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Cross-classified random effects modelling (CCREM) is a special case of multi-level modelling where the units of one level are nested within two cross-classified factors. Typically, CCREM analyses omit the random interaction effect of the cross-classified factors. We investigate the impact of the omission of the interaction effect on parameter estimates and standard errors. Results from a Monte Carlo simulation study indicate that, for fixed effects, both coefficients estimates and accompanied standard error estimates are not biased. For random effects, results are affected at level 2 but not at level 1 by the presence of an interaction variance and/or a correlation between the residual of level two factors. Results from the analysis of the Early Childhood Longitudinal Study and the National Educational Longitudinal Study agree with those obtained from simulated data. We recommend that researchers attempt to include interaction effects of cross-classified factors in their models.
Shi et al. (Tue,) studied this question.