.EQ.OCITYID)GO TO 30 GO TO 29 ENDIF DO 13 I=1,8 IF(LINE(I).EQ.0)GO TO 14 IMAT(IRMAT(ID),IRMAT(LINE(I)))=1 IF(ID.GT.LASTID)LASTID=ID GO TO 10 ENDFLGZ=1 RESTART=1 DO 31 I=1,NUID WRITE(3,FMT1)(IMAT(I,J),J=1,NUID) IF(RESTART.EQ.0)GO TO 3 REWIND 3 RETURN STOP END SUBROUTINE CHSET(CHMAT,CHRMAT,NCHAR,NCHP,NUID,PRESTAT, 18TATUS,UID) IMPLICIT INTEGER(A-Z) REAL CHMAT(19,19,2),STATUS(NUID),PRESTAT(NUID),CNT DIMENSION CHRMAT(NUID),IMAT(47,47),UID(48), lFMTl(3) Do 1 I=1,NCHP Do 1 J=l,NCHP Do 1 K=l,2 CHMAT(I,J,K)=0 Do 2 I=1,NUID STATUS(I)=0 ENCODE(30,1001,FMT1)NUID FORMAT('(',12,'Il)') Do 3 I=1,NUID READ(3,FMT1)(IMAT(I,J),J=1,NUID) DO 10 I=1,NUID CNT=0 Do 8 J=1,NUID IF(IMAT(I,J) .EQ. 0.AND. IMAT(J,I).EQ.0)GO TO 8 CNT=CNT+1 CONTINUE Do 9 J=1,NUID IF(IMAT(I,J).EQ.0.AND.IMAT(J,I).EQ.0)GO To 9 STATUS(I)=STATUS(I)+(PRESTAT(I)-PRESTAT(J))/CNT IF(IMAT(I,J).EQ.0)GO TO 9 CHMAT(NCHP,NCHP,1)=CHMAT(NCHP,NCHP,1)+1 IF(IMAT(J,I).EQ.1)THEN 109 9 10 19 20 CHMAT(NCHP,NCHP,2)=CHMAT(NCHP,NCHP,2)+.5 ELSE CHMAT(NCHP,NCHP,2)=CHMAT(NCHP,NCHP,2)+1 ENDIF CHMAT(NCHP,CHRMAT(J),1)=CHMAT(NCHP,CHRMAT(J),1)+l CHMAT(CHRMAT(I),NCHP,1)=CHMAT(CHRMAT(I),NCHP,1)+1 CHMAT(CHRMAT(I),CHRMAT(J),1)=CHMAT(CHRMAT(I),CHRMAT l(J),l)+l IF(IMAT(J,I).EQ.1)THEN IF(CHRMAT(I).EQ.CHRMAT(J))THEN CHMAT(CHRMAT(I),CHRMAT(J),2)=CHMAT(CHRMAT(I), lCHRMAT(J),2)+.5 ELSE CHMAT(CHRMAT(I),CHRMAT(J),2)=CHMAT(CHRMAT(I), lCHRMAT(J),2)+1 ENDIF ELSE CHMAT(CHRMAT(I),CHRMAT(J),2)=CHMAT(CHRMAT(I), lCHRMAT(J),2)+l IF(CHRMAT(I).NE.CHRMAT(J))THEN CHMAT(CHRMAT(J),CHRMAT(I),2)=CHMAT(CHRMAT(J), lCHRMAT(I),2)+l ENDIF ENDIF CONTINUE CONTINUE DO 20 I=1,NCHAR DO 19 J=1,NCHAR CHMAT(I,NCHP,2)=CHMAT(I,NCHP,2)+CHMAT(I,J,2) CHMAT(NCHP,I,2)=CHMAT(I,NCHP,2) RETURN END SUBROUTINE PCHDSET(CHMAT,CMAT,DMAT,NCHAR,NCHP,NSETS, 1NUID,PCHMAT) IMPLICIT INTEGER(A-Z) REAL CHMAT(19,19,2),DMAT(19,19,2),PCHMAT(19,19,2) DIMENSION CMAT(NCHAR) DO 1 I=1,NCHP DO 1 J=1,NCHP DO 1 K=l,2 DMAT(I,J,K)=0 PCHMAT(NCHP,NCHP,1)=REAL(NUID*(NUID-l)) PCHMAT(NCHP,NCHP,2)=PCHMAT(NCHP,NCHP,1)/2 DO 10 I=1,NCHAR PCHMAT(I,I,1)=REAL(CMAT(I)*(CMAT(I)-1)) PCHMAT(I,I,2)=PCHMAT(I,I,1)/2 PCHMAT(I,NCHP,1)=REAL(CMAT(I)*(NUID-l)) PCHMAT(I,NCHP,2)=PCHMAT(I,I,2)+REAL(CMAT(I)*(NUID- 110 10 20 28 30 1CMAT(I))) PCHMAT(NCHP,I,1)=REAL(NUID*CMAT(I)-CMAT(I)) PCHMAT(NCHP,I,2)=PCHMAT(I,NCHP,2) DO 9 J=l,NCHAR IF(I.NE.J)PCHMAT(I,J,1)=PCHMAT(I,J,2)=REAL(CMAT(I)* 1CMAT (J) ) CONTINUE CONTINUE DO 30 K=l,2 DMAT(NCHP,NCHP,K)=CHMAT(NCHP,NCHP,K) 1 /(PCHMAT(NCHP,NCHP,K)) DO 30 J=1,NCHAR IF(PCHMAT(NCHP,J,K).NE.0)THEN DMAT(NCHP,J,K)=CHMAT(NCHP,J,K)/PCHMAT(NCHP,J,K) ENDIF IF(PCHMAT(J,NCHP,K).NE.0)THEN DMAT(J,NCHP,K)=CHMAT(J,NCHP,K)/PCHMAT(J,NCHP,K) ENDIF DO 30 I=1,NCHAR IF(PCHMAT(I,J,K).NE.0)THEN DMAT(I,J,K)=CHMAT(I,J,K)/PCHMAT(I,J,K) ENDIF CONTINUE RETURN END SUBROUTINE RPSETl(CHMAT,DMAT,NCHAR,NCHP,PCHMAT,PMAT, lRMAT) IMPLICIT INTEGER(A-Z) REAL CHMAT(19,19,2),DMAT(19,19,2),P(6),PK,PS,PCHMAT l(l9,l9,2),PMAT(6,19,19,2),RMAT(6,19,19,2) DIMENSION K(6),N(6) Do 10 I=1,NCHAR Do 9 J=1,NCHAR IF(I.EQ.J)THEN Do 5 Y=l,6. DO 5 X=l,2 RMAT(Y,I,J,X)=PMAT(Y,I,J,X)=0 GO TO 9 ENDIF DO 8 x=1,2 IF(DMAT(J,NCHP,X).NE.0)THEN RMAT(1,I,J,X)=DMAT(I,NCHP,X)/DMAT(J,NCHP,X) ENDIF IF(DMAT(NCHP,J,X).NE.0)THEN RMAT(2,I,J,X)=DMAT(NCHP,I,X)/DMAT(NCHP,J,X) ENDIF IF(DMAT(J,J,X).NE.0)THEN 111 RMAT(3,I,J,X)=DMAT(I,I,X)/DMAT(J,J,X) ENDIF IF(DMAT(I,J,X).NE.0)THEN RMAT(4,I,J,X)=DMAT(I,I,X)/DMAT(I,J,X) ENDIF IF(DMAT(J,I,X).NE.0)THEN RMAT(5,I,J,X)=DMAT(I,I,X)/DMAT(J,I,X) ENDIF IF(DMAT(J,J,X).NE.0)THEN RMAT(6,I,J,X)=DMAT(I,J,X)/DMAT(J,J,X) ENDIF K(1)=INT(CHMAT(I,NCHP,X)) N(l)=INT(PCHMAT(I,NCHP,X)) P(1)=DMAT(J,NCHP,X) K(2)=INT(CHMAT(NCHP,I,X)) N(2)=INT(PCHMAT(NCHP,I,X)) P(2)=DMAT(NCHP,J,X) K(3)=INT(CBMAT(I,I,X)) N(3)=INT(PCHMAT(I,I,X)) P(3)=DMAT(J,J,X) K(4)=INT(CHMAT(I,I,X)) N(4)=INT(PCHMAT(I,I,X)) P(4)=DMAT(I,J,X) K(5)=INT(CHMAT(I,I,X)) N(5)=INT(PCHMAT(I,I,X)) P(5)=DMAT(J,I,X) K(6)=INT(CHMAT(I,J,X)) N(6)=INT(PCHMAT(I,J,X)) P(6)=DMAT(J,J,X) DO 8 Y=l,6 CALL MDBIN(K(Y),N(Y),P(Y),PS,PK,IER) PMAT(Y,I,J,X)=PS IF(IER.NE.0)WRITE(4,101)K(Y),N(Y),P(Y),PS,PK,IER,I,J,X FORMAT(214,3F8.S,I6,4X,3I3) CONTINUE CONTINUE CONTINUE RETURN END SUBROUTINE RPSETZ(CHMAT,CHMATX,DMAT,DMATX,NCHAR,NCHP, 112 1PCHMAT,PCHMATX,RMAT) IMPLICIT INTEGER(A-Z) REAL CHMAT(19,19,2),CHMATX(5,18,2),DMAT(19,19,2), 1DMATX(5,18,2),PCHMAT(19,19,2),PCHMATX(5,18,2), 2RMAT(6,19,19,2) DO 10 I=1,NCHAR DO 5 X=1,2 CHMATX(2,1,X)=CHMAT(I,NCHP,X)-CHMAT(I,I,X) PCHMATX(2,I,X)=PCHMAT(I,NCHP,X)-PCHMAT(I,I,X) CHMATX(3,I,X)=CHMAT(NCHP,I,X)-CHMAT(I,I,X) PCHMATX(3,I,X)=PCHMAT(NCHP,I,X)-PCHMAT(I,I,X) CHMATX(1,1,1)=CHMAT(NCHP,NCHP,1)-CHMAT(I,NCHP,1) PCHMATX(1,I,1)=PCHMAT(NCHP,NCHP,l)-PCHMAT(I,NCHP,1) CHMATX(4,I,l)=CHMAT(NCHP,NCHP,l)-CHMAT(I,NCHP,1) -CHMAT(NCHP,I,1)+CHMAT(I,I,l) PCHMATX(4,1,l)=PCHMAT(NCHP,NCHP,l)-PCHMAT(I,NCHP,1) -PCHMAT(NCHP,I,1)+PCHMAT(I,I,1) CHMATX(5,1,1)=CHMAT(NCHP,NCHP,l)-CHMAT(NCHP,I,1) PCHMATX(5,I,l)=PCHMAT(NCHP,NCHP,1)-PCHMAT(NCHP,I,1) CHMATX(1,1,2)=CHMAT(NCHP,NCHP,2)-CHMAT(I,I,2) PCHMATX(1,1,2)=PCHMAT(NCHP,NCHP,2)-PCHMAT(I,I,2) CHMATX(4,I,2)=CHMAT(NCHP,NCHP,2)-CHMAT(I,NCHP,2) PCHMATX(4,1,2)=PCHMAT(NCHP,NCHP,2)-PCHMAT(I,NCHP,2) CHMATX(5,1,2)=CHMAT(NCHP,NCHP,2)-CHMAT(I,1,2) PCHMATX(5,1,2)=PCHMAT(NCHP,NCHP,2)-PCHMAT(I,I,2) DO 29 y=1,5 Do 29 I=1,NCHAR DO 29 x=1,2 IF(PCHMATX(Y,I,X).EQ.0)THEN DMATX(Y,I,X)=0 GO TO 29 ENDIF DMATX(Y,I,X)=CHMATX(Y,I,X)/PCHMATX(Y,I,X) CONTINUE DO 39 I=1,NCHAR DO 39 x=1,2 IF(DMATX(1,I,X).NE.0)THEN RMAT(1,I,NCHP,X)=DMAT(I,NCHP,X)/DMATX(l,I,X) ENDIF IF(DMATX(5,I,X).NE.0)THEN RMAT(2,I,NCHP,X)=DMAT(NCHP,I,X)/DMATX(5,1,X) ENDIF IF(DMATX(4,I,X).NE.0)THEN RMAT(3,I,NCHP,X)=DMAT(I,I,X)/DMATX(4,I,X) ENDIF IF(DMATX(2,I,X).NE.0)THEN RMAT(4,I,NCHP,X)=DMAT(I,I,X)/DMATX(2,1,X) 113 ENDIF IF(DMAT(3,I,X).NE.0)THEN RMAT(5,I,NCHP,X)=DMAT(I,I,X)/DMATX(3,1,X) ENDIF IF(DMATX(4,I,X).NE.0)THEN RMAT(6,I,NCHP,X)=DMATX(2,1,X)/DMATX(4,I,X) ENDIF IF(DMAT(I,NCHP,X).NE.0)THEN RMAT(1,NCHP,I,X)=DMATX(1,I,X)/DMAT(I,NCHP,X) ENDIF IF(DMAT(NCHP,I,X).NE.0)THEN RMAT(2,NCHP,I,X)=DMATX(5,1,X)/DMAT(NCHP,I,X) ENDIF IF(DMAT(I,I,X).NE.0)THEN RMAT(3,NCHP,I,X)=DMATX(4,1,X)/DMAT(I,I,X) ENDIF IF(DMATX(3,I,X).NE.0)THEN RMAT(4,NCHP,I,X)=DMATX(4,I,X)/DMATX(3,1,X) ENDIF IF(DMATX(2,I,X).NE.0)THEN RMAT(5,NCHP,I,X)=DMATX(4,I,X)/DMATX(2,I,X) ENDIF IF(DMAT(I,I,X).NE.0)THEN RMAT(6,NCHP,I,X)=DMATX(3,I,X)/DMAT(I,I,X) ENDIF CONTINUE RETURN END SUBROUTINE RPSET3(CHMAT,CHMATX,DMAT,DMATX,NCHAR,NCHP, 1PCHMAT,PCHMATX,PMAT) IMPLICIT INTEGER(A-Z) REAL CHMAT(19,19,2),CHMATX(5,18,2),DMAT(19,19,2), lDMATX(5,18,2),P(6,2),PCHMAT(19,19,2),PCHMATX 2(5,18,2),PK,PS,PMAT(6,19,19,2) DIMENSION K(6,2),N(6,2) DO 19 I=1,NCHAR Do 19 x=1,2 K(1,l)=INT(CHMAT(I,NCHP,X)) N(l,l)=INT(PCHMAT(I,NCHP,X)) P(l,l)=DMATX(l,I,X) K(2,1)=INT(CHMAT(NCHP,I,X)) N(2,1)=INT(PCHMAT(NCHP,I,X)) P(2,l)=DMATX(5,I,X) K(3,1)=INT(CHMAT(I,I,X)) N(3,1)=INT(PCHMAT(I,I,X)) 114 P(3,1)=DMATX(4,I,X) K(4,l)=INT(CHMAT(I,I,X)) N(4,1)=INT(PCHMAT(I,I,X)) P(4,1)=DMATX(2,I,X) K(5,1)=INT(CHMAT(I,I,X)) N(5,1)=INT(PCHMAT(I,I,X)) P(5,1)=DMATX(3,I,X) K(6,1)=INT(CHMATX(2,I,X)) N(6,1)=INT(PCHMATX(2,I,X)) P(6,l)=DMATX(4,I,X) K(1,2)=INT(CHMATX(1,I,X)) N(l,2)=INT(PCHMATX(1,I,X)) P(1,2)=DMAT(I,NCHP,X) K(2,2)=INT(CHMATX(5,I,X)) N(2,2)=INT(PCHMATX(5,I,X)) P(2,2)=DMAT(NCHP,I,X) K(3,2)=INT(CHMATX(4,I,X)) N(3,2)=INT(PCHMATX(4,I,X)) P(3,2)=DMAT(I,I,X) K(4,2)=INT(CHMATX(4,I,X)) N(4,2)=INT(PCHMATX(4,I,X)) P(4,2)=DMATX(3,I,X) K(5,2)=INT(CHMATX(4,I,X)) N(5,2)=INT(PCHMATX(4,I,X)) P(5,2)=DMATX(2,I,X) K(6,2)=INT(CHMATX(3,I,X)) N(6,2)=INT(PCHMATX(3,I,X)) P(6,2)=DMAT(I,I,X) DO 19 Y=l,6 Do 19 w=1,2 CALL MDBIN(K(Y,W),N(Y,W),P(Y,W),PS,PK,IER) IF(W.EQ.1)PMAT(Y,I,NCHP,X)=PS IF(W.EQ.2)PMAT(Y,NCHP,I,X)=PS 19 IF(IER.NE.0)WRITE(4,101)K(Y,W),N(Y,W),P(Y,W),PS, lPK,IER,I,J,X 191 FORMAT(214,3F8.5,I6,4X,313) RETURN END 115 SUBROUTINE WRITEl(CHMAT,CHMATX,CMAT,DMAT,DMATX, lNCHAR,NCHP,NUID,OCITYID,PCHMAT,PCHMATX,STATUS,UID,Z) IMPLICIT INTEGER(A-Z) REAL CHMAT(19,19,2),DMAT(19,19,2),DMATX(5,18,2), 1 PCHMAT(19,19,2),STATUS(NUID),TSTATUS DIMENSION CMAT(NCHAR),UID(48) TSTATUS=9 WRITE(4,101)OCITYID,Z 191 FORMAT(1HT,25X,'CMAT VECTOR FOR CITY',I3,', SET', 113.////) WRITE(4,102)(CMAT(I),I=1,NCHAR) 192 FORMAT(llI4,/////) WRITE(4,103)OCITYID,Z 193 FORMAT(' STATUS VECTOR FOR CITY',I3,', SET',I3,/) DO 19 I=1,NUID TSTATUS=TSTATUS+STATUS(I) 19 WRITE(4,104)OCITYID,UID(I),STATUS(I) 1941 FORMAT(10X,212,5X,F9.3) TSTATUS=TSTATUS/(2*NUID) WRITE(4,1041)TSTATUS 141 FORMAT(5X,'TOTAL',9X,F9.3) WRITE(4,105)OCITYID,Z 195 FORMAT(1HT,30X,'TABLES FOR CHOICES, CITY',13,', SET', 113.///) x=1 CALL WRITElA(CHMAT,CHMATX,DMAT,DMATX,NCHAR,NCHP,PCHMAT, 1PCHMATX,X) WRITE(4,107)OCITYID,Z 197 FORMAT(1H1,26X,'TABLES FOR TIES, CITY',I3,' SET',13) x=2 CALL WRITElA(CHMAT,CHMATX,DMAT,DMATX,NCHAR,NCHP,PCHMAT, 1PCHMATX,X) RETURN END SUBROUTINE WRITElA(CHMAT,CHMATX,DMAT,DMATX,NCHAR,NCHP, 1PCHMAT,PCHMATX,X) IMPLICIT INTEGER(A-Z) REAL CHMAT(19,19,2),CHMATX(5,18,2),DMAT(19,19,2), 1DMATX(5,18,2),PCHMAT(19,19,2),PCHMATX(S,18,2) DIMENSION NUMBER(33),FMT1(3),FMT2(3) ENCODE(30,1001,FMT1)NCHP 1001 FORMAT('(IIO,',IZ,'(3X,F9.5))') ENCODE(30,1002,FMT2)NCHP 1002 FORMAT('(9X,',I2,'(10X,IZ),/)') ELVN=19 DO 1 I=1,ELVN 1 NUMBER(I)=I 116 101 12 102 14 103 16 104 22 105 106 23 107 24 101 102 WRITE(4,101) FORMAT(//,30X,'ACTUAL CHOICE COUNT MATRIX',/) WRITE(4,FMT2)(NUMBER(I),I=1,NCHAR),ELVN Do 12 I=1,NCHAR WRITE(4,FMT1)I,(CHMAT(I,J,X),J=l,NCHAR),CHMAT(I, lNCHP,X) WRITE(4,FMT1)ELVN,(CHMAT(NCHP,J,X),J=l,NCHAR),CHMAT 1(NCHP,NCHP,X) WRITE(4,102) FORMAT(//,28X,'POSSIBLE CHOICE COUNT MATRIX',/) WRITE(4,FMT2)(NUMBER(I),I=1,NCHAR),ELVN Do 14 I=1,NCHAR WRITE(4,FMT1)I,(PCHMAT(I,J,X),J=1,NCHAR),PCHMAT(I, lNCHP,X) WRITE(4,FMT1)ELVN,(PCHMAT(NCHP,J,X),J=l,NCHAR),PCHMAT 1(NCHP,NCHP,X) WRITE(4,103) FORMAT(//,33X,'CHOICE DENSITY MATRIX',/) WRITE(4,FMT2)(NUMBER(I),I=1,NCHAR),ELVN Do 16 I=1,NCHAR WRITE(4,FMT1)I,(DMAT(I,J,X),J=1,NCHAR),DMAT(I,NCHP,X) WRITE(4,FMT1)ELVN,(DMAT(NCHP,J,X),J=1,NCHAR),DMAT 1(NCHP,NCHP,X) WRITE(4,104) FORMAT('T',//,35X,'CHMATX MATRIX',//) Do 22 I=1,NCHAR WRITE(4,105)I,(CHMATX(Y,I,X),Y=1,5),CHMAT(I,I,X) FORMAT(Il0,6(3X,Fl0.5)) WRITE(4,106) FORMAT(//,35X,'PCHMATX MATRIx',//) Do 23 I=1,NCHAR WRITE(4,105)I,(PCHMATX(Y,I,X),Y=l,5),PCHMAT(I,I,X) WRITE(4,107) FORMAT(//,35X,'DMATX MATRIx',//) DO 24 I=1,NCHAR WRITE(4,105)I,(DMATX(Y,I,X),Y=1,5),DMAT(I,I,X) RETURN END SUBROUTINE WRITEZ(NCHAR,NCHP,PMAT,RMAT) IMPLICIT INTEGER(A-Z) REAL PMAT(6,19,19,2),RMAT(6,19,19,2) ELVN=19 DO 10 I=1,NCHAR WRITE(4,101)I FORMAT(1H1,20X,'RATIOS, PROBABILITIES FOR CHARACT lERISTIC ',IZ,//) WRITE(4,102) FORMAT(/,50X,'FOR CHOICES',/) 117 103 105 10 22 26 DO 2 J=1,NCHAR IF(I.EQ.J)GO TO 2 WRITE(4,103)J,(RMAT(Y,I,J,1),Y=l,6),(PMAT(Y,I,J,1), 1Y=l,6) FORMAT(I10,4X,6(F8.5,1X),10X,6(F8.5,1X)) CONTINUE WRITE(4,103)ELVN,(RMAT(X,I,NCHP,1),X=1,6),(PMAT(Y,I, lNCHP,l),Y=1,6) WRITE(4,105) FORMAT(//,53X,'FOR TIES',/) DO 6 J=l,NCHAR IF(I.EQ.J)GO To 6 WRITE(4,193)J,(RMAT(x,I,J,2).X=1.6).(PMAT(Y.I.J.2). 1Y=1,6) CONTINUE WRITE(4,193)ELVN,(RMAT(X,I,NCHP,2),x=1,6).(PMAT(Y,I, 1NCHP,2),Y=1,6) CONTINUE WRITE(4,101)ELVN WRITE(4,102) Do 22 I=1,NCHAR WRITE(4,103)I,(RMAT(X,NCHP,I,1),X=l,6),(PMAT(Y, lNCHP,I,l),Y=l,6) WRITE(4,105) Do 26 I=1,NCHAR WRITE(4,103)I,(RMAT(X,NCHP,I,2),X=l,6),(PMAT(Y, 1NCHP,I,2),Y=1,6) RETURN END 118 APPENDIX IV COMPONENTS OF INDEXES OF INTERSECTION AND CONSOLIDATION AND THEIR RELIABILITY ( Cronbach's alpha ). 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