Previous studies that explored the impact of misspecification of cross-classified data structure as strictly hierarchical are limited to random intercept models. This study examined the effects of misspecification of a two-level, cross-classified, random effect model (CCREM) where both the level-1 intercept and slope were allowed to vary randomly. Results suggest that ignoring one of the crossed factors produced considerably underestimated standard errors for: 1) the regression coefficients of the level-1 predictor; 2) the inappropriately modeled predictor associated with the misspecified crossed factor; and 3) and their interaction. This misspecification also resulted in a significant inflation of the level-1 residual variances and the intercept and slope variance components across the levels of the remaining crossed factor in hierarchical linear model.
Ye, F., & Daniel, L. (2017). The Impact of Inappropriate Modeling of Cross-Classified Data Structures on Random-Slope Models. Journal of Modern Applied Statistical Methods, 16(2), 458-484. doi: 10.22237/jmasm/1509495900