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…

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)

Several themes which are common to both econometrics and psychometrics are surveyed. The themes are illustrated by reference to permanent income hypotheses, simultaneous equation models, adaptive expectations and partial adjustment schemes, and by reference to test score theory, factor analysis, and time-series models. (Author)

An example demonstrates that Joreskog's suggested sufficient conditions for identifying unknown parameters in a confirmatory factor analytic model with correlated factors are not sufficient. Sufficient conditions are presented. (Author/JKS)

A Monte Carlo study was performed to test under what conditions and to what degree various alternatives would be superior to multiple linear regression (MLR). The criteria used was the mean squared error of prediction of individual scores and the mean squared error of estimation of the regression weights. Populations were simulated containing…

A method for the estimation of covariance structure models under polynomial constraints (such as quadratic constraints) is presented. Estimation is on maximum likelihood principles, and the test statistics, parameter estimates, and standard errors are based on a statistical theory which takes the constraints into account. (Author/JKS)

A variety of algorithms for analyzing covariance structures are considered. Additionally, two methods of estimation, maximum likelihood, and weighted least squares are considered. Comparisons are made between these algorithms and factor analysis. (Author/JKS)

Similarities between regression analysis and analysis of variance are noted and it is argued that the former has advantages over the latter. It is also argued that canonical correlation analysis is more suitable than factor analysis in certain cases. The argument is illustrated with four recent pieces of educational research. (DG)

Two major and two minor principles are shown to serve to generate a large number of multivariate models, including canonical analysis, factor analysis, and latent trait test theory. The statistical underpinnings of the theory are discussed. (Author/JKS)

Identification and explication of construct relationships, under conditions of extraneous variable control in multiple regression and its multivariate analog, canonical analysis, were studied. Several data models were generated as a function of the interaction of partial correlation and orthogonal linear transformations on nursing examination…

A general approach to analysis of covariance structures is considered, in which the variances and covariances or correlations of the observed variables are directly expressed in terms of the parameters of interest. The statistical problems of identification, estimation and testing of such covariance or correlation structures are discussed.…

The relationship of multiple linear regression to various multivariate statistical techniques is discussed. The importance of the standardized partial regression coefficient (beta weight) in multiple linear regression as it is applied in path, factor, LISREL, and discriminant analyses is emphasized. The multivariate methods discussed in this paper…

This study was concerned with various schemes for reducing the number of variables in a multivariate analysis. Two sets of illustrative data were used; the numbers of criterion groups were 3 and 5. The proportion of correct classifications was employed as an index of discriminatory power of each subset of variables selected. Of the four procedures…

This paper illustrates the transformation of a raw data matrix into a matrix of associations, and then into a factor matrix. Factor analysis attempts to distill the most important relationships among a set of variables, thereby permitting some theoretical simplification. In this heuristic data, a correlation matrix was derived to display…

Path analysis was used to reanalyze Kropp and Stoker's data from tests designed to evaluate Bloom's taxonomy of educational objectives in the cognitive domain. Scores for 1,128 students in grades nine through twelve were analyzed separately by grade level for four content areas on six taxonomic levels. A measure of general ability was also…