Latent Trait Item Analysis and Facet Theory—A Useful Combination

Abstract

Computer programs for fitting latent trait models to data provide indices of item misfit. An analysis of the consistency of item misfit determination is presented. Two content-equivalent forms of 71 items representing the behavioral domain of arithmetic skills were gener ated. Each item was defined in terms of its combina tion of facet elements, and the ith item on each form represented the same selection of facets. The dichoto mously scored responses to the two forms were ana lyzed using the computer programs NOHARM and BICAL. Misfitting items were identified by use of the residual covariances in the case of NOHARM and To tal-t and Between-t in the case of BICAL. The con sistency of misfit was measured by the extent of agreement in selection of misfitting items across the parallel forms. It was found that the analysis of resid ual covariances provided a more consistent means of determining item misfit. It was concluded that the use of the Between- t and Total-t indices as a basis for ed iting items should be viewed cautiously. In addition, misfitting items were grouped according to common facet elements and reasons for misfit were postulated. Thus, the analysis of residual covariances of items de fined in terms of their combination of facet elements seems to provide a very satisfactory method of item analysis.