In most research, linear regression analyses are performed without taking into account published results (i.e., reported summary statistics) of similar previous studies. Although the prior density in Bayesian linear regression could accommodate such prior knowledge, formal models for doing so are absent from the literature. The goal of this…

In this article, we present a Bayes factor solution for inference in multiple regression. Bayes factors are principled measures of the relative evidence from data for various models or positions, including models that embed null hypotheses. In this regard, they may be used to state positive evidence for a lack of an effect, which is not possible…

Due to its extensive applicability and computational ease, moderated multiple regression (MMR) has been widely employed to analyze interaction effects between 2 continuous predictor variables. Accordingly, considerable attention has been drawn toward the supposed multicollinearity problem between predictor variables and their cross-product term.…

This is an application of contemporary multilevel regression modeling to the prediction of academic performances of 1st-year college students. At a first level of analysis, the data come from N greater than 16,000 students who were college freshman in 1994-1995 and who were also participants in high-level college athletics. At a second level of…

The presence of suppression (and multicollinearity) in multiple regression analysis complicates interpretation of predictor-criterion relationships. The mathematical conditions that produce suppression in regression analysis have received considerable attention in the methodological literature but until now nothing in the way of an analytic…

Person fit is the degree to which an item response model fits for individual examinees. Reise (2000) described how two-level logistic regression can be used to detect heterogeneity in person fit, evaluate potential predictors of person fit heterogeneity, and identify potentially aberrant individuals. The method has apparently never been applied to…