Estimation of Extensions to the Multiple-Membership and Cross-Classified Random Effects Models

• In Event: Multilevel Modeling: Nonnested Multilevel Data, Measurement Invariance, and Nonlinear Models

Abstract

This study assessed estimation of four two-level models that can be used to handle multiple-membership data structures (e.g., students clustered within schools with some students mobile across schools). The four models included the multiple membership random effects model (MMREM), the cross-classified random effects model (CCREM) and two extensions. The MMREM extension (unMMREM) allows unique level-2 variance components. The CCREM (rCCREM) extension allows non-zero correlations between pairs of level-2 cross-classified factor residuals. A simulation study and analysis of real data were conducted. No substantial bias was found in fixed effects estimates across models. Only unMMREM estimates of the level-1 residuals’ variance were substantially biased. rCCREM estimates of level-2 variances were mostly unbiased although MMREM, unMMREM and CCREM estimates were substantially biased.

Authors

• Andee Kaplan, University of Iowa

• Susan Natasha Beretvas, The University of Texas - Austin