Accuracy of attribute estimation in the crossed random effects linear logistic test model: impact of Q-matrix misspecification

A simulation study is designed to explore the accuracy of attribute parameter estimation in the crossed random effects linear logistic test model (CRELLTM) with the impact of Q-matrix misspecification on attribute parameter estimation using the SAS® GLIMMIX procedure with a scaling constraint on item parameter. In addition, the impact of the interactions of Q-matrix misspecification with other manipulated factors, such as population distribution, sample size, and Q-matrix density, on parameter estimation is also investigated. The results indicated that misspecification type and percent have a considerable impact on the bias and root mean squared error of attribute estimates, especially under the conditions of high percent misspecification and over-misspecification. However, attribute correlation between the estimated and true parameters is not affected by misspecification type and percent. Other manipulated variables have no impact or interaction effects with Q-matrix misspecifications on attribute estimates. Since the Q-matrix is an indispensable element in applying the crossed random effects linear logistic test model, specifying an appropriate Q-matrix is a crucial task and must be completed with generous assistance from content and subject experts.