The relations among alternative parameterizations of the binary factor analysis (FA) model and two-parameter logistic (2PL) item response theory (IRT) model have been thoroughly discussed in literature (e.g., Lord & Novick, 1968; Takane & de Leeuw, 1987; McDonald, 1999; Wirth & Edwards, 2007; Kamata & Bauer, 2008). However, the…

Large-scale surveys such as the Programme for International Student Assessment (PISA), the Teaching and Learning International Survey (TALIS), and the Programme for the International Assessment of Adult Competences (PIAAC) use advanced statistical models to estimate scores of latent traits from multiple observed responses. The comparison of such…

This study investigated the interaction of disciplinary and interdisciplinary learning in a team-taught, first-year, interdisciplinary sustainability course. We surveyed (pre/post) both STEM (science, technology, engineering, and mathematics) and non-STEM majors (N = 241), assessing attitudes and content knowledge. Responses were analyzed using…

Linear factor analysis models used to examine constructs underlying the responses are not very suitable for dichotomous or polytomous response formats. The associated problems cannot be eliminated by polychoric or tetrachoric correlations in place of the Pearson correlation. Therefore, we considered parameters obtained from the NOHARM and FACTOR…

An overview of popular software packages for conducting dimensionality assessment in multidimensional models is presented. Specifically, five popular software packages are described in terms of their capabilities to conduct dimensionality assessment with respect to the nature of analysis (exploratory or confirmatory), types of data (dichotomous,…

We apply collaborative filtering (CF) to dichotomously scored student response data (right, wrong, or no interaction), finding optimal parameters for each student and item based on cross-validated prediction accuracy. The approach is naturally suited to comparing different models, both unidimensional and multidimensional in ability, including a…

This study leveraged the complementary nature of confirmatory factor (CFA), item response theory (IRT), and latent class (LCA) analyses to strengthen the rigor and sophistication of evaluation of two new measures of the Air Force Academy's "leader of character" definition--the Character Mosaic Virtues (CMV) and the Leadership Mosaic…

How to compute and report subscores for a test that was originally designed for reporting scores on a unidimensional scale has been a topic of interest in recent years. In the research reported here, we describe an application of multidimensional item response theory to identify a subscore structure in a test designed for reporting results using a…

After a test is developed, most content validation analyses shift from ascertaining domain definition to studying domain representation and relevance because the domain is assumed to be set once a test exists. We present an approach that allows for the examination of alternative domain structures based on extant test items. In our example based on…

This paper introduces five commonly used approaches to analyzing multiple-choice test data. They are classical test theory, factor analysis, cluster analysis, item response theory, and model analysis. Brief descriptions of the goals and algorithms of these approaches are provided, together with examples illustrating their applications in physics…

This article considers a structured latent curve model for multiple repeated measures. In a structured latent curve model, a smooth nonlinear function characterizes the mean response. A first-order Taylor polynomial taken with regard to the mean function defines elements of a restricted factor matrix that may include parameters that enter…

It is shown that goodness-of-fit criteria developed for the evaluation of multivariate structural models can be applied to assist in evaluating the dimensionality of a test consisting of binary items, and correlative methods regularly used in factor analysis can be employed to diagnose causes of misfit. (Author)