(1979). Social Networks and Psychology. Connections, 2 - INSNA

- 70 -city's organizational structure, including both the number of local organizations as well as organizationallinks to the extralocal environment, affect another aspect of that organizational structure, the existenceof wheel-like networks as measured by city-wide associations . Here the condition available for study ishow recently the city has become large ; we argue that time works against locally measurable causation oflocal events . In brief, this means our having expected the strength of the predicted statistical relationsto vary inversely with how long the city had had at least 50,000 inhabitants . The newer the city, thestronger the covariation among the city's structural properties .The Problem of Empirical IsomorphismWe examined the largest city (ignoring ones with fewer than 100,000 inhabitants) in each of 104 (outof 110) standard metropolitan statistical areas (SMSAs) for which data were complete . The sheer numberof organizations of all kinds that were located in the area (standardized by number of inhabitants) constitutedone component of prediction (source : U .S . Bureau of the Census, County Business Patterns, 1962) .The number of national headquarters of voluntary associations (source : Gale Research Bureau, Encyclopediaof Associations 1961) constituted the (now widely used) surrogate measure of the city's external links(see Turk, 1977 : 40-43, 93 for discussions of the indicator's validity and use) . The dependent variablewas the number of voluntary associations mentioned by knowledgable informants in 1961 as being highlyvisible and relevant to such broad properties as city-wide consensus, cohesion, and civic pride ; anymention of contest against such an association caused us to remove it from consideration . (For detaileddescription of this measure, which has been used extensively, and for assessments of its reliability andvalidity see Turk, 1977 : 66-73 .) That these associations, once they are mentioned as important to thecity, are likely to have been focal organizations in networks is a reasonable assumption, as the followingexamples will show : Chambers of commerce, booster groups, and other kinds of business, professional, andservice clubs ; community chest and other kinds of fund-raising organizations (not simply drives) ; a laborcouncil and a taxpayer's association . As we have mentioned, each city was also classified according tothe census year in which it first had 50,000 inhabitants . 1920-1960 was considered "new ;" 1890-1910,"fairly new" ; and before 1890 was called "old ."The phrasing of our substantive problem demands departure from path or factor analysis and from otherpopular techniques that describe social units as though covariation among properties were simply linearand additive . We argue that most socialstructural theory, including network theory, requires thedesignation of joint or multiplicative effects . Not only may sociology be too closely wedded to linearityand additivity, but it might also fail to give nonmonotonicity its full due .Here we expected that how long a city has been large, how many organizations there are within it ornearby, and how many of these different organizations are externally linked to operate multiplicativelyin ways to be described . The contribution made by number of organizations to such joint effects wasexpected to be nonmonotonic .Specification of our model began with measuring each SMSA's deviation from the mean number of organizations. Having too few organizations is taken to mean little need for those wheel-like networks likelyto have city-wide associations at their hubs . Having too many is taken as an impediment to the occurrenceof these networks . Thus, all things equal, departure from the mean number of organizations reduces thelikelihood of city-wide associations . The absolute value of such deviation in number of organizations(DNoOrg) was multiplied by two dummy variables that measured, respectively, whether or not the city is"new" (N) and whether or not it is "fairly new" (FN) . The number and variety of external links (Ext) wasmultiplied by the same two dummy variables . These four products -- one of them based on a nonmonotonicfunction -- constituted the predictors of city-wide associations (CityWAss) . They produced the followingresults in the form of standardized partial regression coefficients (beta weights) :City WAss = - .19DNoOrg x N - .20DNoOrg x FN - .16Ext x N - .13Ext x FNAll coefficients are in the expected direction and significant at least at the .10 level . Elevenpercent of the variation is explained by this equation . However, the similarity of results between thenew and fairly new cities, as well as hindsight provided by a cluster analysis to be published elsewhere(Turk and Hanada, 1978), led to some modifications in our specification .We recognized, first, that capacity alone, in the form of low external linkage, could not influencethe occurrence of city-wide associations unless there also existed a need for them . Capacity and needoperate multiplicatively ; where either one is absent, nothing will happen at all . Nor can low externallinkage overcome the negative effects of too many organizations . Unexpectedly, however, the clusteranalysis also suggested that external linkage did not impede city-wide associations in cities that hadnearly the mean number of associations . These observations may be summarized as follows : Among citiesthat are not too old (NO), (1) how close each one is to having the mean number of organizations affectsthe occurrence of city-wide associations independently of the amount of external linkage ; and (2) externallinkage has its effect only insofar as the number of organizations deviates from the mean, but does notdeviate too far . This second observation required construction of a dummy variable that refers to citiesmidway in their deviation from the mean number of organizations (MDNoOrg) . Its use in the following equation(having modified Ext by removing the effect of age of city, with which it is highly correlated),