No matter how strong the theoretical infrastructure of a study is, if the measurement instruments do not have the necessary psychometric qualities, there will be a question of trust in interpreting the findings, and it will be inevitable to make wrong decisions with the results. One of the important steps in scale development/adaptation studies is…

Rubin and Thayer ("Psychometrika," 47:69-76, 1982) proposed the EM algorithm for exploratory and confirmatory maximum likelihood factor analysis. In this paper, we prove the following fact: the EM algorithm always gives a proper solution with positive unique variances and factor correlations with absolute values that do not exceed one,…

This article presents a state-space modeling (SSM) technique for fitting process factor analysis models directly to raw data. The Kalman smoother via the expectation-maximization algorithm to obtain maximum likelihood parameter estimates is used. To examine the finite sample properties of the estimates in SSM when common factors are involved, a…

Numerous procedures have been suggested for determining the number of factors to retain in factor analysis. However, previous studies have focused on comparing methods using normal data sets. This study had two phases. The first phase explored the Kaiser method, Scree test, Bartlett's chi-square test, Minimum Average Partial (1976&2000),…

Normal theory maximum likelihood (ML) is by far the most popular estimation and testing method used in structural equation modeling (SEM), and it is the default in most SEM programs. Even though this approach assumes multivariate normality of the data, its use can be justified on the grounds that it is fairly robust to the violations of the…

The details of EM algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models. An example is presented to demonstrate potential problems in other approaches to maximum likelihood factor analysis. (Author/JKS)

Considers a class of estimation procedures for the factor model. The procedures are shown to yield estimates possessing the same asymptotic sampling properties as those from estimation by maximum likelihood or generalized last squares, both special members of the class. General expressions for the derivatives needed for Newton-Raphson…

The fundamental mathematical model of L. L. Thurstone's common factor analysis is reviewed, and basic covariance matrices of maximum likelihood factor analysis and alpha factor analysis are presented. The methods are compared in terms of computational and scaling contrasts. Weighting and the appropriate number of common factors are considered.…

In maximum likelihood factor analysis, there arises a situation whereby improper solutions occur. The causes of those improper solution are discussed and illustrated. (JKS)

In this article the authors develop a model that employs a factor analysis structure at Level 2 of a two-level hierarchical linear model (HLM). The model (HLM2F) imposes a structure on a deficient rank Level 2 covariance matrix [tau], and facilitates estimation of a relatively large [tau] matrix. Maximum likelihood estimators are derived via the…

Nonlinear common factor models with polynomial regression functions, including interaction terms, are fitted by simultaneously estimating the factor loadings and common factor scores, using maximum likelihood and least squares methods. A Monte Carlo study gives support to a conjecture about the form of the distribution of the likelihood ratio…

This study examined the effect of type of correlation matrix on the robustness of LISREL maximum likelihood and unweighted least squares structural parameter estimates for models with categorical variables. The analysis of mixed matrices produced estimates that closely approximated the model parameters except where dichotomous variables were…

A multitrait-multimethod matrix containing two methods of measuring 12 personality traits was analyzed and confirmatory factor analysis was applied to the data. Although unexplained variance remained, method factors and a general personality factor significantly improved the fit of a model containing only trait factors. (Author/RL)

In traditional factor analysis, the variance-covariance matrix or the correlation matrix has often been a form of inputting data. In contrast, in Bayesian factor analysis, the entire data set is typically required to compute the posterior estimates, such as Bayes factor loadings and Bayes unique variances. We propose a simple method for computing…

Despite advances in common factor analysis, a review of 89 studies published in four selected journals between 1963 and 1976 indicated that behavioral scientists preferred principal components analysis, followed by varimax or orthogonal rotation. Resultant row sums of squares of factor matrices from principal component analyses of real data sets…