Parallel analysis has been considered one of the most accurate methods for determining the number of factors in factor analysis. One major advantage of parallel analysis over traditional factor retention methods (e.g., Kaiser's rule) is that it addresses the sampling variability of eigenvalues obtained from the identity matrix, representing the…

No matter how strong the theoretical infrastructure of a study is, if the measurement instruments do not have the necessary psychometric qualities, there will be a question of trust in interpreting the findings, and it will be inevitable to make wrong decisions with the results. One of the important steps in scale development/adaptation studies is…

The measurement error in principal components extracted from a set of fallible measures is discussed and evaluated. It is shown that as long as one or more measures in a given set of observed variables contains error of measurement, so also does any principal component obtained from the set. The error variance in any principal component is shown…

There is a lack of research on the effects of outliers on the decisions about the number of factors to retain in an exploratory factor analysis, especially for outliers arising from unintended and unknowingly included subpopulations. The purpose of the present research was to investigate how outliers from an unintended and unknowingly included…

The Kaiser Measures of Sampling Adequacy (MSA) were derived for a typical six-concept Semantic Differential. The overall indices indicated that both concept and total correlation matrices would lead to comparable decisions regarding the psychometric quality of the sample data sets. The individual MSA's, however, revealed considerable variability…

Principal components analysis is generalized to the case where any of the variables under consideration can be nominal, ordinal or interval. Hotelling's original formulation is seen to be a special case of this generalization. (JKS)

The composite direct-product model for the multitrait-multimethod (MTMM) matrix is reparamaterized as a second-order factor analysis model. This process facilitates the use of widely available computer programs--LISREL and LISCOMP--for fitting the model. If bounds on phi and theta are not imposed to avoid inadmissible values, convergence problems…

A procedure for estimating the reliability of a factorially complex composite is considered. An application of its use with Scholastic Aptitude Test data is provided. (Author/JKS)

Many data analysis problems in psychology may be posed conveniently in terms which place the parameters to be estimated on one side of an equation and an expression in these parameters on the other side. A rule for improving the rate of convergence of the iterative solution of such equations is developed and applied to four problems. (Author/RC)

Psychometricians working in factor analysis and econometricians working in regression with measurement error in all variables are both interested in the rank of dispersion matrices under variation of diagonal elements. This paper reviews both fields; points out various small errors; and presents a methodological comparision of factor analysis and…

Three techniques for assessing the adequacy of correlation matrices for factor analysis were applied to four examples from the literature. The methods compared were: (1) inspection of the off diagonal elements of the anti-image covariance matrix S(to the 2nd) R(to the -1) and S(to the 2nd); (2) the Measure of Sampling Adequacy (M.S.A.), and (3)…

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 method of factor extraction specific to a binary matrix, illustrated here as a person-by-item response matrix, is presented. The extraction procedure, termed ERGO, differs from the more commonly implemented dimensionalizing techniques, factor analysis and multidimensional scaling, by taking into consideration item difficulty. Utilized in the…

Attributional style as it has been operationalized in the Attributional Style Questionnaire (ASQ) was critically assessed. A sample of 538 senior high school and college students completed the ASQ. The resulting ASQ data were then intercorrelated, factor analyzed, and compared to hypothesized matrices for all items, good outcome items, and bad…

A Monte Carlo study of five indices of dimensionality of binary items used a computer model that allowed sampling of both items and people. Five parameters were systematically varied in a factorial design: (1) number of common factors from one to five; (2) number of items, including 20, 30, 40, and 60; (3) sample sizes of 125 and 500; (4) nearly…