Traditionally, confirmatory factor analytic models are tested against a null model of total independence. Using randomly generated factors in a matrix of 46 aptitude tests, this approach is shown to be unlikely to reject even random factors. An alternative null model, based on a single general factor, is suggested. In addition, an index of model…

The Monte Carlo method was used, and the factors considered were (1) level of main effects in the population; (2) level of interaction effects in the population; (3) alpha level used in determining whether to pool; and (4) number of degrees of freedom. The results indicated that when the ratio degrees of freedom (axb)/degrees of freedom (within)…

A multitrait-multimethod matrix containing two methods of measuring 12 personality traits was analyzed and confirmatory factor analysis was applied to the data. Although unexplained variance remained, method factors and a general personality factor significantly improved the fit of a model containing only trait factors. (Author/RL)

Often, all of the variables in a model are latent, random, or subject to measurement error, or there is not an obvious dependent variable. When any of these conditions exist, an appropriate method for estimating the linear relationships among the variables is Least Principal Components Analysis. Least Principal Components are robust, consistent,…

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…

Despite advances in common factor analysis, a review of 89 studies published in four selected journals between 1963 and 1976 indicated that behavioral scientists preferred principal components analysis, followed by varimax or orthogonal rotation. Resultant row sums of squares of factor matrices from principal component analyses of real data sets…

The general goal of this paper is to help researchers conduct appropriately designed goodness of fit studies for item response model applications. The specific purposes are to describe: (1) an up-to-date set of promising and useful methods for addressing a variety of goodness of fit questions; and (2) current research studies to advance this set…

A method for statistical analysis of semantic differential data in educational evaluation is discussed. Estimated scores for unobserved affective variables are obtained using the canonical factor regression method. This method overcomes previous prolems of bias and inefficiency in computing composite affective indices. In an application of the…

A set of symbols is presented along with logical operators which represent the possible manipulations of the linear model. The use of these symbols and operators is to simplify the representation of analysis of variance models, correlation models and factor analysis models. (Author)