A simple and effective method to test the dimensionality axiom of the Rasch model

A simple method is introduced to test the di-mensionality axiom in the Rasch model. The method consists of a suitable partitioning of the data set. This partitioning is based on the responses to some of the items being investigated. The items used for this purpose are called the external cri-terion items. data are presented indi-cating the effectiveness of the method in instances where the traditional test procedures fail. It was recently pointed out by several authors (Gustafsson, 1980; Gustafsson & Lindblad, 1978; Stelzl, 1979; van Wollenberg, 1979,1980a) the traditional global statistics for the Rasch model, such as the conditional likelihood ratio (Andersen, 1973), the of Martin-Lot (1973), the test of and Panchapakesan (1969), and the Fischer- Scheiblechner test (~~s~h~r ~. Scheiblechner, 1970), are essentially insensitive to violation of the unidimensionality axiom. These tests are standardiy applied to a raw partitioning of the set. The insensitivity of the tests is ascociatcd with this partitioning (van den Wollenberg, 1979). When tests are applied to other types of partitioning, violation of the unidimensionality may become manifest, although this is in no way guaranteed to occur. Martin-Lof (1973) pr~s~~t~d ~, method to test whether two sets of items measure the same latent trait. This test, however, requires an a priori hypothesis about which items belong to one trait and which to the other. This of is as a rule not available, so the method of Martin-Löf has only limited applicability. Van den Wollenberg (1979,1980a) introduced two new test statistics, Q, and Q,. The statistic is obtained as follows. For each ~t~~m~e~r~ ~ combination the following statistic is defined: Here nri is the number of subjects in ~~~~~®~~~ ~ ~ positively responding to item i n,,- the number of in level-group r negatively to this item, The is obtained as Downloaded from the Digital Conservancy at the University of Minnesota