Residual Normality Assumption and the Estimation of Multiple Membership Random Effects Models

Abstract

While conventional hierarchical linear modeling is applicable to purely hierarchical data, a multiple membership random effects model (MMrem) is appropriate for nonpurely nested data wherein some lower-level units manifest mobility across higher-level units. Although a few recent studies have investigated the influence of cluster-level residual nonnormality on hierarchical linear modeling estimation for purely hierarchical data, no research has examined the statistical performance of an MMrem given residual non-normality. The purpose of the present study was to extend prior research on the influence of residual non-normality from purely nested data structures to multiple membership data structures. Employing a Monte Carlo simulation study, this research inquiry examined two-level MMrem parameter estimate biases and inferential errors. Simulation factors included the level-two residual distribution, sample sizes, intracluster correlation coefficient, and mobility rate. Results showed that estimates of fixed effect parameters and the level-one variance component were robust to level-two residual non-normality. The level-two variance component, however, was sensitive to level-two residual non-normality and sample size. Coverage rates of the 95% credible intervals deviated from the nominal value assumed when level-two residuals were non-normal. These findings can be useful in the application of an MMrem to account for the contextual effects of multiple higher-level units.