The effect of missing data methods on parameter estimation of polytomous multi-dimensional IRT models

In this study, it is aimed to examine the effects of missing data handling methods on item and ability parameters obtained from the Multidimensional Generalized Partial Credit Model (M-GPCM) and Multidimensional Graded Response Model (M-GRM) in multidimensional data sets with different missing mechanisms and different rates of missing data. Ability and item parameters were generated. Two-dimensional complete item responses were generated using the specified ability and item parameters. From the complete item responses, missingness rates of 5%, 10%, and 20% with missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR) mechanisms were generated. The data sets with missing data were completed with series mean imputation (SM), regression imputation (RI), and expectation maximization (EM). The parameters obtained from the completed data sets were compared with the parameters obtained from the complete data set. For all parameters, the average errors were lower than the other missingness rates in data sets with 5% missingness. For item discrimination parameters, RI and EM performed better than SM in all conditions. RI was found to be the method with the lowest error. For the category boundary intersection parameters, RI performs the best in the MCAR and MAR, while the errors obtained from the methods are very high in the MNAR. For the recovery of ability parameters, very low average RMSEs were obtained in all condition compared to the item parameters. It was observed that the method that produced the lowest RMSEs in all conditions was EM, unlike the item parameters.