The present paper introduces a general multidimensional model to measure individual differences in learning within a single administration of a test. Learning is assumed to result from practicing the operations involved in solving the items. The model accounts for the possibility that the ability to learn may manifest differently for correct and…

Statistical analysis of categorical data often relies on multiway contingency tables; yet, as the number of categories and/or variables increases, the number of table cells with few (or zero) observations also increases. Unfortunately, sparse contingency tables invalidate the use of standard good-ness-of-fit statistics. Limited-information fit…

Interest in Bayesian analysis of item response theory (IRT) models has grown tremendously due to the appeal of the paradigm among psychometricians, advantages of these methods when analyzing complex models, and availability of general-purpose software. Possible models include models which reflect multidimensionality due to designed test structure,…

In this paper, we investigate two purported problems with Bayesian Knowledge Tracing (BKT), a popular statistical model of student learning: "identifiability" and "semantic model degeneracy." In 2007, Beck and Chang stated that BKT is susceptible to an "identifiability problem"--various models with different…

In this paper, we investigate two purported problems with Bayesian Knowledge Tracing (BKT), a popular statistical model of student learning: "identifiability" and "semantic model degeneracy." In 2007, Beck and Chang stated that BKT is susceptible to an "identifiability problem"--various models with different…

The assumption of conditional independence between the responses and the response times (RTs) for a given person is common in RT modeling. However, when the speed of a test taker is not constant, this assumption will be violated. In this article we propose a conditional joint model for item responses and RTs, which incorporates a covariance…

Item response theory (IRT) has gained an increasing popularity in large-scale educational and psychological testing situations because of its theoretical advantages over classical test theory. Unidimensional graded response models (GRMs) are useful when polytomous response items are designed to measure a unified latent trait. They are limited in…

Using a complex simulation study we investigated parameter recovery, classification accuracy, and performance of two item-fit statistics for correct and misspecified diagnostic classification models within a log-linear modeling framework. The basic manipulated test design factors included the number of respondents (1,000 vs. 10,000), attributes (3…

The item response times (RTs) collected from computerized testing represent an underutilized type of information about items and examinees. In addition to knowing the examinees' responses to each item, we can investigate the amount of time examinees spend on each item. Current models for RTs mainly focus on parametric models, which have the…

Cognitive diagnostic analyses have been advocated as methods that allow an assessment to function as a formative assessment to inform instruction. To use this approach, it is necessary to first identify the skills required for each item in the test, known as a Q-matrix. However, because the construct being tested and the underlying cognitive…

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 the social sciences, latent traits often have a hierarchical structure, and data can be sampled from multiple levels. Both hierarchical latent traits and multilevel data can occur simultaneously. In this study, we developed a general class of item response theory models to accommodate both hierarchical latent traits and multilevel data. The…

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…

This paper studies three models for cognitive diagnosis, each illustrated with an application to fraction subtraction data. The objective of each of these models is to classify examinees according to their mastery of skills assumed to be required for fraction subtraction. We consider the DINA model, the NIDA model, and a new model that extends the…

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.…