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theses

Cognitive diagnosis models (CDMs) have received increasing attention in recent years. The goal of CDMs is to classify examinees into different latent classes with unique attribute patterns indicating mastery or nonmastery on a set of skills or attributes of interest. Although a large number of CDMs can be found in the literature, most of them are developed for dichotomous response data. This dissertation proposes a general cognitive diagnosis model for a special type of polytomously scored items, where item categories are attained in a sequential manner, and explicitly associated with some attributes. The conditional probability of answering a category correctly given that the previous categories have been performed successfully is defined as emph{processing function}, and modeled using the generalized deterministic inputs, noisy ``and'' gate (G-DINA; de la Torre, 2011) model. The resulting model is referred to as the emph{sequential} G-DINA model. To relate response categories to attributes, a category-level Q-matrix is used. When the attribute and category association is specified a priori, the proposed model has the flexibility to allow different cognitive processes (e.g., conjunctive, disjunctive) to be modeled at different steps within a single item. This model can be extended for items, where categories cannot be explicitly linked to attributes, and for items with unordered categories. Item parameters of the proposed model are estimated using the marginal maximum likelihood estimation via expectation-maximization algorithm. Like the traditional Q-matrix, the category-level Q-matrix is most likely to be developed by experts, and thus tends to be subjective. In this dissertation, a Q-matrix validation procedure is developed for the sequential G-DINA model to empirically identify and correct misspecifications in the category-level Q-matrix. This validation method is implemented in a stepwise manner based on the Wald test and an item discrimination index. Simulation studies are conducted to evaluate the performance of the proposed procedure in terms of the true positive and false positive rates. A condensation rule is an important component for most CDMs, including the sequential G-DINA model, in that it specifies how the latent attributes are employed simultaneously to make a manifest item response. Although the G-DINA model has been used as the processing function, it is important to empirically determine whether the G-DINA model can be further constrained according to the cognitive processes involved in each step. In this dissertation, the performance of the Wald test and the likelihood ratio test are examined in determining the appropriate condensation rule for each step. More specifically, a simulation study is used to evaluate the Type I error and power of these hypothesis tests concerning whether the DINA model, DINO model, and extit{A}-CDM can be used in place of the G-DINA model as the processing function for the steps that involved more than one attribute. Taken together, this dissertation develops a set of psychometric tools including statistical models and procedures for graded response data. These tools can facilitate the use of constructed-response items, which are typically scored polytomously, in cognitively diagnostic assessments. The performance of the proposed models and procedures are examined using both Monte Carlo simulation studies and real data.

ETD_8221

Ph.D.

Includes bibliographical references

by Wenchao Ma

doi:10.7282/T3DN485F

ETD doctoral

The author owns the copyright to this work.