Several special cases of the general Rasch model, varying in complexity, were investigated to determine whether they could successfully model realistic multidimensional item response data. Whether the parameters of the model could be readily interpreted was also investigated. The models investigated included: (1) the vector model; (2) the product term model; (3) the vector and product term model; (4) the reduced vector and product term model; and (5) the item cluster model. Of the models investigated, all but the reduced vector and product term model and the item cluster model were rejected as being incapable of modelling realistic multidimensional data. The item cluster model appears to be a useful model, but its applications may be limited in scope. Of the models studied, the reduced vector and product term model was found to be the most capable of modelling realistic multidimensional data. Although the estimation of the parameters of the reduced vectors and product term model may be more difficult than it would be for other models, this model appears to be the model that is most worth pursuing. (Author/PN)