In administration of individually administered intelligence tests, items are commonly presented in a sequence of increasing difficulty, and test administration is terminated after a predetermined number of incorrect answers. This practice produces stochastically censored data, a form of nonignorable missing data. By manipulating four factors…

This paper describes how item response theory (IRT) methods of test-equating could be applied to the maintenance of public examination standards in England. IRT methods of test-equating have been sparingly applied to the main public examinations in England, namely the General Certificate of Secondary Education (GCSE), the equivalent of a school…

Parameter recovery was assessed within mixture confirmatory factor analysis across multiple estimator conditions under different simulated levels of mixture class separation. Mixture class separation was defined in the measurement model (through factor loadings) and the structural model (through factor variances). Maximum likelihood (ML) via the…

Despite the widespread popularity of growth curve analysis, few studies have investigated robust growth curve models. In this article, the "t" distribution is applied to model heavy-tailed data and contaminated normal data with outliers for growth curve analysis. The derived robust growth curve models are estimated through Bayesian…

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…

There are two mainstream curricula for international school students at the junior high level: the International Baccalaureate (IB) Middle Years Programme (MYP) and the Cambridge International General Certificate of Secondary Education (IGCSE). The former was developed in the mid-1990s and is currently being relaunched in a 21st-century approach.…

An examinee faced with a test item will engage in solution behavior or rapid-guessing behavior. These qualitatively different test-taking behaviors bias parameter estimates for item response models that do not control for such behavior. A mixture Rasch model with item response time components was proposed and evaluated through application to real…

Doubly bounded continuous data are common in the social and behavioral sciences. Examples include judged probabilities, confidence ratings, derived proportions such as percent time on task, and bounded scale scores. Dependent variables of this kind are often difficult to analyze using normal theory models because their distributions may be quite…

In Iran, high school graduates enter university after taking a very difficult entrance exam called the Konkoor. Therefore, only the top-performing students are admitted by universities to continue their bachelor's education in statistics. Surprisingly, statistically, most of such students fall into the following categories: (1) do not succeed in…

The present study presents the formulation of graded response models in the multilevel framework (as nonlinear mixed models) and demonstrates their use in estimating item parameters and investigating the group-level effects for specific covariates using Bayesian estimation. The graded response multilevel model (GRMM) combines the formulation of…

Walking readers step by step through complex concepts, this book translates missing data techniques into something that applied researchers and graduate students can understand and utilize in their own research. Enders explains the rationale and procedural details for maximum likelihood estimation, Bayesian estimation, multiple imputation, and…

In sequential mastery testing (SMT), assessment via computer is used to classify examinees into one of two mutually exclusive categories. Unlike paper-and-pencil tests, SMT has the capability to use variable-length stopping rules. One approach to shortening variable-length tests is stochastic curtailment, which halts examination if the probability…

This paper describes and evaluates the use of measurement decision theory (MDT) to classify examinees based on their item response patterns. The model has a simple framework that starts with the conditional probabilities of examinees in each category or mastery state responding correctly to each item. The presented evaluation investigates: (1) the…

The capacity of Bayesian methods in estimating complex statistical models is undeniable. Bayesian data analysis is seen as having a range of advantages, such as an intuitive probabilistic interpretation of the parameters of interest, the efficient incorporation of prior information to empirical data analysis, model averaging and model selection.…