Model Selection for Longitudinal Social Networks

This paper concerns model selection for a class of continuous-timeMarkov chains for modeling longitudinal social networks. Many models of thiskind have been proposed in the literature (Holland and Leinhardt, 1977a,b;Wasserman, 1977, 1980b,a; Snijders, 1996, 2001) but until recently likelihood-based inference has only been explored under the assumption of dyad indepen-dence. Using data augmentation it was shown in Koskinen (2004b) how theclass of continuous-time Markov chains open to likelihood-based inference canbe extended to entail more complex dependence structures. Arguably, the maintheoretical motivation behind models for longitudinal social networks is to inferwhat components are important in the dynamics of social interaction. This callsfor statistical procedures for testing hypothesis, something which in the absenceof procedures for conducting model selection, is limited to inspection of posteriorcredibility regions. The Bayesian paradigm is well suited for model selection butthe relative complexity of this class of models prevents the use of any standardtechniques for calculating the relevant quantities (the evaluated likelihood andmarginal likelihood respectively). Although an analytically tractable form forthe likelihood function is not strictly necessary for performing parameter infer-ence (c.f. Koskinen, 2004b), most model selection techniques rely heavily on theassumption that the likelihood can easily be evaluated. We identify a familyof models, with the property that they have the reciprocity model Wasserman(1977) as special case, for which the scheme of Chib and Jeliazkov (2001) forestimating the marginal likelihood can be adapted, thus providing the posteriordistribution over a set of models. If the analysis is restricted to comparisonsbetween nested models, the likelihood function does not have to be evaluatedand model selection need not be restricted to models with the reciprocity modelas a special case. The procedure is illustrated using van de Bunt’s (1999) fresh-men students, a stochastic actor oriented model (Snijders, 1996, 2001, 2004)and partial Bayes factors.