Lord's Wald test for differential item functioning (DIF) has not been studied extensively in the context of the multidimensional item response theory (MIRT) framework. In this article, Lord's Wald test was implemented using two estimation approaches, marginal maximum likelihood estimation and Bayesian Markov chain Monte Carlo estimation, to detect…

Mixed-effects models (MEMs) and latent growth models (LGMs) are often considered interchangeable save the discipline-specific nomenclature. Software implementations of these models, however, are not interchangeable, particularly with small sample sizes. Restricted maximum likelihood estimation that mitigates small sample bias in MEMs has not been…

Different estimation procedures have been developed for the unidimensional three-parameter item response theory (IRT) model. These techniques include the marginal maximum likelihood estimation, the fully Bayesian estimation using Markov chain Monte Carlo simulation techniques, and the Metropolis-Hastings Robbin-Monro estimation. With each…

The current study used simulated data to investigate the properties of a newly proposed method (Yao's rater model) for modeling rater severity and its distribution under different conditions. Our study examined the effects of rater severity, distributions of rater severity, the difference between item response theory (IRT) models with rater effect…

This study demonstrated the equivalence between the Rasch testlet model and the three-level one-parameter testlet model and explored the Markov Chain Monte Carlo (MCMC) method for model parameter estimation in WINBUGS. The estimation accuracy from the MCMC method was compared with those from the marginalized maximum likelihood estimation (MMLE)…

Maximum likelihood (ML) estimation of generalized linear mixed models (GLMMs) is technically challenging because of the intractable likelihoods that involve high dimensional integrations over random effects. The problem is magnified when the random effects have a crossed design and thus the data cannot be reduced to small independent clusters. A…

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…

A hierarchical latent regression model is suggested to estimate nested and nonnested relationships in complex samples such as found in the National Assessment of Educational Progress (NAEP). The proposed model aims at improving both parameters and variance estimates via a two-level hierarchical linear model. This model falls naturally within the…

The use of hierarchical models in social science research is discussed, with emphasis on causal inference and consideration of the limitations of hierarchical models. The increased use of Gibbs sampling and other Markov-chain Monte Carlo methods in the application of hierarchical models is recommended. (SLD)