Revised Parallel Analysis With Nonnormal Ability and a Guessing Parameter

Previous work showing that revised parallel analysis can be effective with dichotomous items has used a two-parameter model and normally distributed abilities. In this study, both two- and three-parameter models were used with normally distributed and skewed ability distributions. Relatively minor skew and kurtosis in the underlying ability distribution had almost no effect on Type I error for unidimensional data and reduced power for two-dimensional data slightly with smaller sample sizes of 400. Using a two-parameter model on three-parameter data produced dramatically increased rejection rates for the unidimensional data. Using the correct three-parameter model reduced the unidimensional rejection rates but yielded lower power than the two-parameter data in some conditions.