Strategies for model selection within the regression framework typically involve choices among several sometimes competing criteria. In this article, the interrelated criteria of goodness-of-fit and parameter invariance are explored with respect to a class of maximum likelihood network autocorrelation models. A GLS measure of generalized goodness-of-fit, R2G, is proposed for these models based on the equivalence of ML and GLS in the exponential family. This R2G statistic can be used to test for stability of parameters across various samples or subsamples. A second test of parameter invariance across subsamples is proposed: Schwarz's (1978) information Criterion. An example illustrates how these identification and testing procedures may be jointly used to help select the most adequate model for a given data set.
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