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…

Factor analysis is a statistical method for describing the associations among sets of observed variables in terms of a small number of underlying continuous latent variables. Various authors have proposed multilevel extensions of the factor model for the analysis of data sets with a hierarchical structure. These Multilevel Factor Models (MFMs)…

In this article, we present a Bayes factor solution for inference in multiple regression. Bayes factors are principled measures of the relative evidence from data for various models or positions, including models that embed null hypotheses. In this regard, they may be used to state positive evidence for a lack of an effect, which is not possible…

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…

Bifactor latent structures were introduced over 70 years ago, but only recently has bifactor modeling been rediscovered as an effective approach to modeling "construct-relevant" multidimensionality in a set of ordered categorical item responses. I begin by describing the Schmid-Leiman bifactor procedure (Schmid & Leiman, 1957) and highlight its…

Exploratory factor analysis (EFA) is often conducted with ordinal data (e.g., items with 5-point responses) in the social and behavioral sciences. These ordinal variables are often treated as if they were continuous in practice. An alternative strategy is to assume that a normally distributed continuous variable underlies each ordinal variable.…

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…

The presence of suppression (and multicollinearity) in multiple regression analysis complicates interpretation of predictor-criterion relationships. The mathematical conditions that produce suppression in regression analysis have received considerable attention in the methodological literature but until now nothing in the way of an analytic…

It seems that just when we are about to lay P-technique factor analysis finally to rest as obsolete because of newer, more sophisticated multivariate time-series models using latent variables--dynamic factor models--it rears its head to inform us that an obituary may be premature. We present the results of some simulations demonstrating that even…

Similarities between latent class models with K classes and linear factor models with K-1 factors are investigated. Specifically, the mathematical equivalence between the covariance structure of the two models is discussed, and a Monte Carlo simulation is performed using generated data that represents both latent factors and latent classes with…

This paper describes the Confirmatory Factor Analysis (CFA) parameterization of the Profile Analysis via Multidimensional Scaling (PAMS) model to demonstrate validation of profile pattern hypotheses derived from multidimensional scaling (MDS). Profile Analysis via Multidimensional Scaling (PAMS) is an exploratory method for identifying major…

A sufficient condition in terms of the unique variances of a common factor model is given for the results of factor analysis to come closer to those of principal components analysis. In general, vectors corresponding to loading matrices can be related to each other by a specific measure of closeness, which is illustrated. (SLD)

This article examines the methodological foundations of exploratory factor analysis (EFA) and suggests that it is properly construed as a method for generating explanatory theories. In the first half of the article it is argued that EFA should be understood as an abductive method of theory generation that exploits an important precept of…

As psychologists increasingly employ more elaborate and comprehensive data collection schemes, sophisticated analytic techniques will play an ever more important role in understanding behavioral data. This paper outlines one such promising technique, Tucker's three-mode factor analysis, which enables the researcher to explore new taxonomic…

This article describes and proposes an unrestricted factor analytic procedure to: (a) assess the dimensionality and structure of a balanced personality scale taking into account the potential effects of acquiescent responding, and (b) correct the individual trait estimates for acquiescence. The procedure can be considered as an extension of ten…