Performance evaluation of recent information criteria for selecting multilevel models in Behavioral and Social Sciences

This study was designed to find the best strategy for selecting the correct multilevel model among several alternatives taking into account variables such as intraclass correlation, number of groups (m), group size (n), or others as parameter values and intercept-slope covariance. First, we examine this question in a simulation study and second, to illustrate the behavior of the criteria and to explore the generalizability of the findings, a previously published educational dataset is analyzed. The results showed that none of the selection criteria behaved correctly under all the conditions or was consistently better than the others. The intraclass correlation somewhat affects the performance of all selection criteria, but the extent of this influence is relatively minor compared to sample size, parameter values, and correlation between random effects. A large number of groups appears more important than a large number of individuals per group in selecting the best model (m >= 50 and n >= 20 is suggested). Finally, model selection tools such as Akaike's Information Criterion (AIC) or the conditional AIC are recommend when it is assumed that random effects are correlated, whereas use of the Schwarz's Bayesian Information Criterion or the consistent AIC are advantageous for uncorrelated random effects