Polytomous attributes, particularly those defined as part of the test development process, can provide additional diagnostic information. The present research proposes the polytomous generalized deterministic inputs, noisy, "and" gate (pG-DINA) model to accommodate such attributes. The pG-DINA model allows input from substantive experts…

This article proposes a generalized distance discriminating method for test with polytomous response (GDD-P). The new method is the polytomous extension of an item response theory (IRT)-based cognitive diagnostic method, which can identify examinees' ideal response patterns (IRPs) based on a generalized distance index. The similarities between…

For one reason or another, various sources of information, namely, ancillary variables and correlational structure of the latent abilities, which are usually available in most testing situations, are ignored in ability estimation. A general model that incorporates these sources of information is proposed in this article. The model has a general…

Cognitive or skills diagnosis models are discrete latent variable models developed specifically for the purpose of identifying the presence or absence of multiple fine-grained skills. However, applications of these models typically involve dichotomous or dichotomized data, including data from multiple-choice (MC) assessments that are scored as…

Sample size ranks as one of the most important factors that affect the item calibration task. However, due to practical concerns (e.g., item exposure) items are typically calibrated with much smaller samples than what is desired. To address the need for a more flexible framework that can be used in small sample item calibration, this article…

Lack of sufficient reliability is the primary impediment for generating and reporting subtest scores. Several current methods of subscore estimation do so either by incorporating the correlational structure among the subtest abilities or by using the examinee's performance on the overall test. This article conducted a systematic comparison of four…

Recent work has shown that multidimensionally scoring responses from different tests can provide better ability estimates. For educational assessment data, applications of this approach have been limited to binary scores. Of the different variants, the de la Torre and Patz model is considered more general because implementing the scoring procedure…

Assessments consisting of different domains (e.g., content areas, objectives) are typically multidimensional in nature but are commonly assumed to be unidimensional for estimation purposes. The different domains of these assessments are further treated as multi-unidimensional tests for the purpose of obtaining diagnostic information. However, when…

The authors present a Markov Chain Monte Carlo (MCMC) parameter estimation procedure for the generalized graded unfolding model (GGUM) and compare it to the marginal maximum likelihood (MML) approach implemented in the GGUM2000 computer program, using simulated and real personality data. In the simulation study, test length, number of response…