Effects of overextracting factors and components within and between maximum likelihood factor analysis and principal components analysis were examined through computer simulation of a range of factor and component patterns. Results demonstrate similarity of component and factor scores during overextraction. Overall, results indicate that…

A simulation study was conducted to investigate the application of expected a posteriori (EAP) trait estimation in computerized adaptive tests (CAT) based on the partial credit model and compare it with maximum likelihood estimation (MLE). Results show the conditions under which EAP and MLE provide relatively accurate estimation in CAT. (SLD)

Describes and assesses missing data methods currently used to analyze data from matrix sampling designs implemented by the National Assessment of Educational Progress. Several improved methods are developed, and these models are evaluated using an EM algorithm to obtain maximum likelihood estimates followed by multiple imputation of complete data…

Used three scoring methods (maximum likelihood estimation, expected a posteriori estimation, and biweight estimation) to estimate the latent trait values when nonmodel response vectors (NRVs) were present. Also investigated the relationship between the detection rate of a person-fit index and the error in the latent trait estimate. Discusses the…

The choice of constraints used to identify a simple factor model can affect the shape of the likelihood. Specifically, under some nonzero constraints, standard errors may be inestimable even at the maximum likelihood estimate (MLE). For a broader class of nonzero constraints, symmetric normal approximations to the modal region may not be…

Covariance structure models are applied to gene expression data using a factor model, a path model, and their combination. The factor model is based on a few factors that capture most of the expression information. A common factor of a group of genes may represent a common protein factor for the transcript of the co-expressed genes, and hence, it…

Through a large-scale simulation study, this article compares item parameter estimates obtained by the marginal maximum likelihood estimation (MMLE) and marginal Bayes modal estimation (MBME) procedures in the 3-parameter logistic model. The impact of different prior specifications on the MBME estimates is also investigated using carefully…

This article illustrates a method for fitting straight lines to data that is resistant to outliers and might therefore sometimes be preferred to the customary least squares procedure.

In this article, a maximum likelihood (ML) approach for analyzing a rather general two-level structural equation model is developed for hierarchically structured data that are very common in educational and/or behavioral research. The proposed two-level model can accommodate nonlinear causal relations among latent variables as well as effects…

This article proposes a general latent variable approach to discrete-time survival analysis of nonrepeatable events such as onset of drug use. It is shown how the survival analysis can be formulated as a generalized latent class analysis of event history indicators. The latent class analysis can use covariates and can be combined with the joint…

In this study, we examine the role of academic preparation in the transition from community colleges to four-year institutions. We address two specific questions: To what extent do academically unprepared students transfer to four-year institutions? And, can positive experiences in community colleges diminish the role of inadequate academic…

We illustrate a class of multidimensional item response theory models in which the items are allowed to have different discriminating power and the latent traits are represented through a vector having a discrete distribution. We also show how the hypothesis of unidimensionality may be tested against a specific bidimensional alternative by using a…

In order to obtain conditional maximum likelihood estimates, the so-called conditioning estimates have to be calculated. In this paper a method is examined that does not calculate these constants exactly, but approximates them using Monte Carlo Markov Chains. As an example, the method is applied to the conditional estimation of both item and…

The accuracy of the Markov Chain Monte Carlo (MCMC) procedure Gibbs sampling was considered for estimation of item parameters of the two-parameter logistic model. Data for the Law School Admission Test (LSAT) Section 6 were analyzed to illustrate the MCMC procedure. In addition, simulated data sets were analyzed using the MCMC, marginal Bayesian…

Item response theory (IRT) has proven to be a very powerful and useful measurement tool. However, most of the IRT models that have been proposed, and all of the models commonly used, require the assumption of unidimensionality, which prevents their application to a wide range of tests. The few models that have been proposed for use with…