Model fit indices are being increasingly recommended and used to select the number of factors in an exploratory factor analysis. Growing evidence suggests that the recommended cutoff values for common model fit indices are not appropriate for use in an exploratory factor analysis context. A particularly prominent problem in scale evaluation is the…

This paper aims to illustrate how data visualization could be utilized to identify errors prior to modeling, using an example with multi-dimensional item response theory (MIRT). MIRT combines item response theory and factor analysis to identify a psychometric model that investigates two or more latent traits. While it may seem convenient to…

The primary objective of this study was to examine the effect of missing data on goodness of fit statistics in confirmatory factor analysis (CFA). For this aim, four missing data handling methods; listwise deletion, full information maximum likelihood, regression imputation and expectation maximization (EM) imputation were examined in terms of…

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…

This article describes a method based on Pratt's measures and demonstrates its use in exploratory factor analyses. The article discusses the interpretational complexities due to factor correlations and how Pratt's measures resolve these interpretational problems. Two real data examples demonstrate the calculation of what we call the…

Bi-factor analysis is a form of confirmatory factor analysis originally introduced by Holzinger and Swineford ("Psychometrika" 47:41-54, 1937). The bi-factor model has a general factor, a number of group factors, and an explicit bi-factor structure. Jennrich and Bentler ("Psychometrika" 76:537-549, 2011) introduced an exploratory form of bi-factor…

Students with significant cognitive disabilities present an assessment dilemma that centers on access and validity in large-scale testing programs. Typically, access is improved by eliminating construct-irrelevant barriers, while validity is improved, in part, through test standardization. In this article, one state's alternate assessment data…

A number of psychometricians have argued for the use of parallel analysis to determine the number of factors. However, parallel analysis must be viewed at best as a heuristic approach rather than a mathematically rigorous one. The authors suggest a revision to parallel analysis that could improve its accuracy. A Monte Carlo study is conducted to…

Identifying collaboration between learners in a course is an important challenge in education for two reasons: First, depending on the courses rules, collaboration can be considered a form of cheating. Second, it helps one to more accurately evaluate each learners competence. While such collaboration identification is already challenging in…

This article presents information on the development and initial validation of the 16-item Response to Intervention (RTI) Beliefs Scale. The scale is designed to measure the extent to which educators working in schools hold beliefs consistent with the tenets of RTI. The authors administered the instrument to 2,430 educators in 62 elementary…

Dynamic factor analysis models with time-varying parameters offer a valuable tool for evaluating multivariate time series data with time-varying dynamics and/or measurement properties. We use the Dynamic Model of Activation proposed by Zautra and colleagues (Zautra, Potter, & Reich, 1997) as a motivating example to construct a dynamic factor…

Objective: To investigate the underlying phenotypic constructs in autism spectrum disorders (ASD) and to identify genetic loci that are linked to these empirically derived factors. Method: Exploratory factor analysis was applied to two datasets with 28 selected Autism Diagnostic Interview-Revised (ADI-R) algorithm items. The first dataset was from…

The researchers examined if scores from the original Psychological Need Satisfaction in Exercise Scale (Wilson, Rogers, Rodgers, & Wild, 2006) were invariant from a modified version specific to physical activity and then examined measurement invariance of scores across groups on the modified scale. Three groups were examined: (a) Students/staff…

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…

The purpose of this study was to use differential item functioning (DIF) and latent mixture model analyses to explore factors that explain performance differences on a large-scale mathematics assessment between examinees allowed to use a calculator or who were afforded item presentation accommodations versus those who did not receive the same…