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Activity Number: 192
Type: Contributed
Date/Time: Monday, July 30, 2012 : 10:30 AM to 12:20 PM
Sponsor: Section for Statistical Programmers and Analysts
Abstract - #306475
Title: The Performance of the Linear Logistic Test Model and the 2-Pl Constrained Model When the Q-Matrix Is Misspecified: A Simulation Study
Author(s): George MacDonald*+ and Jeffrey Kromrey and Sarah VanIngen
Companies: University of South Florida and University of South Florida and University of South Florida
Address: 4202 East Fowler Avenue, Tampa, FL, 33620, United States
Keywords: Simulation ; LLTM ; 2-PL Constrained

In the report, Adding it Up: Helping Children Learn Mathematics, the Mathematics Learning Committee from the National Research Council suggested that student learning and performance could be enhanced if conceptual understanding was taught at the same time as procedural fluency. Fischer (1973) introduced a model called the linear logistic test model (LLTM) that is capable of bridging cognitive processing models and psychometric models. Fischer found that differentiating calculus items could be explained by cognitive operations that the examinee must implement. The specification of the cognitive operations are quantified in a Q-Matrix. Most model fit analysis do not address the correctness of the constructed Q-Matrix, therefore, the amount of model misspecification that the Q-Matrix can tolerate and still function adequately is unknown. This simulation study examined the extent to which the LLTM and the 2-Pl constrained models, an extension of the LLTM, function well when the Q-Matrix is: properly specified; under specified; balanced misspecified, and over specified The results of the simulation will be interpreted and the implications for educational assessment will be discussed.

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