Demonstrates that traditional exploratory factor analytic methods, when applied to correlation matrices, cannot be used to estimate unattenuated factor loadings. Presents a mathematical basis for the accurate estimation of such values when the disattenuated correlation matrix or the covariance matrix is used as input. Explains how the equations…

A simulation study was conducted to identify the best hot-deck variation to impute missing values. The three variations included in the study were the hot-deck random, the hot-deck sequential, and the hot-deck distance. The properties of these methods were investigated under three levels of the proportion of incomplete records and four levels…

Presents a LISREL model for the estimation of the repeated measures analysis of variance (ANOVA) with a patterned covariance matrix. The model is demonstrated for a 5 x 2 (Time x Group) ANOVA in which the data are assumed to be serially correlated. Similarities with the Statistical Analysis System PROC MIXED model are discussed. (SLD)

The problem of combining information to estimate standardized partial regression coefficients in a linear model is considered. A combined estimate obtained from the pooled correlation matrix is proposed, and its large sample distribution is obtained. This estimate can be generalized to address situations in which not every study measures every…

The purpose of this paper is to examine the validity of regression estimates when skewed dichotomous scales are used as independent variables. When Pearson product-moment correlations are used to measure zero-order associations involving dichotomous variables, the resulting coefficients underestimate the true associations. As a result, using…

An algorithm, based on a solution for C. I. Mosier's oblique Procrustes rotation problem, is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. Results are of interest for missing value and tetrachoric correlation, indefinite matrix correlation, and constrained…

An algorithm for obtaining initial values for the minimization process in covariance structure analysis is developed that is more generally applicable for computing parameters connected to latent variables than the currently existing ones. The algorithm is formulated in terms of the RAM model but can be extended. (SLD)

Two measures of association between sets of variables have been proposed for set correlation: the proportion of generalized variance, and the proportion of additionive variance. Because these measures are strongly positively biased, approximate expected values and estimators of these measures are derived and checked. (Author/BW)

A Monte Carlo study was conducted to compare the efficiency of Listwise deletion, Pairwise deletion, Allvalue, and Samemean methods in estimating the correlation matrix from data that had randomly occurring missing values. The four methods were compared in a 3x3x4 factorial design representing sample size, proportion of incomplete records in the…

A method for estimating the first eigenvalue of random data correlation matrices is reported, and its precision is demonstrated via comparison to the method of S. J. Allen and R. Hubbard (1986). Data generated in Monte Carlo simulations with 10 sample sizes reaching up to 1,000 were used. (SLD)

Estimation techniques for generating the covariance matrix for two new tests and an existing test without the necessity of any examinee having to take two complete tests is presented. An application of these techniques to linear, observed-score, test equating is presented. (Author/JKS)

Combining information to estimate standardized partial regression coefficients in a linear model is discussed. A combined estimate obtained from the pooled correlation matrix is proposed, and its large sample distribution is obtained. The method is generalized to handle a random effects model in which correlation parameters vary across studies.…

The stability of psychometric "g," the general factor of intelligence, is investigated in simulated correlation matrices and in typical empirical data from a large battery of mental tests. "G" is robust and almost invariant across methods of analysis. A reasonable strategy for estimating "g" is suggested. (SLD)

A Monte Carlo investigation of simplex fitting as a method of determining the dimensionality of binary data matrices was conducted. Examination of the fit of correlation matrices with a known factor structure to correlation matrices that represent the perfect simplex shows that simplex fitting is a feasible approach under some circumstances. (SLD)

Three correlation matrices (PEARSON, POLYCHORIC, and TOBIT) were used to obtain reliability estimates on ordered polytomous variable models. A Monte Carlo study with different levels of variable asymmetry and 400 sample correlation matrices demonstrated that the PEARSON matrix did not perform as well as did the other 2 matrices. (SLD)