Cognitive diagnostic models (CDMs) are a family of psychometric models designed to provide categorical classifications for multiple latent attributes. CDMs provide more granular evidence than other psychometric models and have potential for guiding teaching and learning decisions in the classroom. However, CDMs have primarily been conducted using…

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…

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…

This paper explores multilevel modeling approaches for 2-group randomized experiments in which a treatment condition involving clusters of individuals is compared to a control condition involving only ungrouped individuals, otherwise known as partially nested cluster randomized designs (PNCRTs). Strategies for comparing groups from a PNCRT in the…

Markov chain Monte Carlo (MCMC) methods enable a fully Bayesian approach to parameter estimation of item response models. In this simulation study, the authors compared the recovery of graded response model parameters using marginal maximum likelihood (MML) and Gibbs sampling (MCMC) under various latent trait distributions, test lengths, and…

Based on the usual factor analysis model, this paper investigates the relationship between improper solutions and the number of factors. The properties of the noniterative estimation method of M. Ihara and Y. Kano in exploratory factor analysis are also discussed. The estimators were compared in a Monte Carlo experiment. (TJH)

Two sets of real sorting data from 50 college students are used to compare results of multidimensional scaling of raw co-occurrence frequencies or dissimilarity measures (D) and profile distances (delta) to determine which yields a better representation of the underlying structure of 2 sets of stimuli. Slight differences are discussed. (SLD)

A Monte Carlo study was conducted to estimate the small sample standard errors and statistical bias of psychometric statistics commonly used in the analysis of achievement tests. The statistics examined in this research were: (1) the index of item difficulty; (2) the index of item discrimination; (3) the corrected item-total point-biserial…