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…

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…

Longitudinal studies are permeating clinical trials in psychiatry. Therefore, it is of utmost importance to study the psychometric properties of rating scales, frequently used in these trials, within a longitudinal framework. However, intrasubject serial correlation and memory effects are problematic issues often encountered in longitudinal data.…

Orlando and Thissen (2000) developed an item fit statistic for binary item response theory (IRT) models known as S-X[superscript 2]. This article generalizes their statistic to polytomous unfolding models. Four alternative formulations of S-X[superscript 2] are developed for the generalized graded unfolding model (GGUM). The GGUM is a…

U.S. state educational testing programs administer tests to track student progress and hold schools accountable for educational outcomes. Methods from item response theory, especially Rasch models, are usually used to equate different forms of a test. The most popular method for estimating Rasch models yields inconsistent estimates and relies on…

Results of this simulated study indicate that, when unidimensional stimulus sets are scaled in two dimensions using a rational starting configuration, the nature of the two-dimensional configuration can indicate the general form of the function mapping psychological dissimilarity--represented as distance in the scaling model--onto the observed…

A unidimensional model for responses to statements that have an unfolding structure was constructed from the cumulative Rasch model for ordered response categories. A joint maximum likelihood estimation procedure was investigated. Analyses of data from a small simulation and a real data set show that the model is readily applicable. (SLD)

This article applies a weighted maximum likelihood (WML) latent trait estimator to the generalized partial credit model (GPCM). The relevant equations required to obtain the WML estimator using the Newton-Raphson algorithm are presented, and a simulation study is described that compared the properties of the WML estimator to those of the maximum…

Comparing variability of test scores across alternate forms, test conditions, or subpopulations is a fundamental problem in psychometrics. A confidence interval for a ratio of standard deviations is proposed that performs as well as the classic method with normal distributions and performs dramatically better with nonnormal distributions. A simple…