The costs of simplicity : why multilevel models may benefit from accounting for cross-cluster differences in the effects of controls

Context effects, where a characteristic of an upper-level unit or cluster (e.g., a country) affects outcomes and relationships at a lower level (e.g., that of the individual), are a primary object of sociological inquiry. In recent years, sociologists have increasingly analyzed such effects using quantitative multilevel modeling. Our review of multilevel studies in leading sociology journals shows that most assume the effects of lower-level control variables to be invariant across clusters, an assumption that is often implausible. Comparing mixed-effects (random-intercept and slope) models, cluster-robust pooled OLS, and two-step approaches, we find that erroneously assuming invariant coefficients reduces the precision of estimated context effects. Semi-formal reasoning and Monte Carlo simulations indicate that loss of precision is largest when there is pronounced cross-cluster heterogeneity in the magnitude of coefficients, when there are marked compositional differences among clusters, and when the number of clusters is small. Although these findings suggest that practitioners should fit more flexible models, illustrative analyses of European Social Survey data indicate that maximally flexible mixed-effects models do not perform well in real-life settings. We discuss the need to balance parsimony and flexibility, and we demonstrate the encouraging performance of one prominent approach for reducing model complexity.