A way of identifying non-random patterns of effects on a group of individuals as a result of some intervention when a sample of participants is arrayed according to some indices of similarity is presented. The principle of proximal similarity and the concept of pattern matching provide the background for this effort. Major advantages are the…

The difference between compensatory and non-compensatory item response theory (IRT) models in terms of the dimensionality of test data generated by them, and its effect on the model-data-fit were examined. The STRESS (proportion of variance not accounted for by the multidimensional scaling model) and RSQ (proportion of variance accounted for by…

The effects of varying degrees of correlation between abilities and of various correlation configurations between item parameters on ability and item parameter estimation using the three parameter logistic model were examined. Ten two-trait configurations and one unidimensional test configuration for 30 item tests were simulated. Each…

The following seven statistical procedures are compared in terms of the ability to recover a unidimensional latent trait from Likert-type data: (1) factor analysis based on Pearson correlations (FA-PR); (2) factor analysis based on polychoric correlations (FA-PL); (3) the graded response model in item response theory (IRT-GRM); (4) internal…

A multidimensional item response theory (IRT) model for polytomously scored items, based on the graded response model and using the normal ogive, is developed; and an EM algorithm that may be used to estimate the parameters of the model is also discussed. The model is illustrated through a simulation study in which the polytomous item responses of…