The accuracy of item parameter estimates in the multidimensional item response theory (MIRT) model context is one that has not been researched in great detail. This study examines the ability of two confirmatory factor analysis models specifically for dichotomous data to properly estimate item parameters using common formulae for converting factor…

Scale linking is the process of developing the connection between scales of two or more sets of parameter estimates obtained from separate test calibrations. It is the prerequisite for many applications of IRT, such as test equating and differential item functioning analysis. Unidimensional scale linking methods have been studied and applied…

In Ramsay-curve item response theory (RC-IRT), the latent variable distribution is estimated simultaneously with the item parameters of a unidimensional item response model using marginal maximum likelihood estimation. This study evaluates RC-IRT for the three-parameter logistic (3PL) model with comparisons to the normal model and to the empirical…

In tests with time limits, items at the end are often not reached. Usually, the pattern of missing responses depends on the ability level of the respondents; therefore, missing data are not ignorable in statistical inference. This study models data using a combination of two item response theory (IRT) models: one for the observed response data and…

Tests of model misfit are often performed to validate the use of a particular model in item response theory. Douglas and Cohen (2001) introduced a general nonparametric approach for detecting misfit under the two-parameter logistic model. However, the statistical properties of their approach, and empirical comparisons to other methods, have not…

Ramsay curve item response theory (RC-IRT) was recently developed to detect and correct for nonnormal latent variables when unidimensional IRT models are fitted to data using maximum marginal likelihood estimation. The purpose of this research is to evaluate the performance of RC-IRT for Likert-type item responses with varying test lengths, sample…

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)

DETECT is a nonparametric "full" dimensionality assessment procedure that clusters dichotomously scored items into dimensions and provides a DETECT index of magnitude of multidimensionality. Four factors (test length, sample size, item response theory [IRT] model, and DETECT index) were manipulated in a Monte Carlo study of bias, standard error,…

Orlando and Thissen (2000, 2003) proposed an item-fit index, S-X[superscript 2], for dichotomous item response theory (IRT) models, which has performed better than traditional item-fit statistics such as Yen's (1981) Q[subscript 1] and McKinley and Mill's (1985) G[superscript 2]. This study extends the utility of S-X[superscript 2] to polytomous…

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…

Previous work on the effects of dimensionality on parameter estimation for dichotomous models is extended to the graded response model. Datasets are generated that differ in the number of latent factors as well as their interdimensional association, number of test items, and sample size. (SLD)

Examined the effects of test length and sample size on the alternate forms reliability and equating of simulated mathematics tests composed of constructed response items scaled using the two-parameter partial credit model. Results suggest that, to obtain acceptable reliabilities and accurate equated scores, tests should have at least 8 6-point…

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…

Compared differential item functioning detection rates for logistic regression and analysis of variance for dichotomously scored items using simulated data and varying test length, sample size, discrimination rate, and underlying ability. Explains why the logistic regression method is recommended for most applications. (SLD)

Many of the currently available statistical indexes to detect answer copying lack sufficient power at small [alpha] levels or when the amount of copying is relatively small. Furthermore, there is no one index that is uniformly best. Depending on the type or amount of copying, certain indexes are better than others. The purpose of this article was…