Model selection for Cognitive Social Structures
Johan H. Koskinen · Research Explorer (The University of Manchester) · 2004
Measurement accuracy is an inherent problem in social networkanalysis. The issue of actor accuracy in the reporting of their interactions withothers, was raised by Bernard, Killworth and Sailer (e.g. Bernard et al., 1980)and provoked extensive debate. Krackhardt (1987) later introduced the conceptof Cognitive Social Structures and several methods for aggregating different ac-tor reports on the network into a single graph, with the aid of which for examplethe congruence of reports could be gaged. Often when this data collecting para-digm is used the interest is in correlating bias on the part of the perceivers withexogenous attributes of the perceivers (e.g. Bondonio, 1998; Casciaro, 1998; Cas-ciaro et al., 1999). A statistical model for aggregating separate reports into asingle consensus network, with the additional benefit of allowing estimates ofactor accuracy to be obtained in the process, was proposed by Batchelder et al.(1997). Using an extension of this model and a Bayesian approach we are ableto incorporate effects of known covariates and network effects on perceptionalbiases. In Koskinen (2002a) it was suggested that the conditional probabilityof reporting a tie as present when a tie is really present (or absent) be modeledusing a probit link function. This is further elaborated here with a special focuson finding standard reference priors that enables model selection. The mainobstacle is that the model is not fully identified, something which can not besolved in any obvious way through restrictions or highly informative priors. Theproposed solution is to asses a posteriori which are the main determinants ofidentifying conditions. We present a procedure for choosing prior distributionsand provide the necessary adjustments to the original sampling scheme.