This paper is concerned with the study of similarities and differences in factor structures between different groups. A common situation occurs when a battery of tests has been administered to samples of examinees from several populations.

https://files.eric.ed.gov/fulltext/ED055110.pdf

Simultaneous factor analysis in several populations

Intraclass correlation reliablity estimates are based on the assumption that the various measures are equivalent. Joreskog's (1970) general model for the analysis of covariance structures can be used to test the validity of this assumption.

Intraclass Reliability Estimates: Testing Structural Assumptions

Various models for sets of congeneric tests are considered, including models appropriate for the analysis of multitrait-multimethod data. All models are illustrated with real data. The special cases when two or more tests within a set are tau-equivalent or parallel are also considered. All data analyses are done within the framework of a general model by Joreskog [1970].

Statistical analysis of sets of congeneric tests

We consider a model in which one observes multiple indicators and multiple causes of a single latent variable. In terms of the multivariate regression of the indicators on the causes, the model implies restrictions of two types: (i) the regression coefficient matrix has rank one, (ii) the residual variance-covariance matrix satisfies a factor analysis model with one common factor. The first type of restriction is familiar to econometricians and the second to psychometricians. We derive the maximum-likelihood estimators and their asymptotic variance-covariance matrix. Two alternative “limited information” estimators are also considered and compared with the maximum-likelihood estimators in terms of efficiency.

Estimation of a Model with Multiple Indicators and Multiple Causes of a Single Latent Variable

A general method for estimating the unknown coefficients in a set of linear structural equations is described. In its most general form the method allows for both errors in equations (residuals, disturbances) and errors in variables (errors of measurement, observational errors) and yields estimates of the residual variance-covariance matrix and the measurement error variances as well as estimates of the unknown coefficients in the structural equations, provided all these parameters are identified. Two special cases of this general method are discussed separately. One is when there are errors in equations but no errors in variables. The other is when there are errors in variables but no errors in equations. The methods are applied and illustrated using artificial, economic and psychological data.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/j.2333-8504.1970.tb00783.x

A general method for estimating a linear structural equation system

Acovs a general computer program for analysis of covariance structures

MF-$0.65 HC-$3.29 *Computer Programs; Factor Analysis; *Factor Structure; Hypothesis Testing; *Mathematical Models; *Research Methodology; *Sampling; Statistical Analysis A computer program for simultaneously factor analyzing dispersion matrices obtained from independent groups is described. This program is useful when a battery of tests has been administered to samples of examinees from several populations and one wants to study similarities and differences in factor structure between the different populations. (CK)

/pdf/sifasp-a-general-computer-program-for-simultaneous-factor-1imo9sn283.pdf

Sifasp a general computer program for simultaneous factor analysis in several populations

/pdf/new-rapid-algorithms-for-factor-analysis-by-unweighted-least-35c0pu2jke.pdf

New Rapid Algorithms for Factor Analysis by Unweighted Least Squares, Generalized Least Squares and Maximum Likelihood.

Joreskog, Karl G.; And Others ACOVSM: A General Computer Program for Analysis of Covariance Structures Including Generalized MANOVA. Educational Testing Service, Princeton, N.J. RB-71-1 Jan 71 69p. EDRS Price ME-$0.65 HC-$3.29 *Analysis of Covariance, *Analysis of Variance, *Computer Programs, Mathematics, *Models, Multiple Regression Analysis, Statistical Analysis, *Statistics Joreskog's general method for analysis of covariance structures was developed for estimating a model involving structures of a very general form on means, variances, and covariances of multivariate observations. This method achieves a great deal of generality and flexibility, in that it is capable of handling most standard statistical models as well as many nonstandard and complicated ones. This paper describes a computer program for the method. When the variance-covariance matrix of the observed variables is unconstrained, the method may be used to estimate location parameters and to test linear hypotheses about them. For example, the program may be used to handle such standard problems as multivariate regression, ANOVA, and MANOVA. A unique feature of the method is that it can also be used when the variance-covariance matrix is constrained tc be of a certain form. Various other models involving correlated errors or errors of measurement can also be handled. An illustration of how input data is set up, and what the printout looks like for two small sets of data, are included. (Author/CK)

/pdf/acovsm-a-general-computer-program-for-analysis-of-covariance-2h8haw23z2.pdf

Marielle van Thillo

Papers

Acovs a general computer program for analysis of covariance structures

Sifasp a general computer program for simultaneous factor analysis in several populations

New Rapid Algorithms for Factor Analysis by Unweighted Least Squares, Generalized Least Squares and Maximum Likelihood.

Acovsm: a general computer program for analysis of covariance structures including generalized manova1