Statistical models for social support networks: Application of exponential models to undirected graphs with dyadic dependencies

Abstract

Research on the relationship between social support and general well-being often focuses on the personal support network, the group of individuals upon whom one calls for assistance in any given situation. With more sophisticated theories of social support, researchers no longer consider the mere availability of social ties but look instead at the flow of specific resources through a social network. The structure of this network may hold valuable information about the network's effectiveness in providing support. The network measures commonly used describe the characteristics of the social network but provide neither a standard nor a means for comparison. Recent advances in the exponential modeling of social networks, however, allow statistical tests of hypotheses about network structure. The most common method employs loglinear analysis to fit the exponential models to the networks and to obtain maximum likelihood estimates of the model parameters. These methods make the restrictive assumption that the different ties within a network are independent of each other. This assumption may not be tenable in the case of social support networks, in which all network members are tied at least indirectly through the focal individual. One solution to this problem that has been proposed uses pseudolikelihood estimation procedures to fit exponential models under assumptions of certain types of dependencies among the network ties. The pseudolikelihood estimates, although not identical to the maximum likelihood estimates, are often quite close. This dissertation (a) examines the use of both maximum likelihood and pseudolikelihood methodologies in the study of social support networks and (b) examines a modification of the pseudolikelihood procedure that may yield parameter estimates that are closer to the maximum likelihood estimates than are the pseudolikelihood estimates.