Maximum likelihood and Bayesian ability estimation in multidimensional item response models can lead to paradoxical results as proven by Hooker, Finkelman, and Schwartzman ("Psychometrika" 74(3): 419-442, 2009): Changing a correct response on one item into an incorrect response may produce a higher ability estimate in one dimension.…

A multinormal partial credit model for factor analysis of polytomously scored items with ordered response categories is derived using an extension of the Dutch Identity (Holland in "Psychometrika" 55:5-18, 1990). In the model, latent variables are assumed to have a multivariate normal distribution conditional on unweighted sums of item…

Indefinite symmetric matrices that are estimates of positive-definite population matrices occur in a variety of contexts such as correlation matrices computed from pairwise present missing data and multinormal based methods for discretized variables. This note describes a methodology for scaling selected off-diagonal rows and columns of such a…

Item factor analysis has a rich tradition in both the structural equation modeling and item response theory frameworks. The goal of this paper is to demonstrate a novel combination of various Markov chain Monte Carlo (MCMC) estimation routines to estimate parameters of a wide variety of confirmatory item factor analysis models. Further, I show…

Motivated by Gibbons et al.'s (Appl. Psychol. Meas. 31:4-19, "2007") full-information maximum marginal likelihood item bifactor analysis for polytomous data, and Rijmen, Vansteelandt, and De Boeck's (Psychometrika 73:167-182, "2008") work on constructing computationally efficient estimation algorithms for latent variable…

In this paper we discuss the use of a recent dimension reduction technique called Locally Linear Embedding, introduced by Roweis and Saul, for performing an exploratory latent structure analysis. The coordinate variables from the locally linear embedding describing the manifold on which the data reside serve as the latent variable scores. We…

There is a unity underlying the diversity of models for the analysis of multivariate data. Essentially, they constitute a family of models, most generally nonlinear, for structural/functional relations between variables drawn from a behavior domain. (Author)

Prior to a three-way component analysis of a three-way data set, it is customary to preprocess the data by centering and/or rescaling them. Harshman and Lundy (1984) considered that three-way data actually consist of a three-way model part, which in fact pertains to ratio scale measurements, as well as additive "offset" terms that turn the ratio…

With reference to the authors' previous paper (1985), it is proposed that loglinear analysis can be used to detect interactions in a multiway contingency table and explore the form of these interactions with correspondence analysis. Correspondence analysis assists in finding a model with restrictions on the interaction parameters. (TJH)

In many instances it is reasonable to assume that the population covariance matrix has positive elements. This assumption implies for the single factor analysis model that the loadings and regression weights for best linear factor prediction are positive. For the multiple factor analysis model where each variable loads on a single factor and a…

Equivalence of marginal likelihood of the two-parameter normal ogive model in item response theory and factor analysis of dichotomized variables was formally proved. Ordered and unordered categorical data and paired comparisons data were discussed, and a taxonomy of data for the models was suggested. (Author/GDC)

The practicality of using the EM algorithm for maximum likelihood estimation of item parameters in the marginal distribution is presented. The EM procedure is shown to apply to general item-response models. (Author/JKS)

An estimate and upper-bound estimate for the reliability of a test composed of binary items is derived from the multidimensional latent trait theory of R. D. Bock and M. Aitken (1981). The practical uses of such estimates are discussed. (SLD)

Relations between latent trait and latent class models for item response data are examined. Conditions are given for two-latent class and two-parameter normal ogive models to agree, and relations between their item parameters are presented. Results are illustrated with data from the Law School Admission Test. (SLD)