The Q-matrix Design for Compensatory Multidimensional IRT Models
The Q-matrix of multidimensional item response theory(MIRT)models is restricted to binary variables and catpures the re-lationship between items and demensions.Different Q-matrices can impact the model identifiability and accuracy of parameter esti-mates in MIRT models.Previous studies have found that items measuring one dimension tend to produce more accurate parameter esti-mates in compensatory MIRT models.However,items measuring more than one dimension may produce more accurate ability vector esti-mates because they have higher discrimination.In this article,we further investigated the effects of Q-matrix design on parameter esti-mates through simulation study under non-adaptive testing scenario.The simulation results showed that(1)compared to other Q-ma-trix designs,between-item multidimensionality design only had an advantage in item parameter estimates;(2)under almost all condi-tions,the Q-matrix contained both items guaranteeing model identifiability and items measuring two dimensions not only produced more accurate ability vector estimates than other Q-matrix designs,but also provided acceptable item parameters recovery.
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