Rasch models of multidimensionality between items and within items

This chapter focuses on Rasch measurement and extends it to multidimensional Rasch models. The author first clarifies multidimensionality at two levels: the item level and the test level. With this two way classification, three kinds of tests are formed: undimensional tests, multidimensional between-item tests, and multidimensional within-item tests. The author describes a multidimensional Rasch model, the multidimensional random coefficients multinomial logit (MRCML) model, for multidimensional tests. The model, when applied to multidimensional between-item tests, is more efficient than are unidimensional models in terms of model fit and reliability indices. The model can also be applied to investigate scale interaction of multidimensional within item tests. The item parameters derived from the model field interpretation within frameworks of unidimensional models. Through analysis of empirical data, some applications of the MRCML model to multidimensional tests are demonstrated.