This paper presents a method for studying the similarities and differences in factor structures across different populations. It addresses the common scenario where a set of tests is administered to samples from various populations. The method is based on a general model where parameters in the factor analysis models (factor loadings, variances, covariances, and unique variances) can be assigned arbitrary values or constrained to be equal. The model is estimated using maximum likelihood, yielding a chi-square goodness-of-fit statistic. By computing solutions under different specifications, various hypotheses can be tested. The method can handle any degree of invariance, from no invariance to complete invariance. The number of tests and common factors need not be the same across groups, but there should be a common core of tests. The paper also discusses the identification of parameters, estimation procedures, and the choice of start values for the minimization algorithm. A numerical illustration using data from Meredith's study is provided to demonstrate the application of the method. The results suggest two possible models for the data, one with a complex factor structure and another with a simpler structure but different variance-covariance matrices across populations.This paper presents a method for studying the similarities and differences in factor structures across different populations. It addresses the common scenario where a set of tests is administered to samples from various populations. The method is based on a general model where parameters in the factor analysis models (factor loadings, variances, covariances, and unique variances) can be assigned arbitrary values or constrained to be equal. The model is estimated using maximum likelihood, yielding a chi-square goodness-of-fit statistic. By computing solutions under different specifications, various hypotheses can be tested. The method can handle any degree of invariance, from no invariance to complete invariance. The number of tests and common factors need not be the same across groups, but there should be a common core of tests. The paper also discusses the identification of parameters, estimation procedures, and the choice of start values for the minimization algorithm. A numerical illustration using data from Meredith's study is provided to demonstrate the application of the method. The results suggest two possible models for the data, one with a complex factor structure and another with a simpler structure but different variance-covariance matrices across populations.