Over the course of instruction, instructors generally collect a great deal of information about each student. Integrating that information intelligently requires models for how a student's proficiency changes over time. Armed with such models, instructors can "filter" the data--more accurately estimate the student's current proficiency…

A Bayesian approach is developed for analyzing nonlinear structural equation models with nonignorable missing data. The nonignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm is used to produce the joint Bayesian estimates of…

A Bayesian procedure to estimate the three-parameter normal ogive model and a generalization to a model with multidimensional ability parameters are discussed. The procedure is a generalization of a procedure by J. Albert (1992) for estimating the two-parameter normal ogive model. The procedure will support multiple samples from multiple…

A version of sequential mastery testing is studied in which response behavior is modeled by an item response theory (IRT) model. First, a general theoretical framework is sketched that is based on a combination of Bayesian sequential decision theory and item response theory. A discussion follows on how IRT based sequential mastery testing can be…

This paper aims to describe a Bayesian approach to modeling and estimating cognitive models both in terms of statistical machinery and actual instrument development. Such a method taps the knowledge of experts to provide initial estimates for the probabilistic relationships among the variables in a multivariate latent variable model and refines…

Used simulations of computerized adaptive tests to evaluate results yielded by four commonly used ability estimation methods: maximum likelihood estimation (MLE) and three Bayesian approaches. Results show clear distinctions between MLE and Bayesian methods. (SLD)

Marginal maximum likelihood estimation equations are derived for the structural parameters of the Saltus model, and a computing approximation is suggested based on the EM algorithm. The solution is illustrated with simulated data and an example from the domain of mixed number subtraction. (SLD)

Derives three reliability estimates for the Bayes modal estimate (BME) and the maximum-likelihood estimate (MLE) of theta in computerized adaptive tests (CATs). Computes the three reliability estimates and the true reliabilities of both BME and MLE for seven simulated CATs. Results show the true reliabilities for BME and MLE to be nearly identical…

The effect of person misfit to an item response theory model on a mastery/nonmastery decision was investigated. Furthermore, it was investigated whether the classification precision can be improved by identifying misfitting respondents using person-fit statistics. A simulation study was conducted to investigate the probability of a correct…

Bayesian network models offer a large degree of flexibility for modeling dependence among observables (item outcome variables) from the same task that may be dependent. This paper explores four design patterns for modeling locally dependent observations from the same task: (1) No context--Ignore dependence among observables; (2) Compensatory…

The effects of five ability estimators, that is, maximum likelihood estimator, weighted likelihood estimator, maximum a posteriori, expected a posteriori, and Owen's sequential estimator, on the performances of the item response theory-based adaptive classification procedure on multiple categories were studied via simulations. The following…

A two-level regression model is imposed on the ability parameters in an item response theory (IRT) model. The advantage of using latent rather than observed scores as dependent variables of a multilevel model is that this offers the possibility of separating the influence of item difficulty and ability level and modeling response variation and…

Some alternative criteria for item selection in adaptive testing are proposed that take into account uncertainty in the ability estimates. A simulation study shows that the likelihood weighted information criterion is a good alternative to the maximum information criterion. Another good alternative uses a Bayesian expected a posteriori estimator.…

Several models of information integration are developed and analyzed in the context of a prototypical pattern-recognition task. Evaluation, integration, and decision-making processes are specified for each. Simulations and predictions are carried out to provide a measure of identifiability or extent to which they can be distinguished from one…

This paper presents the development of the fusion model skills diagnosis system (fusion model system), which can help integrate standardized testing into the learning process with both skills-level examinee parameters for modeling examinee skill mastery and skills-level item parameters, giving information about the diagnostic power of the test.…