The Impact of Omitting Random Interaction Effects in Cross-Classified Random Effect Modeling

Abstract

The present study examines bias in parameter estimates and standard error in cross-classified random effect modeling (CCREM) caused by omitting the random interaction effects of the cross-classified factors, focusing on the effect of a sample size within cells and ratio of a small cell. A Monte Carlo simulation study was conducted to compare the correctly specified and the misspecified CCREM. While there was negligible bias in fixed effects, substantial biases were found in the random effects of the misspecified model depending on the number of samples within a cell and the proportion of small cells. However, in the case of the correctly specified model, no bias occurred. The present study suggests considering the random interaction effects when conducting CCREM to avoid overestimation of variance components and to calculate an accurate value of estimation. The implications of this study are to illuminate the conditions of cross-classification ratio and to provide a meaningful reference for applied researchers using CCREM.

Keywords:

• Cross-classified random effect modeling
• estimation bias
• HLM
• random interaction effect
• simulation studies

Notes

1 For the results of relative parameters and relative standard error in detail, see Appendix A.

2 When the correlation is 0.4, the bias in the graphs signifies the bias from the value of true parameter, 1.00.