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…

Issues in the detection and interpretation of interaction effects between quantitative variables in multiple regression analysis are discussed. Recent discussions associated with problems of multicollinearity are reviewed in the context of the conditional nature of multiple regression with product terms. (TJH)

The cross-validated classification accuracies of three predictor weighting strategies (least squares, ridge regression, and reduced rank) were compared under varying simulated data conditions for the two-group classification problem. Results were somewhat similar to previous findings with multiple regression when absolute rather than relative…

Interpretation of multivariate models requires knowing how much the fit of the model is impaired by changes in the parameters. The relation of parameter change to loss of goodness of fit can be called parameter sensitivity. Formulas are presented for assessing the sensitivity of multiple regression and principal component weights. (Author/JKS)

Set correlation is a multivariate generalization of multiple regression/correlation analysis that features the employment of overall measures of association interpretable as proportions of variance and the use of set-partialled sets of variables. The statistical development of the theory and several examples are presented. (Author/JKS)

Tables for selecting sample size in correlation studies are presented. Some of the tables allow selection of sample size so that r (or r[squared], depending on the statistic the researcher plans to interpret) will be within a target interval around the population parameter with probability 0.95. The intervals are [plus or minus] 0.05, [plus or…

A core assumption of the standard multiple regression model is independence of residuals, the violation of which results in biased standard errors and test statistics. The structural equation model (SEM) generalizes the regression model in several key ways, but the SEM also assumes independence of residuals. The multilevel model (MLM) was…