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…

Measurement invariance (MI) is required for validly comparing latent constructs measured by multiple ordinal self-report items. Non-invariances may occur when disregarding (group differences in) an acquiescence response style (ARS; an agreeing tendency regardless of item content). If non-invariance results solely from neglecting ARS, one should…

Assessing the measurement model (MM) of self-report scales is crucial to obtain valid measurements of individuals' latent psychological constructs. This entails evaluating the number of measured constructs and determining which construct is measured by which item. Exploratory factor analysis (EFA) is the most-used method to evaluate these…

Short forms of psychometric scales have been commonly used in educational and psychological research to reduce the burden of test administration. However, it is challenging to select items for a short form that preserve the validity and reliability of the scores of the original scale. This paper presents and evaluates multiple automated methods…

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…

The purpose of this article is to highlight the distinction between the reliability of test scores and the fit of psychometric measurement models, reminding readers why it is important to consider both when evaluating whether test scores are valid for a proposed interpretation and/or use. It is often the case that an investigator judges both the…

The issue of measurement invariance commonly arises in factor-analytic contexts, with methods for assessment including likelihood ratio tests, Lagrange multiplier tests, and Wald tests. These tests all require advance definition of the number of groups, group membership, and offending model parameters. In this paper, we study tests of measurement…

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…

This article proposes several statistics for assessing individual fit based on two unidimensional models for continuous responses: linear factor analysis and Samejima's continuous response model. Both models are approached using a common framework based on underlying response variables and are formulated at the individual level as fixed regression…

Parallel analysis has been shown to be suitable for dimensionality assessment in factor analysis of continuous variables. There have also been attempts to demonstrate that it may be used to uncover the factorial structure of binary variables conforming to the unidimensional normal ogive model. This article provides both theoretical and empirical…

A common question in test evaluation is whether an a priori assignment of items to subtests is supported by empirical data. If the analysis results indicate the assignment of items to subtests under study is not supported by data, the assignment is often adjusted. In this study the authors compare two methods on the quality of their suggestions to…

The impact of outliers on Cronbach's coefficient [alpha] has not been documented in the psychometric or statistical literature. This is an important gap because coefficient [alpha] is the most widely used measurement statistic in all of the social, educational, and health sciences. The impact of outliers on coefficient [alpha] is investigated for…

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)