This study explored alternative methods of estimating the number of latent dimensions represented by binary test data. The alternative methods vary in their complexity and include: (1) the minimum average partial correlation technique (MAP; W. Velicer, 1976) applied to phi correlations between binary responses; (2) the bootstrapped parallel…

An Educational Testing Service (ETS) procedure was evaluated, which is based on item response theory and estimates true scores on tests not taken. The reading, vocabulary, and mathematics tests of high school seniors from the National Longitudinal Study (NLS) of 1972 and the High School and Beyond (HSB) seniors of 1980 and 1982 were found to share…

DETECT is a nonparametric, conditional covariance-based procedure to identify dimensional structure and the degree of multidimensionality of test data. The ability composite or conditional score used to estimate conditional covariance plays a significant role in the performance of DETECT. The number correct score of all items in the test (T) and…

Three common methods for equating parameter estimates from binary item response theory models are extended to the generalized grading unfolding model (GGUM). The GGUM is an item response model in which single-peaked, nonmonotonic expected value functions are implemented for polytomous responses. GGUM parameter estimates are equated using extended…

When categorical responses were simulated from a Multidimensional Many-FACETS Rasch Compensatory Model (MMFRCM), the effects of ability, task difficulty, and step difficulty estimates with the unidimensional Many-FACETS Rasch Model (MFRM; Linacre, 1999) were examined in terms of three error indexes, average absolute difference (AAD), bias, and…

The purpose of this study was to assess the dimensionality of attitudinal data arising from unfolding models for discrete data and to compute rough estimates of item and individual parameters for use as starting values in other estimation parameters. One- and two-dimensional simulated test data were analyzed in this study. Results of limited…

Developed a full maximum likelihood method for obtaining joint estimates of variances and correlations among continuous and polytomous variables with incomplete data that are missing at random with an ignorable missing mechanism. Simulation results and an empirical example illustrate the approach. (SLD)

Varied the number of items and categories per item to explore the effects on estimation of item parameters in the nominal response model. Simulation results show that increasing the number of items had little effect on item parameter recovery, but increasing the number of categories increased the error variance of the parameter estimates. (SLD)

Investigated the effect of item parameter drift on ability estimates under item response theory, simulating item response data for two testing occasions for the two-parameter logistic model under several crossed conditions. Results show that item parameter drift under the simulated conditions had a small effect on ability estimates. (SLD)

A simulation study compared three methods of estimating parameters within structural equation models (SEM) with polytomous variables. These methods appear in three SEM computer software packages: (1) LISREL (Joreskog and Sorbom, 1996) with PRELIS (Joreskog and Sorbom); (2) EQS (Bentler, 1995); and (3) the new Mplus (Muthen and Muthen, 1998). The…

Developed a method for conditional pairwise estimation in the Rasch model for ordered response categories using principal components analysis and evaluated the procedure through a simulation study. Results show that the quality of the estimates is excellent. (SLD)

Compared the quality of item parameter estimates for marginal maximum likelihood (MML) and Markov Chain Monte Carlo (MCMC) with the nominal response model using simulation. The quality of item parameter recovery was nearly identical for MML and MCMC, and both methods tended to produce good estimates. (SLD)

Investigated incorporating a testlet definition into the estimation of the conditional standard error of measurement (SEM) for tests composed of testlets using five conditional SEM estimation methods. Results from 3,876 tests from the Iowa Tests of Basic Skills and 1,000 simulated responses show that item-based methods provide lower conditional…

A simulation study was conducted to identify the best hot-deck variation to impute missing values. The three variations included in the study were the hot-deck random, the hot-deck sequential, and the hot-deck distance. The properties of these methods were investigated under three levels of the proportion of incomplete records and four levels…

In this study, the robustness of item parameter estimates with respect to the underlying distribution of abilities was explored. Using simulated datasets, item parameters were derived from a large sample representing the population versus samples representing a subset of ability and subsequently compared for possible mismatch. Comparisons were…