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theses

Classification error probabilities (CEPs) are estimates of the amount of misclassification in the measurement model conditional on the true latent class memberships. CEPs can be used in several ways to improve the inferences drawn from cognitive diagnosis models (CDMs). To develop methodologies that facilitate the use of CDMs in practical research, this dissertation uses CEPs to accomplish three objectives: (1) to examine the conditional classification accuracy and generalizability of a cognitively diagnostic assessment; (2) to introduce correction weights that can improve a three-step approach for latent-class regression, which relate latent class memberships to predictor variables, and (3) to apply the same correction weights to select the best subset of predictor variables in the context of latent-class regression. In the first study, an application of CEPs fills a gap in literature on CDM validity by serving as an index of classification accuracy conditional on the latent class memberships. This index can also be extended to predict the classification accuracy of the assessment for a different population. Results show that the proposed index not only recovers the empirical values, but outperforms existing procedures based on the Monte Carlo approach. In the second study, CEPs are used to improve the inferences in latent-class regression. Compared to the one-step procedure, which estimates the measurement model and regression parameters simultaneously, the three-step procedure is desirable from an applied researchers’ perspective because it simplifies latent-class regression by implementing the estimations involved in separate steps. However, it also leads to parameter estimation bias. This study uses CEP-derived weights to improve parameter estimation in various types of latent-class regression. Finally, the third study extends the latent-class regression in the second study by incorporating a regularization procedure that permits variable selection. Results show that incorporating measurement error (as measured by CEP) in the variable selection process leads to a subset of nonredundant variables that more clearly shows the relationship between predictors and examinee classification. In addition, compared to the standard approach, using the CEP-based weights leads to fewer instances of estimation noncovergence. With a general aim to address needs in conditional classification accuracy, correcting bias in parameter estimation, and high-dimension variable selection in the context of CDMs, this dissertation uses CEPs to accomplish three objectives: (1) to examine the conditional classification accuracy and generalizability of the assessment, (2) introduce correction weights for the three-step approach that result in improved parameter estimation, and (3) apply these correction weights to regularized latent-class regression to select variables.

ETD_8220

Ph.D.

Includes bibliographical references

by Charles Joseph Iaconangelo

doi:10.7282/T3W95D95

ETD doctoral

The author owns the copyright to this work.