Model Selection Based on Information Criteria in Multilevel Modeling
Despite the advantages of information criteria for model selection and their inclusion in most multilevel modeling (MLM) programs, the literature on model selection in MLM is dominated by NHT (cf. Bryk & Raudenbush, 1992; Hox, 2002; Kreft & de Leeuw, 1998; Longford, 1995; Snijders & Bosker, 1999). What may contribute to this neglect of information criteria is unfamiliarity with these measures and a lack of understanding of the rationale behind them: Their rather simple appearance may give the erroneous impression that these measures were “invented” in an ad hoc fashion, rather than that they are soundly rooted in, for instance, information theory or Bayesian statistics. In addition, it is not always clear how to apply information criteria within the MLM context. Specific questions that may arise here are whether or not the random effects themselves should be penalized (an issue for all three information criteria considered here), and what the actual number of observations is (in case of the BIC).