- 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) st<strong>and</strong>ard metropolitan statistical areas (SMSAs) for which data were complete . The sheer numberof organizations of all kinds that were located in the area (st<strong>and</strong>ardized 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 <strong>and</strong> use) . The dependent variablewas the number of voluntary associations mentioned by knowledgable informants in 1961 as being highlyvisible <strong>and</strong> relevant to such broad properties as city-wide consensus, cohesion, <strong>and</strong> 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, <strong>and</strong> for assessments of its reliability <strong>and</strong>validity 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, <strong>and</strong> other kinds of business, professional, <strong>and</strong>service clubs ; community chest <strong>and</strong> other kinds of fund-raising organizations (not simply drives) ; a laborcouncil <strong>and</strong> 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" ; <strong>and</strong> before 1890 was called "old ."The phrasing of our substantive problem dem<strong>and</strong>s departure from path or factor analysis <strong>and</strong> from otherpopular techniques that describe social units as though covariation among properties were simply linear<strong>and</strong> 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 linearity<strong>and</strong> 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, <strong>and</strong> 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) <strong>and</strong> whether or not it is "fairly new" (FN) . The number <strong>and</strong> 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 st<strong>and</strong>ardized 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 <strong>and</strong> significant at least at the .10 level . Elevenpercent of the variation is explained by this equation . However, the similarity of results between thenew <strong>and</strong> fairly new cities, as well as hindsight provided by a cluster analysis to be published elsewhere(Turk <strong>and</strong> 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 <strong>and</strong> 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 ; <strong>and</strong> (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),
provided the following improved specification :CityWAss =- .28DNoOrg x NO - .28MDNoOrg x Ext x NOBoth st<strong>and</strong>ardized partial regression coefficients are in the expected direction <strong>and</strong> significant atthe .005 level . The explained variation has increased by one-third to 15 percent . Clearly, both impuritiesin the indicators (three described the city, for example, <strong>and</strong> one the SMSA) <strong>and</strong> necessarily arbitraryassumptions about measurement in at least one case (the mean as reference point) affected the unexplainedvariation . It is also true, however, that we have not included all of the relevant variables ; such was notour intention . Further, our subsequent work will attempt to separate the level of need, which the numberof organizations estimates, from the level of incapacity measured by that same indicator .But what of main effects or lower order statistical interaction? This question is frequently askedas a matter of routine, because of the close association likely between interactive terms <strong>and</strong> theirconstituents . But the question, "What of higher order interaction?" could be posed for this very samereason at other times when only simpler effects have been reported . The last is less routinely asked --because of the methodological customs, we believe, to which we have already referred . Bowing to custom,however, where observance might impeach our finding, we did allow our two effects of theoretical interestto compete with all lower order effects in a stepwise regression procedure . The hypothesized equationresulted . All other variables save one failed to meet the probability of .50 required for entry ; thisone, which failed to reach the .30 level, served to increase the hypothesized effects .ConclusionsIt is possible to predict a surrogate measure of rudimentary networks that consist of focal <strong>and</strong> otherorganizations within urban settings . Though the area of application is new, the conceptual models arenot -- making use as they did of the Hobbesian solution to social order, of Simmel's discussion of theeffect of numbers of organized elements on supraorganization, <strong>and</strong> of sociology's long concern with societal-environmentalconstraints placed on free interplay among sub-societal events .Using these conceptual guides, it has proven possible to identify some multiplicative <strong>and</strong> nonmonotoniccorrelates of associations that represent the shared interests of a city's other organizations . By theirvery nature these associations suggest the presence of interorganizational networks that approximate stars(wheels) . If the city is not very old, the correlates are (1) the extent to which the number of organizationsmakes city-wide associations necessary but not impossible <strong>and</strong> (2) the extent to which external linksare few, provided that the number of organizations is such as to signify either marginal need or marginalincapacity .There is danger, as we have suggested, in undue preoccupation with method without substance . It wouldbe sad if network analysis were to be held captive by modern techniques -- however exciting <strong>and</strong> superiorto our own crude network measure some of these are . That sociology has unduly emphasized monotonicity,linearity, <strong>and</strong> additivity for so long should provide a pointed lesson . 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