In this article the authors focus on the issue of the nonuniqueness of the maximum likelihood (ML) estimator of proficiency level in item response theory (with special attention to logistic models). The usual maximum a posteriori (MAP) method offers a good alternative within that framework; however, this article highlights some drawbacks of its…

Students conducted inquiry using simulations within a rich learning environment for 4 science topics. By applying educational data mining to students' log data, assessment metrics were generated for two key inquiry skills, testing stated hypotheses and designing controlled experiments. Three models were then developed to analyze the transfer of…

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…

Moving one's eyes while reading is one of the most complex everyday tasks humans face. To perform efficiently, readers must make decisions about when and where to move their eyes every 200-300ms. Over the past decades, it has been demonstrated that these fine-grained decisions are influenced by a range of linguistic properties of the text, and…

A new class of parametric models that generalize the multivariate probit model and the errors-in-variables model is developed to model and analyze ordinal data. A general model structure is assumed to accommodate the information that is obtained via surrogate variables. A hybrid Gibbs sampler is developed to estimate the model parameters. To…

We develop a Bayesian hierarchical model for the analysis of ordinal data from multirater ranking studies. The model for a rater's score includes four latent factors: one is a latent item trait determining the true order of items and the other three are the rater's performance characteristics, including bias, discrimination, and measurement error…

To better understand the statistical properties of the deterministic inputs, noisy "and" gate cognitive diagnosis (DINA) model, the impact of several factors on the quality of the item parameter estimates and classification accuracy was investigated. Results of the simulation study indicate that the fully Bayes approach is most accurate when the…

Both testlet design and hierarchical latent traits are fairly common in educational and psychological measurements. This study aimed to develop a new class of higher order testlet response models that consider both local item dependence within testlets and a hierarchy of latent traits. Due to high dimensionality, the authors adopted the Bayesian…

In recent years, many computerized test systems have been developed for diagnosing students' learning profiles. Nevertheless, it remains a challenging issue to find an adaptive testing algorithm to both shorten testing time and precisely diagnose the knowledge status of students. In order to find a suitable algorithm, four adaptive testing…

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…

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…

Recently, researchers have investigated differences in decision making based on description and experience. We address the issue of when experience-based judgments of probability are more accurate than are those based on description. If description is well understood ("transparent") and experience is misleading ("wicked"), it…

Application of Bayesian item selection criteria in computerized adaptive testing might result in improvement of bias and MSE of the ability estimates. The question remains how to apply Bayesian item selection criteria in the context of constrained adaptive testing, where large numbers of specifications have to be taken into account in the item…

Multinomial processing tree models are widely used in many areas of psychology. A hierarchical extension of the model class is proposed, using a multivariate normal distribution of person-level parameters with the mean and covariance matrix to be estimated from the data. The hierarchical model allows one to take variability between persons into…

The educational field has now accumulated an extensive literature reporting on values of the intraclass correlation coefficient, a parameter essential to determining the required size of a planned cluster randomized trial. We propose here a simple simulation-based approach including all relevant information that can facilitate this task. An…