[Goodness of fit in polytomous items: Type I error rates and empirical power for three fit-indexes]

Applications of Item Response Theory require assessing the agreement between observations and model predictions at the item level. This paper compares approaches applied to polytomous scored items in a simulation study. Three fit-indexes are calculated: traditional chi-square index obtained by grouping examinees according to their estimated trait, an alternative that uses posterior distribution of trait and the third method, in which examinees are grouped according their observed total scores. Various conditions are simulated by manipulating test length (10, 20 and 40 items), number of categories (3, 4 and 5) and sample size (500, 1000 and 2000 examinees). Power and Type I error rates are described. Chi-square statistics based on posterior probabilities showed the best performance, especially with larger sample sizes and shorter test lengths.