We study flexible Bayesian methods that are amenable to a wide range of learning problems involving complex high dimensional data structures, with minimal tuning. We consider parametric and semiparametric Bayesian models, that are applicable to both static and dynamic data, arising from a multitude of areas such as economics, finance and…

Commonality components have been defined as a method of partitioning squared multiple correlations. The asymptotic joint distribution of all possible squared multiple correlations is derived. The asymptotic joint distribution of linear combinations of squared multiple correlations is obtained as a corollary. (Author/JKS)

Commentary is presented on the preceding articles in this issue of the journal. Critical commentary is made article by article, and some general recommendations are made. (See TM 503 664 through 670). (JKS)

The problem of selecting regression variables using cost criteria is considered. A method is presented which approximates the optimal solution of one of several criterion functions which might be employed. Examples are given and the results are compared with the results of other methods. (Author/JKS)

A simple roof is presented: that the squared multiple correlation of a variable with the remaining variables in the set of variables is a lower bound to the communality of that variable. (Author/JKS)

The use of interaction and non-linear terms in multiple regression poses problems for determining parsimonious models. Several computer programs for using these terms are discussed. (JKS)

A statistical analysis procedure is developed, based on the notion that many educational programs are dynamic interventions in natural growth processes, and is called value-added analysis. The theory of value-added analysis, and several applications are presented. (Author/JKS)

Path analysis is a data analytic technique for estimating the strengths of hypothesized relationships among a group of variables for a particular sample. Strategies for the use of path analysis are discussed in detail in this extensive article. (JKS)

Interpretations regarding the effects of exogenous and endogenous variables on endogenous variables in linear structural equation systems depend upon the convergence of a matrix power series. The test for convergence developed by Joreskog and Sorbom is shown to be only sufficient, not necessary and sufficient. (Author/JKS)

Problems in testing main effects in regression analysis when there is interaction are discussed. A method by which main effects can be tested independently of the interaction is developed and compared with the hierarchical method. The method provides control of the type I error rate, but is quite conservative. (Author/JKS)

Longley proposed a set of data for use in testing regression programs. This paper shows that the numerically accurate solution is likely to be an unreasonable estimate of the regression coefficients for this problem. This is true because the accuracy of the data and appropriateness of the model may affect the solution more than the computational…

Three mathematical models and their enrollment projections for higher education in Georgia are presented. The first model is an extrapolation of current trends. The second model is a simple linear regression model based on steady growth. The third is a multiple regression model attempting to account for the influences of several variables…

A general class of regression models for ordered categorised data is developed and discussed. Thier properties are contrasted with log linear models and other methods of analysis. The general problem of fitting by maximum likelihood is discussed and solved. The models are shown to be multivariate extensions of generalised linear models and the…

The degree of nonorthogonality in a factorial design was systematically increased. Five methods of dealing with nonorthogonality were selected and applied: two were least squares solutions (Method 1 and Method 2); two were approximate solutions (the unweighted means analysis and the method of expected frequencies); and the fifth was the…

To the data analyst, outliers can present both a problem and an opportunity. Stray or outlying observations can severly distort estimates of a distribution's central tendency (like the mean) and estimates of one variable's relationship to another (like the regression coefficient). These problems are frequent and serious, and as a result,…