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…

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 analysis of an m-group model is considered. A convenient stage III prior is proposed, and cases when the posterior distributions take on a simple form are exhibited. The behavior of various point estimators of the linear parameters of the model are explored in a Monte Carlo study. In the simple model considered, the O'Hagan estimator…

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.…

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)

The technical problems involved in obtaining Bayesian model estimates for the regression parameters in m similar groups are studied. The available computer programs, BPREP (BASIC), and BAYREG, both written in FORTRAN, require an amount of computer processing that does not encourage regular use. These programs are analyzed so that the performance…

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…

Least squares and Bayes methods were used in a cross validation study conducted for comparison purposes. The study applies to situations with the following conditions: predictor data are given on the same scales; criterion data may be given on different scales; and it is necessary to pool data even though criterion scale differences exist. Such a…

Classical multiple regression was compared with Bayesian m-group regression, complete with cross-validation. The setting was a post-developmental studies situation in a comprehensive community college. A secondary purpose of the study was to incorporate an advisor prediction of grade point average (GPA) as input into both regression procedures.…

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…

Classical statistical methods and the small enrollments in graduate departments have constrained the Graduate Record Examinations (GRE) Validity Study Service to providing only validities for single predictors. Estimates of the validity of two or more predictors, used jointly, are considered too unreliable because the corresponding prediction…