Estimating the Hausman Test for Rasch with poorly fitted items

In this study, an assessment that was difficult for a sample was used as a demonstration of the bootstrap method for estimating the Hausman test for Rasch analysis when the items are poorly fitted. A 10-item dichotomously scored test of numerical reasoning was administered to 200 (120 male, 80 female) high school pupils in Nigeria. The INFIT, OUTFIT statistics and standard error inflator showed that the 10 test items did not fit the Rasch model well and 1000 bootstrap replicates of the sample was generated. This paper reports results from the parametric, simulation and bootstrap method for estimating the Hausman test for the Rasch model. The main findings were that the simulation and bootstrap method for estimating the Hausman test for Rasch were statistically better than the parametric method and there was no need to eliminate poorly fitted items as suggested previous in the literature.

Key words: Rasch model, Hausman test