Abstract This study proposes a new Bayesian differential item functioning (DIF) detection method using posterior predictive model checking (PPMC). Item fit measures including infit, outfit, observed score distribution (OSD), and Q1 were considered as discrepancy statistics for the PPMC DIF methods. The performance of the PPMC DIF method was…

Multiple group modeling is one of the methods to address the measurement noninvariance issue. Traditional studies on multiple group modeling have mainly focused on item responses. In computer-based assessments, joint modeling of response times and action counts with item responses helps estimate the latent speed and action levels in addition to…

This study proposes explanatory cognitive diagnostic model (CDM) jointly incorporating responses and response times (RTs) with the inclusion of item covariates related to both item responses and RTs. The joint modeling of item responses and RTs intends to provide more information for cognitive diagnosis while item covariates can be used to predict…

Response accuracy and response time data can be analyzed with a joint model to measure ability and speed of working, while accounting for relationships between item and person characteristics. In this study, person-fit statistics are proposed for joint models to detect aberrant response accuracy and/or response time patterns. The person-fit tests…

A mixed-effects item response theory (IRT) model is presented as a logical extension of the generalized linear mixed-effects modeling approach to formulating explanatory IRT models. Fixed and random coefficients in the extended model are estimated using a Metropolis-Hastings Robbins-Monro (MH-RM) stochastic imputation algorithm to accommodate for…

The assessment of differential item functioning (DIF) is routinely conducted to ensure test fairness and validity. Although many DIF assessment methods have been developed in the context of classical test theory and item response theory, they are not applicable for cognitive diagnosis models (CDMs), as the underlying latent attributes of CDMs are…

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…

The assumption of conditional independence between the responses and the response times (RTs) for a given person is common in RT modeling. However, when the speed of a test taker is not constant, this assumption will be violated. In this article we propose a conditional joint model for item responses and RTs, which incorporates a covariance…

The DINA (deterministic input, noisy, and gate) model has been widely used in cognitive diagnosis tests and in the process of test development. The outcomes known as slip and guess are included in the DINA model function representing the responses to the items. This study aimed to extend the DINA model by using the random-effect approach to allow…

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)…

A Monte Carlo simulation technique for generating dichotomous item scores is presented that implements (a) a psychometric model with different explicit assumptions than traditional parametric item response theory (IRT) models, and (b) item characteristic curves without restrictive assumptions concerning mathematical form. The four-parameter beta…

The difference between item bias and item impact and the way they relate to item validity are discussed from a multidimensional item response theory perspective. The Mantel-Haenszel procedure and the Simultaneous Item Bias strategy are used in a Monte Carlo study to illustrate detection of item bias. (SLD)

These results indicate that in deciding on the data-gathering design to be used in seeking norm information, attention should be given to item characteristics and test length with particular attention paid to the range of biserial correlations between item response and ability. (Author)

Describes a goodness-of-fit statistic that considers the imprecision with which ability is estimated and involves constructing item fit tables based on each examinee's posterior distribution of ability, given the likelihood of the response pattern and an assumed marginal ability distribution. Also describes a Monte Carlo resampling procedure to…

A statistical method, W. F. Stout's statistical test of essential unidimensionality (1990), for exploring the lack of unidimensionality in test data was studied using Monte Carlo simulations. The statistical procedure is a hypothesis test of whether the essential dimensionality is one or exceeds one, regardless of the traditional dimensionality.…