The construction and implementation of user-defined fit tests for use with marginal maximum likelihood estimation and generalized item response models.
Wu (1997) developed a residual based fit statistic for the generalized Rasch model when marginal maximum likelihood estimation is used. This statistic is based upon a comparison of individual's contributions to the sufficient statistics with the expectation of those contributions, for modeled parameters. In this paper, we present a more flexible approach in which linear combinations of individual's contributions to the sufficient statistics are compared to their expectations. This more flexible approach can be used to test the fit of combinations of items. This article first describes briefly the theoretical derivation of the fit statistics, and then illustrates how user-defined fit tests can be implemented for a number of simulated data sets, and for two real data sets. The results show that user-defined fit tests are much more powerful than fit tests at individual parameter level in testing hypothesized violations of the item response model, such as local dependence and multi-dimensionality.
Adams
Raymond J
RJ
University of Melbourne, Austrialia. adams@acer.edu.au
Wu
Margaret L
ML
D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D008962:Models, Theoretical; D011594:Psychometrics / Q000706:statistics & numerical data*; D011795:Surveys and Questionnaires