Re-parameterized regression models may enable tests of crucial theoretical predictions involving interactive effects of predictors that cannot be tested directly using standard approaches. First, we present a re-parameterized regression model for the Linear x Linear interaction of 2 quantitative predictors that yields point and interval estimates…

Despite many articles reporting the problems of dichotomizing continuous measures, researchers still commonly use this practice. The authors' purpose in this article was to understand the reasons that people still dichotomize and to determine whether any of these reasons are valid. They contacted 66 researchers who had published articles using…

Recursive partitioning methods have become popular and widely used tools for nonparametric regression and classification in many scientific fields. Especially random forests, which can deal with large numbers of predictor variables even in the presence of complex interactions, have been applied successfully in genetics, clinical medicine, and…

In multilevel modeling, one often distinguishes between macro-micro and micro-macro situations. In a macro-micro multilevel situation, a dependent variable measured at the lower level is predicted or explained by variables measured at that lower or a higher level. In a micro-macro multilevel situation, a dependent variable defined at the higher…

Appropriately centering Level 1 predictors is vital to the interpretation of intercept and slope parameters in multilevel models (MLMs). The issue of centering has been discussed in the literature, but it is still widely misunderstood. The purpose of this article is to provide a detailed overview of grand mean centering and group mean centering in…

Researchers often have one or more theories or expectations with respect to the outcome of their empirical research. When researchers talk about the expected relations between variables if a certain theory is correct, their statements are often in terms of one or more parameters expected to be larger or smaller than one or more other parameters.…

The article uses confirmatory factor analysis (CFA) as a template to explain didactically multilevel structural equation models (ML-SEM) and to demonstrate the equivalence of general mixed-effects models and ML-SEM. An intuitively appealing graphical representation of complex ML-SEMs is introduced that succinctly describes the underlying model and…