This paper introduces a new algorithm to test uni-dimensionality according to the Rasch model. By adopting a similar idea based on a partial hierarchical cluster analysis, the authors suggest the model is intended to be used prior to the application of other model tests that have power against specific model violations. The ‘cluster analysis’ in the paper was designed to be a strict criterion for selecting items to yield a uni-dimensional cluster, which is based on the belief that items that are on the same dimension should be ‘grouped’ within one cluster. Under the proposed algorithm, the R1c statistics of Glas serves as an important statistic, which is based on the comparison of the expected and observed frequencies of persons giving a positive or negative response, to assess the model fit to the Rasch model.
In the simulation, the dataset is generated so that the firs and the second half were independent item sets but both fit the Rasch model. The results of the simulation have indicated that the algorithm performed best if the simulated person sample was large and if the correlation between person parameters was low. In particular, when compared with the PCA and parallel analysis of tetrachoric correlations, the proposed cluster analytical algorithm seemed to be preferred.
It is suggested that further studies could be done strategically to test its application and performance in other IRT models such 3PL model. More, empirical tests based on data from test of a greater length and a larger number of items are recommended.