The primary purpose of this study was to investigate the invariance properties of the Rasch model using data from standardized achievement tests that were not constructed to conform to the Rasch model. The item responses of approximately '3,400 examinees (Grades 9, 10, 11, and 12) to four separately timed sections of the Iowa Tests of Educational Development were analyzed. The results indicated that the Rasch model does yield reasonably invariant item parameter and ability parameter estimates for different tests and different examinee groups, even though the assumptions of the model are not met.As noted by many measurement experts, the use of latent trait models may help solve some of the measurement problems frequently encountered by practitioners (e.g., linking and equating of tests and building item banks). However, these models usually require rather strong assumptions about the nature of the data. The major assumption of all latent trait models is unidimensionality or, equivalently, local independence of items. Additional assumptions are required for each specific latent trait model. For dichotomously scored items, the oneparameter logistic, or Rasch, model, is the simplest latent trait model and consequently makes the most restrictive assumptions.
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