Measuring individual differences in change with multidimensional Rasch models

Item response models have been developed to explore change measurement, including those proposed by Fischer and his colleagues (e.g., Fischer & Pazer, 1991; Fischer & Ponocny, 1994), Andersen (1985) and Embretson (1991). In this article, we propose another multidimensional Rasch model, the multidimensional random coefficient multinomial logit (MRCML) model (Adams, Wilson, & Wang, 1997). All these models are briefly reviewed and compared. The MRCML can be applied to not only polytomous items but also investigation of variations in item difficulties. Based on variations in difficulties across occasions and items, five kinds of models are proposed. Some simulation studies were conducted to examine parameter recovery of the MRCML model under various testing situations. All the parameters were recovered very well. A real data set was analyzed to show applications of the MRCML to measuring individual differences in change.