Consequences of Unmodeled Nonlinear Effects in Multilevel Models

Abstract

Applications of multilevel models have increased markedly during the past decade. In incorporating lower-level predictors into multilevel models, a key interest is often whether or not a given predictor requires a random slope, that is, whether the effect of the predictor varies over upper-level units. If the variance of a random slope significantly differs from zero, the focus of the analysis may then shift to explaining this heterogeneity with upper-level predictors through the testing of cross-level interactions. As shown in this article, however, both the variance of the random slope and the cross-level interaction effects may be entirely spurious if the relationship between the lower-level predictor and the outcome is nonlinear in form but is not modeled as such. The importance of conducting diagnostics to detect nonlinear effects is discussed and demonstrated via an empirical example.