Text

theses

At present, many cognitive diagnosis models (CDMs) have been developed for dichotomous response, several of which have been extended to handle polytomous response. CDMs to handle continuous response, however, have not been extensively explored beyond the recently proposed continuous deterministic inputs, noisy ``and" gate (C-DINA) model and its generalized version. The studies that comprise this dissertation aim to extend model development in the context of continuous response and to address several key issues that arise from its use in CDM. In the first study, a hierarchical framework is employed for using response time to improve examinee ability estimation and classification accuracy. Under this framework, response time and response accuracy are construed as arising from separate continuous, possibly correlated, unidimensional latent variables. A higher-order attribute specification is used to link the general ability to the probability of mastering certain attributes. Results show that both examinee classifications and higher-order ability estimation can be improved by using response time. A real data example is included to demonstrate the viability of the method. In the second study, a new item selection algorithm is presented for computerized adaptive testing applications that use continuous response CDMs. The algorithm uses the Jensen-Shannon divergence, which quantifies the total degree of dissimilarity in a set of two or more probability distributions, as an item selection algorithm. Results demonstrate that the method typically outperforms random item administration with respect to both classification accuracy and test efficiency. A real data example shows that an existing test could be shortened considerably while still producing a high level of classification agreement with the original. In the final study, a new Q-matrix validation procedure is proposed for continuous response CDMs. The method presented is designed to work with a generalized continuous response model, and is based on a weighted least squares regression. The simulation study shows that the method performs increasingly well as item quality increases. The method was also applied to an existing dataset, with results confirming most of the entries in the existing Q-matrix.

ETD_8272

Ph.D.

Includes bibliographical references

by Nathan Daniel Minchen

doi:10.7282/T3N58QH5

ETD doctoral

The author owns the copyright to this work.