Research On The Q Matirx Design For Compensatory Multidimensional Irt Models Under Different Granularity Of Attributes

Recently,more and more researchers have shown interest in two psychometric theories,namely,multidimensional item response theory(MIRT)and cognitive diagnostic assessment(CDA).The two theories can be used to measure complex psychological phenomena and provide more detailed diagnostic information to examinees.The Q-matrix,which is the core element of cognitive diagnostic models(CDMs),can also be incorporated into MIRT models.The Q-matrix captures the relationship between items and attributes and simplifies parameter estimation in these two class models.The Q-matrix design not only represents test blueprint,but also affects the accuracy of diagnostic information in MIRT and CDA.Therefore,many researchers have conducted studies on the Q-matrix design in MIRT and CDA respectively.However,previous studies have not fully considered the effects of different Q matrix designs on the accuracy of diagnostic information in compensatory MIRT models.Thus,this paper further investigates the effects of Q-matrix design on the accuracy of diagnostic information in the compensatory multidimensional two-parameter logistic model through several simulation studies.One reason for choosing this model is that it is the compensatory MIRT model which can be used for both MIRT and CDA analysis.The results show that:(1)Under conditions with large granularity of attributes,items measuring one attribute tend to produce more accurate item parameter estimates.Besides,items measuring two attributes tend to produce more accurate diagnostic information.(2)Under conditions with small granularity of attributes,the diagnostic accuracy of the compensatory multidimensional two-parameter logistic model improves when the Q-matrix contains isolated information from each measured attribute.Based on the simulations,it can be concluded that the Q-matrix design for compensatory MIRT models should not be complex.