In this article, we present a Bayesian spatial factor analysis model. We extend previous work on confirmatory factor analysis by including geographically distributed latent variables and accounting for heterogeneity and spatial autocorrelation. The simulation study shows excellent recovery of the model parameters and demonstrates the consequences…

The increasing use of ordinal variables in different fields has led to the introduction of new statistical methods for their analysis. The performance of these methods needs to be investigated under a number of experimental conditions. Procedures to simulate from ordinal variables are then required. In this article, we deal with simulation from…

A measure of "clusterability" serves as the basis of a new methodology designed to preserve cluster structure in a reduced dimensional space. Similar to principal component analysis, which finds the direction of maximal variance in multivariate space, principal cluster axes find the direction of maximum clusterability in multivariate space.…

Factor score estimation is a controversial topic in psychometrics, and the estimation of factor scores from exploratory factor models has historically received a great deal of attention. However, both confirmatory factor models and the existence of missing data have generally been ignored in this debate. This article presents a simulation study…

We illustrate the idiographic/nomothetic debate by comparing 3 approaches to using daily self-report data on affect for predicting relationship quality and breakup. The 3 approaches included (a) the first day in the series of daily data; (b) the mean and variability of the daily series; and (c) parameters from dynamic factor analysis, a…

Mixture factor analysis is examined as a means of flexibly estimating nonnormally distributed continuous latent factors in the presence of both continuous and dichotomous observed variables. A simulation study compares mixture factor analysis with normal maximum likelihood (ML) latent factor modeling. Different results emerge for continuous versus…

Exploratory factor analysis (EFA) is a commonly used statistical technique for examining the relationships between variables (e.g., items) and the factors (e.g., latent traits) they depict. There are several decisions that must be made when using EFA, with one of the more important being choice of the rotation criterion. This selection can be…

The standardization of loadings gives a metric to the corresponding latent variable and thus scales the variance of this latent variable. By assigning an appropriately estimated weight to all the loadings on the same latent variable it can be achieved that the average squared loading is 1 as the result of standardization. As a consequence, there…

In the structural equation modeling literature, the normal-distribution-based maximum likelihood (ML) method is most widely used, partly because the resulting estimator is claimed to be asymptotically unbiased and most efficient. However, this may not hold when data deviate from normal distribution. Outlying cases or nonnormally distributed data,…

This study used multilevel modeling of daily diary data to model within-person (state) and between-person (trait) components of coping variables. This application included the introduction of multilevel factor analysis (MFA) and a comparison of the predictive ability of these trait/state factors. Daily diary data were collected on a large (n =…

Bifactor and second-order factor models are two alternative approaches for representing general constructs comprised of several highly related domains. Bifactor and second-order models were compared using a quality of life data set (N = 403). The bifactor model identified three, rather than the hypothesized four, domain specific factors beyond the…

In matrix comparison, the performance of four vector matching indices (the coefficient of congruence, the Pearson product moment correlation, the "s"-statistic, and kappa) was evaluated. Advantages and disadvantages of each index are discussed, and the performance of each was assessed within the framework of principal components…

An alternative content method, allowing bipolar representation and based on separate scaling of quality and intensity, is presented. For comparative purposes the method was used together with a distance method and an ordinary content method, with nine words denoting emotions as stimuli. (Author)

Enriching factor rotation algorithms with the capacity to conduct repeated searches from random starting points can make the tendency to converge to optima that are merely local a way to catch rotations of the input factors that might otherwise elude discovery. Use of the HYBALL computer program is discussed. (SLD)

A relatively simple technique for assessing the convergence of sets of variables across method domains is presented. The technique, two-step principal components analysis, empirically orthogonalizes each method domain into sets of components, and then analyzes convergence among components across domains. (Author)