A central problem in the application of exploratory factor analysis is deciding how many factors to retain ("m"). Although this is inherently a model selection problem, a model selection perspective is rarely adopted for this task. We suggest that Cudeck and Henly's (1991) framework can be applied to guide the selection process.…

Goodness-of-fit testing in factor analysis is based on the assumption that the test statistic is asymptotically chi-square, but this property may not hold in small samples even when the factors and errors are normally distributed in the population. Robust methods such as Browne's (1984) asymptotically distribution-free method and Satorra Bentler's…

A common problem in exploratory factor analysis is how many factors need to be extracted from a particular data set. We propose a new method for selecting the number of major common factors: the Hull method, which aims to find a model with an optimal balance between model fit and number of parameters. We examine the performance of the method in an…

We apply the Supplemented EM algorithm (Meng & Rubin, 1991) to address a chronic problem with the "two-stage" fitting of covariance structure models in the presence of ignorable missing data: the lack of an asymptotically chi-square distributed goodness-of-fit statistic. We show that the Supplemented EM algorithm provides a…

A profile is a vector of scores for one examinee. The mean score in the vector can be interpreted as a measure of overall profile height, the variance can be interpreted as a measure of within person variation, and the ipsatized vector of score deviations about the mean can be said to describe the pattern in the score profile. A within person…

This paper describes the Confirmatory Factor Analysis (CFA) parameterization of the Profile Analysis via Multidimensional Scaling (PAMS) model to demonstrate validation of profile pattern hypotheses derived from multidimensional scaling (MDS). Profile Analysis via Multidimensional Scaling (PAMS) is an exploratory method for identifying major…

A common problem in factor analytic research is determining the number of factors to be extracted. A comprehensive evaluation of the two most commonly used approaches is presented. The authors conclude that the scree criterion is definitely superior to the Kaiser-Guttman criterion. (JKS)

This paper proposes procedures for assessing the fit of a psychometric model at the level of the individual respondent. The procedures are intended for personality measures made up of Likert-type items, which, in applied research, are usually analyzed by means of factor analysis. Two scalability indices are proposed, which can be considered as…

Extension analysis allows for the investigation of relationships between factors from a core set of variables and the variables from an additional, extension set. This frequently results in obtaining negative residual variances, called Heywood cases. Procedures for checking for that problem are presented here. (Author/JKS)

A method of assessing goodness-of-fit for a single factor model is presented. Indices of fit sensitive to the way that correlation matrices are generated are derived from the factor analysis literature. It is proposed that the cumulative distribution function be evaluated for other values of "p" and "m." (TJH)

Describes four approaches to factor analysis of ordinal variables that take proper account of ordinality and compared three of these approaches with respect to parameter estimates and fit using generated data and an empirical data set. Focuses on how to test the model and how to measure model fit. (SLD)

A method is proposed and illustrated for estimating the degree to which a factor rotation to a hypothesized target represents an improvement over rotation to a random target. (Author)

It is shown that the Stone-Coles method is not a content method, but rather an alternative to the ordinary distance methods. As such, it is argued, it is of limited value. (Author)

An empirical sampling distribution of the statistic average trace (E'E) for various orders of A matrices was developed through a Monte Carlo approach. A method is presented which can be used as a guideline in determining whether factor structures obtained from two data sets are congruent. (Author/DEP)

Interpretation of multivariate models requires knowing how much the fit of the model is impaired by changes in the parameters. The relation of parameter change to loss of goodness of fit can be called parameter sensitivity. Formulas are presented for assessing the sensitivity of multiple regression and principal component weights. (Author/JKS)