A reduced social relations model for dyad-constant dependent variables

Dyadic network data occur when each member in a group provides data about each other member in the group (e.g., how much they like each other person). Such data have a complex nesting structure, such that bivariate responses (e.g., Person A’s liking of B and vice versa) are dependent upon out-going and in-coming random effects that are correlated within individuals. Dyadic network models for such data include the social relations model for normal data and the p₂ and j₂ models for dichotomous data, but we have seen no application or generalization to accommodate a rarely discussed type of variable from this framework: variables that are constant within a dyad. Dyad-constant variables could include background variables such as whether a dyad is same or opposite sex or how many years two friends have known each other, which require no special modification to use as predictors (Jorgensen et al., Soc Netw 54:26–40, 2018). But they could also be outcomes, such as the difference in a married couple’s relationship satisfaction or the similarity in symptoms of a (set of) psychological disorder(s). We explore how such dyad-constant outcomes can be modeled, demonstrating on a data set from a clinic for patients with eating disorders.