Nonlinear Multilevel Model Selection Using Information Criteria
Multilevel modeling is a common approach to modeling longitudinal change in behavioral sciences. While many researchers use linear functional forms to model change across time, researchers sometimes anticipate nonlinear change. In such cases, researchers often fit polynomial functional forms, such as quadratic or cubic forms. Polynomial functional forms are suitable in many situations, but there are other functional forms that could potentially better match the researcher’s theory about the nature of the longitudinal change. “Truly” nonlinear models, such as exponential and logistic models, have been used to model biological phenomena and may also be useful for psychological research. Such models, however, are non-nested, meaning that likelihood ratio tests cannot be used to select among models if one or more truly nonlinear models are in the candidate model set. Information criteria offer a flexible framework for model selection that can accommodate truly nonlinear models, but there currently is no research directly exploring the ability of information criteria to select truly nonlinear multilevel models. In this dissertation, two Monte Carlo simulation studies were conducted to examine the performance of two frequently used information criteria: AIC and BIC. The goal of the first study was to examine their ability to select unconditional models with correctly specified nonlinear functional forms. Higher L1 and L2 sample sizes, a higher ICC, and greater distinction between nonlinear functional forms generally improved correct model selection rates, but BIC appeared to be better than AIC when identifying more distinct nonlinear functional forms and AIC appeared to be better when the forms were less distinct. The goal of the second study was to examine the ability of AIC and BIC to select a model with a “more correct” predictor set when the underlying functional form was truly nonlinear. In many cases, information criteria were able to identify models determined to be more correct, but no clear pattern emerged between AIC and BIC. Finally, the utility of truly nonlinear functional forms was demonstrated in two behavioral health applications, both of which contained substantively interesting nonlinear trends that would have been missed if analysis had been limited to the linear functional form.