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…

A challenge associated with traditional mixture regression models (MRMs), which rest on the assumption of normally distributed errors, is determining the number of unobserved groups. Specifically, even slight deviations from normality can lead to the detection of spurious classes. The current work aims to (a) examine how sensitive the commonly…

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…

Bayesian methods are becoming very popular despite some practical difficulties in implementation. To assist in the practical application of Bayesian methods, we show how to implement Bayesian analysis with WinBUGS as part of a standard set of SAS routines. This implementation procedure is first illustrated by fitting a multiple regression model…

This paper details a Bayesian alternative to the use of least squares and equal weighting coefficients in regression. An equal weight prior distribution for the linear regression parameters is described with regard to the conditional normal regression model, and resulting posterior distributions for these parameters are detailed. (Author/CTM)

The utility of least squares multiple regression in predicting new scores from previously established equations is considered. It is shown that in the absence of useful prior information, and when normality assumptions are not violated, least squares multiple regression weights are superior to alternatives recently presented in the literature.…

Bayesian techniques are adapted to the estimation of stimulus-response curves. Illustrative examples deal with estimation of person characteristic curves and item characteristic curves in the context of mental testing, and with estimation of a stimulus-response curve using data from a psychophysical experiment. (Author/JKS)

Bayesian and empirical Bayes approaches to shrinkage estimation of regression coefficients and uses of these in prediction (i.e., analyzing intelligence test data of children with learning problems) are investigated. The two methods are consistently better at predicting response variables than are either least squares or least absolute deviations.…

The theoretical rationales and procedures of five adaptive computer-based instruction models were reviewed: the mathematical model, the regression model, the Bayesian probabilistic model, the testing and branching model, and artificially intelligent instructional systems. Each model is assessed for contrast of methods and forms, identifiable…

Empirical Bayes methods are shown to provide a practical alternative to standard least squares methods in fitting high dimensional models to sparse data. An example concerning prediction bias in educational testing is presented as an illustration. (Author)

Compares classical multiple regression with Bayesian m-group regression, including cross-validation of both methods, in a study to predict first-quarter grade point average in various curricula for community colleges students who had completed developmental studies programs. Finds informal counselor prediction the largest contribution to…

This study addressed concerns about the potential for differential gains in reading during the first 2 years of formal schooling (K-1) versus the next 2 years of schooling (1st-3rd grade). A multilevel piecewise regression with a node at spring 1st grade was used in order to define separate regressions for the two time periods. Empirical Bayes…