Most existing diagnostic models are developed to detect whether students have mastered a set of skills of interest, but few have focused on identifying what scientific misconceptions students possess. This article developed a general dual-purpose model for simultaneously estimating students' overall ability and the presence and absence of…

Despite considerable advances in knowledge tracing algorithms, educational technologies that use this technology typically continue to use older algorithms, such as Bayesian Knowledge Tracing. One key reason for this is that contemporary knowledge tracing algorithms primarily infer next-problem correctness in the learning system, but do not…

Exploring the relationship between student ability and test-taking effort is an important area of study, offering insights into their approach to educational assessments. Previous research shows this relationship, yet there is a scarcity of research comparing the test-taking effort of students. In addition, researchers have frequently employed…

Studied the calculating ability used by a low IQ savant to identify prime numbers in two experiments comparing him to control subjects, one involving reaction time and the other involving inspection time. Concludes that this individual uses a complex computational algorithm to identify primes and discusses the apparent contradiction of his low IQ.…

Reviewed methods of estimating theta suitable for computerized adaptive testing (CAT) and discussed the differences between Fisher and Kullback-Leibler information criteria for selecting items. Examined the accuracy of different CAT algorithms using samples from the National Assessment of Educational Progress. Results show when correcting for…

The interest in the application of large-scale adaptive testing for secure tests has served to focus attention on issues that arise when theoretical advances are made operational. Many such issues in the application of large-scale adaptive testing for secure tests have more to do with changes in testing conditions than with testing paradigms. One…

This paper presents a detailed description of maximum parameter estimation for item response models using the general EM algorithm. In this paper the models are specified using a univariate discrete latent ability variable. When the latent ability variable is discrete the distribution of the observed item responses is a finite mixture, and the EM…

Problems in selection of optimal designs in item-response theory (IRT) models are resolved through a sequential design procedure that is a modification of the D-optimality procedure proposed by Wynn (1970). This algorithm leads to consistent estimates, and the errors in selecting the abilities generally do not greatly affect optimality. (SLD)

In the process of item calibration for a computerized adaptive test (CAT), many well-established calibrating packages show weakness in the estimation of item parameters. This paper introduces an on-line calibration algorithm based on the convexity of likelihood functions. This package consists of: (1) an algorithm that estimates examinee ability…

In constrained adaptive testing, the numbers of constraints needed to control the content of the tests can easily run into the hundreds. Proper initialization of the algorithm becomes a requirement because the presence of large numbers of constraints slows down the convergence of the ability estimator. In this paper, an empirical initialization of…

The case of adaptive testing under a multidimensional logistic response model is addressed. An adaptive algorithm is proposed that minimizes the (asymptotic) variance of the maximum-likelihood (ML) estimator of a linear combination of abilities of interest. The item selection criterion is a simple expression in closed form. In addition, it is…

Proposes an algorithm that minimizes the asymptotic variance of the maximum-likelihood (ML) estimator of a linear combination of abilities of interest. The criterion results in a closed-form expression that is easy to evaluate. Also shows how the algorithm can be modified if the interest is in a test with a "simple ability structure."…

The equivalence of pencil and paper Rasch item calibrations when used in a computer adaptive test administration was explored in this study. Items (n=726) were precalibarted with the pencil and paper test administrations. A computer adaptive test was administered to 321 medical technology students using the pencil and paper precalibrations in the…

Although computerized adaptive tests acquire their efficiency by successively selecting items that provide optimal measurement at each examinee's estimated level of ability, operational testing programs will typically consider additional factors in item selection. In practice, items are generally selected with regard to at least three, often…

A constrained computerized adaptive testing (CAT) algorithm is presented that automatically equates the number-correct scores on adaptive tests. The algorithm can be used to equate number-correct scores across different administrations of the same adaptive test as well as to an external reference test. The constraints are derived from a set of…