Tom A.B. Snijders is Professor of Statistics and Methodology at the Dept. of Sociology, University of Groningen, Emeritus Fellow, Nuffield College, University of Oxford and an Associate Member at the Dept. of Statistics, University of Oxford.
Homophily is a basic feature of social networks. For numerical actor variables, its specification in statistical network models is usually done by means of the absolute difference between ego and alter on the variable under consideration; sometimes, as an alternative, by the ego-alter interaction. It is argued that such specifications are incomplete for continuous actor variables and for ordinal numerical variables with three or more categories. The reason is that ego is not necessarily attracted mostly to others with the same value as ego; often the attraction is to some value between ego's value and the 'social norm'. (Attraction here is to be understood not necessarily as a preference, but rather as an empirical tendency.) Therefore, the usual representation will often amount to a misspecification. This is elaborated in an extension of the usual specification of effects of actor variables in stochastic actor-oriented models for network dynamics. This new specification may have consequences for results of studies of social selection. An example is given.