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…

Critical thinking is one of the important higher-order skills very much treasured in education, but hard to be measured using paper-pencil tests. In line with recent recommendation to measure high-order thinking skills with interactive tasks (vs. static one set of questions), in this study we developed an interactive and automated game-based…

Survey instruments and assessments are frequently used in many domains of social science. When the constructs that these assessments try to measure become multifaceted, multidimensional item response theory (MIRT) provides a unified framework and convenient statistical tool for item analysis, calibration, and scoring. However, the computational…

Item-level fit analysis not only serves as a complementary check to global fit analysis, it is also essential in scale development because the fit results will guide item revision and/or deletion (Liu & Maydeu-Olivares, 2014). During data collection, missing response data may likely happen due to various reasons. Chi-square-based item fit…

Methods to generate random correlation matrices have been proposed in the literature, but very few instances exist where these correlation matrices are structured or where the statistical properties of the algorithms are known. By relying on the tetrad relation discovered by Spearman and the properties of the beta distribution, an algorithm is…

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…

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…

More robust and rigorous psychometric models, such as multidimensional Item Response Theory models, have been advocated for survey applications. However, item responses may be influenced by construct-irrelevant variance factors such as preferences for extreme response options. Through empirical and simulation methods, this study evaluates the use…

Collaborative problem solving (CPS) is a critical competency in a variety of contexts, including the workplace, school, and home. However, only recently have assessment and curriculum reformers begun to focus to a greater extent on the acquisition and development of CPS skill. One of the major challenges in psychometric modeling of CPS is…

This study compares the performance of two estimation algorithms of new usage, the Metropolis-Hastings Robins-Monro (MHRM) and the Hamiltonian MCMC (HMC), with two consolidated algorithms in the psychometric literature, the marginal likelihood via EM algorithm (MML-EM) and the Markov chain Monte Carlo (MCMC), in the estimation of multidimensional…

This study defines subpopulation item parameter drift (SIPD) as a change in item parameters over time that is dependent on subpopulations of examinees, and hypothesizes that the presence of SIPD in anchor items is associated with bias and/or lack of invariance in three psychometric outcomes. Results show that SIPD in anchor items is associated…

We present a semi-parametric approach to estimating item response functions (IRF) useful when the true IRF does not strictly follow commonly used functions. Our approach replaces the linear predictor of the generalized partial credit model with a monotonic polynomial. The model includes the regular generalized partial credit model at the lowest…

Purpose: Agreement across methods for identifying students as inadequate responders or as learning disabled is often poor. We report (1) an empirical examination of final status (postintervention benchmarks) and dual-discrepancy growth methods based on growth during the intervention and final status for assessing response to intervention and (2) a…

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…

Analyzing examinees' responses using cognitive diagnostic models (CDMs) has the advantage of providing diagnostic information. To ensure the validity of the results from these models, differential item functioning (DIF) in CDMs needs to be investigated. In this article, the Wald test is proposed to examine DIF in the context of CDMs. This study…