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This study investigated the item parameter recovery of two methods of factor analysis. The methods researched were a traditional factor analysis of tetrachoric correlation coefficients and an IRT approach to factor analysis which utilizes marginal maximum likelihood estimation using an EM algorithm (MMLE-EM). Dichotomous item response data was generated under the 2-parameter normal ogive model (2PNOM) using PARDSIM software. Examinee abilities were sampled from both the standard normal and uniform distributions. True item discrimination, a, was normal with a mean of .75 and a standard deviation of .10. True b, item difficulty, was specified as uniform [-2, 2]. The two distributions of abilities were completely crossed with three test lengths (n= 30, 60, and 100) and three sample sizes (N = 50, 500, and 1000). Each of the 18 conditions was replicated 5 times, resulting in 90 datasets. PRELIS software was used to conduct a traditional factor analysis on the tetrachoric correlations. The IRT approach to factor analysis was conducted using BILOG 3 software. Parameter recovery was evaluated in terms of root mean square error, average signed bias, and Pearson correlations between estimated and true item parameters. ANOVAs were conducted to identify systematic differences in error indices. Based on many of the indices, it appears the IRT approach to factor analysis recovers item parameters better than the traditional approach studied. Future research should compare other methods of factor analysis to MMLE-EM under various non-normal distributions of abilities.

In this study, an improved correlational procedure for factor-analyzing dichotomously-scored item response data is described and tested. The procedure involves (a) replacing the dichotomous input values with continuous probability values obtained through Rasch analysis; (b) calculating interitem product-moment correlations among the probabilities; and (c) subjecting the correlations to unweighted least-squares factor analysis. Two simulated data sets and an empirical data set (Kentucky Comprehensive Listening Test responses) were used to compare the new procedure with two more traditional techniques, using (a) phi and (b) tetrachoric correlations calculated directly from the dichotomous item-response values. The three methods were compared on three criterion measures: (a) maximum internal correlation; (b) product of the two largest factor loadings; and (c) proportion of variance accounted for. The Rasch-based procedure is recommended for subjecting dichotomous item response data to latent-variable analysis.

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No description available.