Simultaneous Factor Analysis in Several Populations

DOCUMENT RVSUME TM 000 837 Joreskog, Karl G. Simultaneous Factor Analysis in Several Populations. Educational Testing Service, Princeton, N.J. Nov 70 33p, MF-50.65 HC-$3.29 *Factor Analysis; *Factor Structure; Goodness of Fit; Hypothesis Testing; Mathematical Applications; *mathematical Models; *Research Methodology; *sampling; Statistical Analysis Thi,c; paper is concerned with the study of similarities and differences in factor structures between different groups. A common sitUation is when a battery of tests has been administered to samples of examinees from several populations. A very general model is presented, in which any parameter in the factor analysis models (factor loadings, factor variances, factor covariances, and unique variances) for the different groups may be assigned an arbitralry value or constrained to be equal to some other parameter. Given suCh a specification, the model is estimated by the maximum likelihood Method yielding a large sample chi-square of goodness of fit. By computing several solutions under different specifications one can test various hypotheses. The method is capable of dealing with any degree of invariance, from the one extreme, where nothing is invariant, to the other extreme, where everything is invariant. Neither the number of tests nor the number of common factors need to be the same for all groups, but to be at all interesting, it is assumed that there is a common core of tests in each battery that iS the same or at least content-wise comparable. (Author) U.S. DEPARTMENT OF HEALTH, ED U CATI ON & WELFARE OFFICE OF EDUCATION [HIS DOCUMENT HAS SEEN REPRODUCED EXACTLY AS RECEIVED FM THE PERSON OR ORGANIZATIC. ORIGINATING IT. POINTS OF VIEW OR OPINIONS STATED DO NOT NECESSARILY REPRESENT OFFICIAL OFFICE OF EDUCATION POSITION OR POLICY. RB -70-61 SIMULTANEOUS FACTOR ANALYSIS IN SEVERAL POPULATIONS