A nonconverged Markov chain can potentially lead to invalid inferences about model parameters. The purpose of this study was to assess the effect of a nonconverged Markov chain on the estimation of parameters for mixture item response theory models using a Markov chain Monte Carlo algorithm. A simulation study was conducted to investigate the…

This study investigates the effect of multidimensionality on extraction of latent classes in mixture Rasch models. In this study, two-dimensional data were generated under varying conditions. The two-dimensional data sets were analyzed with one- to five-class mixture Rasch models. Results of the simulation study indicate the mixture Rasch model…

A simulation study is a useful tool in examining how validly item response theory (IRT) models can be applied in various settings. Typically, a large number of replications are required to obtain the desired precision. However, many standard software packages in IRT, such as MULTILOG and BILOG, are not well suited for a simulation study requiring…

Test tampering, especially on tests for educational accountability, is an unfortunate reality, necessitating that the state (or its testing vendor) perform data forensic analyses, such as erasure analyses, to look for signs of possible malfeasance. Few statistical approaches exist for detecting fraudulent erasures, and those that do largely do not…

This study examines the utility of four indices for use in model selection with nested and nonnested polytomous item response theory (IRT) models: a cross-validation index and three information-based indices. Four commonly used polytomous IRT models are considered: the graded response model, the generalized partial credit model, the partial credit…

Mixture item response theory models have been suggested as a potentially useful methodology for identifying latent groups formed along secondary, possibly nuisance dimensions. In this article, we describe a multilevel mixture item response theory (IRT) model (MMixIRTM) that allows for the possibility that this nuisance dimensionality may function…

A primary concern with testing differential item functioning (DIF) using a traditional point-null hypothesis is that a statistically significant result does not imply that the magnitude of DIF is of practical interest. Similarly, for a given sample size, a non-significant result does not allow the researcher to conclude the item is free of DIF. To…

This study examines model selection indices for use with dichotomous mixture item response theory (IRT) models. Five indices are considered: Akaike's information coefficient (AIC), Bayesian information coefficient (BIC), deviance information coefficient (DIC), pseudo-Bayes factor (PsBF), and posterior predictive model checks (PPMC). The five…

An item response theory model for dealing with test speededness is proposed. The model consists of two random processes, a problem solving process and a random guessing process, with the random guessing gradually taking over from the problem solving process. The involved change point and change rate are considered random parameters in order to…

Fit of the model to the data is important if the benefits of item response theory (IRT) are to be obtained. In this study, the authors compared model selection results using the likelihood ratio test, two information-based criteria, and two Bayesian methods. An example illustrated the potential for inconsistency in model selection depending on…

Discusses reasons why increasing the number of replications in Monte Carlo simulation studies is not necessary for satisfactory levels of precision and offers guidelines in the context of error tolerance analysis for determining how much precision is needed. (SLD)

Type I error rates of the likelihood ratio test for the detection of differential item functioning (DIF) in the partial credit model were investigated using simulated data. The partial credit model with four ordered performance levels was used to generate data sets of a 30-item test for samples of 300 and 1,000 simulated examinees. Three different…

Compared the quality of item parameter estimates for marginal maximum likelihood (MML) and Markov Chain Monte Carlo (MCMC) with the nominal response model using simulation. The quality of item parameter recovery was nearly identical for MML and MCMC, and both methods tended to produce good estimates. (SLD)

Studied results from five linking methods under the graded-response model using simulated data. Results show that differences in the linking coefficients are small. The five methods yielded similar results for longer common-item links with large sample sizes and when the distribution of item-location parameters matched the underlying trait…

Compared three methods for developing a common metric under item response theory through simulation. For smaller numbers of common items, linking using the characteristic curve method yielded smaller root mean square differences for both item discrimination and difficulty parameters. For larger numbers of common items, the three methods were…