A central problem in the application of exploratory factor analysis is deciding how many factors to retain ("m"). Although this is inherently a model selection problem, a model selection perspective is rarely adopted for this task. We suggest that Cudeck and Henly's (1991) framework can be applied to guide the selection process.…

In this article, we directly question the common practice in growth mixture model (GMM) applications that exclusively rely on the fitting model without covariates for GMM class enumeration. We provide theoretical and simulation evidence to demonstrate that exclusion of covariates from GMM class enumeration could be problematic in many cases. Based…

The comparative format used in ranking and paired comparisons tasks can significantly reduce the impact of uniform response biases typically associated with rating scales. Thurstone's (1927, 1931) model provides a powerful framework for modeling comparative data such as paired comparisons and rankings. Although Thurstonian models are generally…

The logistic person response function (PRF) models the probability of a correct response as a function of the item locations. Reise (2000) proposed to use the slope parameter of the logistic PRF as a person-fit measure. He reformulated the logistic PRF model as a multilevel logistic regression model and estimated the PRF parameters from this…

We apply the Supplemented EM algorithm (Meng & Rubin, 1991) to address a chronic problem with the "two-stage" fitting of covariance structure models in the presence of ignorable missing data: the lack of an asymptotically chi-square distributed goodness-of-fit statistic. We show that the Supplemented EM algorithm provides a…

Used computer simulation methods to examine the sensitivity of model fit criteria to misspecification of the first-level error structure in two-level models of change and to examine the impact of misspecification estimates on the variance parameters, estimates of the fixed effects, and tests of the fixed effects. Discusses problems caused by…

Describes four approaches to factor analysis of ordinal variables that take proper account of ordinality and compared three of these approaches with respect to parameter estimates and fit using generated data and an empirical data set. Focuses on how to test the model and how to measure model fit. (SLD)

Dynamic factor models have been used to analyze continuous time series behavioral data. We extend 2 main dynamic factor model variations--the direct autoregressive factor score (DAFS) model and the white noise factor score (WNFS) model--to categorical DAFS and WNFS models in the framework of the underlying variable method and illustrate them with…

Examined the effects of sample size and other design features on correspondence between factors obtained from analysis of sample data and those present in the population from which the samples were drawn, examining these phenomena in the situation in which the common factor model does not hold exactly in the population. Tested a theoretical…

Latent variable models exist with continuous, categorical, or both types of latent variables. The role of latent variables is to account for systematic patterns in the observed responses. This article has two goals: (a) to establish whether, based on observed responses, it can be decided that an underlying latent variable is continuous or…

Manifest variables in covariance structure analysis are often combined to form parcels for use as indicators in a measurement model. The purpose of the present study was to evaluate four empirical algorithms for creating such parcels, focusing on the effects of dimensionality on accuracy of parameter estimation and model fit. Results suggest that…

We introduce a multidimensional item response theory (IRT) model for binary data based on a proximity response mechanism. Under the model, a respondent at the mode of the item response function (IRF) endorses the item with probability one. The mode of the IRF is the ideal point, or in the multidimensional case, an ideal hyperplane. The model…

This article describes a model for response times that is proposed as a supplement to the usual factor-analytic model for responses to graded or more continuous typical-response items. The use of the proposed model together with the factor model provides additional information about the respondent and can potentially increase the accuracy of the…

Cognitive Differentiation Analysis (CDA) represents a method to measure the correspondence of an individual vector or a composite vector of descriptor ratings to a matrix of pair-wise dissimilarity judgments where both sets of judgments are assumed to be ordinal. The zero intercept regression extension of CDA is described. (TJH)

It is shown that goodness-of-fit criteria developed for the evaluation of multivariate structural models can be applied to assist in evaluating the dimensionality of a test consisting of binary items, and correlative methods regularly used in factor analysis can be employed to diagnose causes of misfit. (Author)