A comparison of parameter estimation algorithms for estimating a polytomous log-linear cognitive diagnosis model for polytomous attributes

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Tyler Jeffrey Strachan (Creator)
Institution
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/
Advisor
Robert Henson

Abstract: Parameter estimation techniques such as an expectation-maximization (EM) algorithm have been used ubiquitously to estimate cognitive diagnosis models (CDM). The primary goal of this study was to utilize polytomous attributes in the polytomous log-linear cognitive diagnosis model (P-LCDM-PA), which is a special case of the general polytomous diagnostic model (GPDM) for polytomous attributes. Then, due to exponentially increasing the number of latent classes, explore the feasibility and efficiency in addition to the quality of parameter estimation of the stochastic expectation-maximization (SEM) and Metropolis-Hastings Robbins-Monro (MH-RM) algorithms relative to the EM algorithm. The SEM and MH-RM algorithms may be more computationally advantageous over an EM algorithm when there exist many latent classes. As the number of measured attributes increases in a diagnostic assessment, the number of latent classes increases exponentially. The large number of classes is even more problematic when polytomous attribute levels are introduced in the diagnostic assessment. The large number of classes becomes computationally challenging when estimating a model using an EM algorithm because for each respondent, the probability of class membership is computed for every latent class. Simulation experiments were conducted examining item parameter recovery in the P-LCDM-PA, correct classification rates, and computational time between the three algorithms.

Additional Information

Publication
Dissertation
Language: English
Date: 2019
Keywords
Cognitive diagnosis models, Computational time, Diagnostic classification models, Parameter estimation

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