A Bayesian solution is suggested to the problem of jointly estimating "k is greater than 1" binomial parameters in conjunction with the problem of testing, in a Bayesian sense, the hypothesis "H" of parametric homogeneity. Applications of the estimates are illustrated with several types of data, including ophthalmological…

An empirical Bayes-maximum likelihood estimation procedure is presented for the application of fuzzy partition models in describing high dimensional discrete response data. The model describes individuals in terms of partial membership in multiple latent categories that represent bounded discrete spaces. (SLD)

A new computerized mastery test is described that builds on the Lewis and Sheehan procedure (sequential testlets) (1990), but uses fuzzy set decision theory to determine stopping rules and the Rasch model to calibrate items and estimate abilities. Differences between fuzzy set and Bayesian methods are illustrated through an example. (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…

Syntactic knowledge is widely held to be partially innate, rather than learned. In a classic example, it is sometimes argued that children know the proper use of anaphoric "one," although that knowledge could not have been learned from experience. Lidz et al. [Lidz, J., Waxman, S., & Freedman, J. (2003). What infants know about syntax but couldn't…

This article proposes a practical method that capitalizes on the availability of information from multiple tests measuring correlated abilities given in a single test administration. By simultaneously estimating different abilities with the use of a hierarchical Bayesian framework, more precise estimates for each ability dimension are obtained.…

I. Klugkist, O. Laudy, and H. Hoijtink (2005) presented a Bayesian approach to analysis of variance models with inequality constraints. Constraints may play 2 distinct roles in data analysis. They may represent prior information that allows more precise inferences regarding parameter values, or they may describe a theory to be judged against the…

Multidimensional adaptive testing (MAT) procedures are proposed for the measurement of several latent traits by a single examination. Bayesian latent trait estimation and adaptive item selection are derived. Simulations were conducted to compare the measurement efficiency of MAT with those of unidimensional adaptive testing and random…

This paper reports the results of a dual-task experiment which investigates the nature of working memory resources used in sentence comprehension. Participants read sentences of varying syntactic complexity (containing subject-and object-extracted relative clauses) while remembering one or three nouns (similar to or dissimilar from the…

In 1994, R. G. Lord and P. E. Levy proposed a variant of control theory that incorporated human information processing principles. The current article evaluates the empirical evidence for their propositions and updates the theory by considering contemporary research on information processing. Considerable support drawing from diverse literatures…

This paper presents a hierarchical Bayes circumplex model for ordinal ratings data. The circumplex model was proposed to represent the circular ordering of items in psychological testing by imposing inequalities on the correlations of the items. We provide a specification of the circumplex, propose identifying constraints and conjugate priors for…

During the 2009-2010 school year, Marzano Research Laboratory (MRL) was commissioned by Promethean Ltd. to conduct a second year evaluation study of the effects of Promethean ActivClassroom on student academic achievement. This report describes the findings from the second year study along with aggregate findings from the first and second year…

Relationships between Bayesian ability estimates and the parameters of a normal population distribution are derived in the context of classical test theory. Analogies are provided for use as approximations in work with item response theory (IRT). The following issues are addressed: (1) the relationship between the distribution of the latent…