Type I error rates and rejection rates for three-dimensionality assessment procedures were studied with data sets simulated to reflect short tests and small samples. Results show that the G-squared difference test (D. Bock, R. Gibbons, and E. Muraki, 1988) suffered from a severely inflated Type I error rate at all conditions simulated. (SLD)

The empirical Type I error rates of Poly-DIMTEST (H. Li and W. Stout, 1995) and the LISREL8 chi square fit statistic (K. Joreskog and D. Sorbom, 1993) were compared with polytomous unidimensional data sets simulated to vary as a function of test length and sample size. The rejection rates for both statistics were also studied with two-dimensional…

Among the most popular techniques used to estimate item response theory (IRT) parameters are those used in the LOGIST and BILOG computer programs. Because of its accuracy with smaller sample sizes or differing test lengths, BILOG has become the standard to which new estimation programs are compared. However, BILOG is still complex and…

A study was conducted to compare, with simulated unidimensional and two-dimensional sets, the Type I error probabilities and rejection rates obtained with two versions of the LISREL computer program, the earlier version PRELIS/LISREL 7 and the later version PRELIS2/LISREL8, a version that corrects the asymptotic covariance matrix. Unidimensional…

The use of indices and statistics based on nonlinear factor analysis (NLFA) has become increasingly popular as a means of assessing the dimensionality of an item response matrix. Although the indices and statistics currently available to the practitioner have been shown to be useful and accurate in many testing situations, few studies have…