Comparison of the Fit of Empirical Data to Two Latent Trait Models.

摘要

Few guidelines exist for selecting from the one and three-parameter logistic latent trait models. This study explored fit of empirical data to these two models in terms of degree of violation of model assumptions. Specifically, unidimensionality, guessing, and equality of item discrimination indices were examined. Additionally, fit statistics were explored for data which varied in both sample size and test length. Chi square statistics were used to compare fit of distributions of observed number-right scores to number right scores predicted from latent trait theory. Using the mean of the conditional distribution of number-right scores for a given ability level as the criterion, the Rasch (one-parameter) model was generally found to be superior in fit to data than the three-parameter model for the five data sets utilized in the study. Fit of data to both models improved as the number of items or persons increased. When short tests were constructed from the data such that item discriminations displayed a broad range, better fit was found for the three-parameter model. Improvement in fit for both models was found for data fulfilling the assumption of unidimensionality. Keywords: Latent trait theory, Cognition, Mathematical models, Psychological tests, Aptitude tests. (SDW)