A multilevel simultaneous equations model for within-cluster dynamic effects, with an application to reciprocal parent–child and sibling effects

There has been substantial interest in the social and health sciences in the reciprocal causal influences that people in close relationships have on one another. Most research has considered reciprocal processes involving only 2 units, although many social relationships of interest occur within a larger group (e.g., families, work groups, peer groups, classrooms). This article presents a general longitudinal multilevel modeling framework for the simultaneous estimation of reciprocal relationships among individuals with unique roles operating in a social group. We use family data for illustrative purposes, but the model is generalizable to any social group in which measurements of individuals in the social group occur over time, individuals have unique roles, and clustering of the data is evident. We allow for the possibility that the outcomes of family members are influenced by a common set of unmeasured family characteristics. The multilevel model we propose allows for residual variation in the outcomes of parents and children at the occasion, individual, and family levels and residual correlation between parents and children due to the unmeasured shared environment, genetic factors, and shared measurement. Another advantage of this method over approaches used in previous family research is it can handle mixed family sizes. The method is illustrated in an analysis of maternal depression and child delinquency using data from the Avon Brothers and Sisters Study.