Whenever one uses a composite scale score from item responses, one is tacitly assuming that the scale is dominantly unidimensional. Investigating the unidimensionality of item response data is an essential component of construct validity. Yet, there is no universally accepted technique or set of rules to determine the number of factors to retain…

Effects of overextracting factors and components within and between maximum likelihood factor analysis and principal components analysis were examined through computer simulation of a range of factor and component patterns. Results demonstrate similarity of component and factor scores during overextraction. Overall, results indicate that…

A Monte Carlo study determined the Inverse Scree Test's shape with various numbers of true groups and under different conditions of distribution shape and sample size. Six simulated distributions of 3,000 subjects each and 1 with 1,500 were created. Findings suggest relative distribution independence, number independence, and modest…

The purpose of the present investigation is to examine the influence of sample size (N) and model complexity on a set of 23 goodness-of-fit (GOF) indices, including those typically used in confirmatory factor analysis. The focus was on two potential problems in assessing GOF: (1) some fit indices are substantially influenced by N so that tests of…

This study considers the problem of performing all pairwise comparisons of column means for a two-by-four additive nonorthogonal factorial analysis of variance (ANOVA) model where cell variances are heterogeneous. Extensions of the following procedures are considered: (1) Games-Howell (1976) procedure; (2) the C. W. Dunnett (1980) T3 and C…

The following seven statistical procedures are compared in terms of the ability to recover a unidimensional latent trait from Likert-type data: (1) factor analysis based on Pearson correlations (FA-PR); (2) factor analysis based on polychoric correlations (FA-PL); (3) the graded response model in item response theory (IRT-GRM); (4) internal…

In this article some results are presented relating to the dimensionality of instruments containing polytomously scored as well as dichotomously scored items, concentrating on the 1992 National Assessment of Educational Progress' (NAEP) mathematics and reading assessment data and several simulated datasets. The maximum likelihood factor analytic…