Spearman's factor-analytic model has been proposed as a unidimensional linear item response theory (IRT) model for continuous item responses. This article first proposes a reexpression of the model that leads to a form similar to that of standard IRT models for binary responses and discusses the item indices of difficulty discrimination and…

This study linked nonlinear profile analysis (NPA) of dichotomous responses with an existing family of item response theory models and generalized latent variable models (GLVM). The NPA method offers several benefits over previous internal profile analysis methods: (a) NPA is estimated with maximum likelihood in a GLVM framework rather than…

In the approach to latent trait models for pure speed tests presented in this article, the subject parameters are treated as random variables with a common gamma distribution, and marginal maximum likelihood estimators are derived for the test difficulties and the parameters of the latent subject distribution. An application of this model to…

Hierarchical Bayes procedures for the two-parameter logistic item response model were compared for estimating item parameters. Simulated data sets were analyzed using two different Bayes estimation procedures, the two-stage hierarchical Bayes estimation (HB2) and the marginal Bayesian with known hyperparameters (MB), and marginal maximum…

Loglinear latent class models are used to detect differential item functioning (DIF). Likelihood ratio tests for assessing the presence of various types of DIF are described, and these methods are illustrated through the analysis of a "real world" data set. (TJH)

A joint maximum likelihood estimation algorithm, based on the partial compensatory multidimensional logistic model (PCML) proposed by L. Zeng (1989), is presented. The algorithm simultaneously estimates item difficulty parameters, the strength of each dimension, and individuals' abilities on each of the dimensions involved in arriving at a correct…

This study was designed to compare the accuracy of three commonly used ability estimation procedures under the graded response model. The three methods, maximum likelihood (ML), expected a posteriori (EAP), and maximum a posteriori (MAP), were compared using a recovery study design for two sample sizes, two underlying ability distributions, and…

An alternative to the Rasch model is introduced. It characterizes strength of response according to the ratio of ability and difficulty parameters rather than their difference. Joint estimation and marginal estimation models are applied to two test data sets. (SLD)

An extension is proposed for the network algorithm introduced by C.R. Mehta and N.R. Patel to construct exact tail probabilities for testing the general hypothesis that item responses are distributed according to the Rasch model. A simulation study indicates the efficiency of the algorithm. (SLD)

The analytically derived asymptotic standard errors (SEs) of maximum likelihood (ML) item estimates can be approximated by a mathematical function without examinees' responses to test items, and the empirically determined SEs of marginal maximum likelihood estimation (MMLE)/Bayesian item estimates can be obtained when the same set of items is…