Analysis of Local Dependence and Multidimensionality in Graphical Loglinear Rasch Models

Abstract

This paper proposes a procedure for analysis of multidimensionality in graphical loglinear Rasch models. The procedure combines exploratory techniques based on analysis of local dependence by coefficients measuring conditional item association and confirmatory techniques fitting and testing the adequacy of graphical loglinear Rasch models. The course of action is motivated by the observation that evidence of conditional item association suggesting multidimensionality may be generated by very different phenomena having nothing to do with multidimensionality. This means that an analysis of conditional association is never enough in itself: additional procedures are required to distinguish between multidimensionality and other causes of local dependence. The procedure for analysis of conditional item association may be regarded as a variation of well-known procedures for analysis of local dependence. Compared to these methods the techniques for the family of Rasch models described in this paper eliminate the bias inherent in conventional methods for analysis of conditional item association.