The Effects of Qmatrıx Misspecification on Item and Model Fit

Abstract

In this study it was aimed to evaluate the effects of various factors such as sample sizes, percentage of misfit items in the test and item quality (item discrimination) on item and model fit in case of misspecification of Q matrix. Data were generated in accordance with DINA model. Q matrix was specified for 4 attributes and 15 items. While data were generated, sample sizes as 1000, 2000, 4000, s and g parameters as low and high discrimination index were manipulated. Three different misspecified Q matrix (overspecified, underspecified and mixed) was developed considering the percentage of misfit items (%20 and %40). In the study, S-X2 was used as item fit statistics. Furthermore absolute (abs(fcor), max(X2)) and relative (-2 log-likelihood, Akaike's information criterion (AIC) and Bayesian information criterion (BIC)) model fit statistics were used. Investigating the results obtained from this simulation study, it was concluded that S-X2 was sufficient to detect misfit items. When the percentage of misfit items in the test was much or Q matrix was both underspecified and overspecified, the correct detection of both abs(fcor) and max(X2) statistics was approximately 1 or 1. In addition, the correct detection rates of both statistics was high under other conditions, too. AIC and BIC were successful to detect model misfit in the cases where the Q matrix underspecified, whereas, they were failed detect model misfit for other cases. It can be said that the performance of BIC was mostly better than other relative model fit statistics to detect model misfit.