Assessing Dimensionality of IRT Models Using Traditional and Revised Parallel Analyses

Abstract

Determining the number of dimensions is extremely important in applying item response theory (IRT) models to data. Traditional and revised parallel analyses have been proposed within the factor analysis framework, and both have shown some promise in assessing dimensionality. However, their performance in the IRT framework has not been systematically investigated. Therefore, we evaluated the accuracy of traditional and revised parallel analyses for determining the number of underlying dimensions in the IRT framework by conducting simulation studies. Six data generation factors were manipulated: number of observations, test length, type of generation models, number of dimensions, correlations between dimensions, and item discrimination. Results indicated that (a) when the generated IRT model is unidimensional, across all simulation conditions, traditional parallel analysis using principal component analysis and tetrachoric correlation performs best; (b) when the generated IRT model is multidimensional, traditional parallel analysis using principal component analysis and tetrachoric correlation yields the highest proportion of accurately identified underlying dimensions across all factors, except when the correlation between dimensions is 0.8 or the item discrimination is low; and (c) under a few combinations of simulated factors, none of the eight methods performed well (e.g., when the generation model is three-dimensional 3PL, the item discrimination is low, and the correlation between dimensions is 0.8).