2008/03/17 by Daniel J. Bauer, Li Cai · 1 citation
Decision Sciences · Mathematics · #Advanced Causal Inference Techniques #Psychometric Methodologies and Testing #Statistical Methods and Bayesian Inference
paper · doi:10.3102/1076998607310504
openalex publication_date 2008/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
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.