Item parameter estimations for multidimensional graded response model under complex structures

Abstract

Item parameter recovery in the compensatory multidimensional graded response model (MGRM) under simple and complex structures with rating-scale item response data was examined. A simulation study investigated factors that influence the precision of item parameter estimation, including sample size, intercorrelation between the dimensions, and test lengths for the MGRM under balanced and unbalanced complex structures, as well as the simple structure. The item responses for the MGRM were generated and analyzed across conditions using the R package mirt. The bias and root mean square error (RMSE) was used to evaluate item parameter recovery. Results suggested that item parameter estimation was more accurate in balanced complex structure conditions than in unbalanced or simple structures, especially when the test length was 40 items, and the sample size was large. Further, the mean bias and RMSE in the recovery of item threshold estimates along the two dimensions for both balanced and unbalanced complex structures were consistent across all conditions.

A 13-item Health of the Nation Outcome Scale (HoNOS-13): validation by item response theory (IRT) in patients with substance use disorder

“…The 2-PL form of MIRT can be written as [ 37 ]: where is the probability that observed scores for item j and respondent i given the ability/trait θ to obtain a score greater than or equal to category k , is the vector of item discrimination parameters for item j on each latent trait m , is the vector of item severity parameters for each category k within item j , is the vector of the latent traits on the dimension and D = 1 or 1.7, a scaling constant ( D = 1.7 to scale the logistic to the normal ogive metric, D = 1 to preserve the logistic metric).…”