, Volume 49, Issue 2, pp 155–173 | Cite as

The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis

  • James C. Anderson
  • David W. Gerbing


A Monte Carlo study assessed the effect of sampling error and model characteristics on the occurrence of nonconvergent solutions, improper solutions and the distribution of goodness-of-fit indices in maximum likelihood confirmatory factor analysis. Nonconvergent and improper solutions occurred more frequently for smaller sample sizes and for models with fewer indicators of each factor. Effects of practical significance due to sample size, the number of indicators per factor and the number of factors were found for GFI, AGFI, and RMR, whereas no practical effects were found for the probability values associated with the chi-square likelihood ratio test.

Key words

Confirmatory factory analysis LISREL Monte Carlo Maximum likelihood 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bearden, W. O., Sharma, S., & Tell, J. E. (1982). Sample size effects on chi-square and other statistics used in evaluating causal models.Journal of Marketing Research, 19, 425–430.Google Scholar
  2. Bentler, P. M. (1983). Some contributions to efficient statistics in structural models: Specification and estimation of moment structures.Psychometrika, 48, 493–517.Google Scholar
  3. Bentler, P. M., & Bonett, D. G. (1980). Significance tests and goodness-of-fit in the analysis of covariance structures.Psychological Bulletin, 88, 588–606.Google Scholar
  4. Boomsma, A. (1982). The robustness of LISREL against small sample sizes in factor analysis models. In K. G. Joreskog and H. Wold (Eds.),Systems under indirect observation: Causality, structure, prediction (Part 1). Amsterdam: North-Holland.Google Scholar
  5. Burt, R. S. (1973). Confirmatory factor-analytic structures and the theory construction process.Sociological Methods and Research, 2, 131–187.Google Scholar
  6. Finn, J. D. (1973).A general model for multivariate analysis. NY: Holt, Rinehart and Winston, Inc.Google Scholar
  7. Games P. A., Keselman, H. J., & Clinch, J. J. (1979). Tests for homogeneity of variance in factorial designs.Psychological Bulletin, 86, 978–984.Google Scholar
  8. Goodman, L. A. (1971). The analysis of multidimensional contingency tables: Stepwise procedures and direct estimation methods for building models for multiple classifications.Technometrics, 13, 33–61.Google Scholar
  9. Gweke, J. F., & Singleton, K. J. (1980). Interpreting the likelihood ratio statistic in factor models when sample size is small.Journal of the American Statistical Association, 75, 133–137.Google Scholar
  10. Hays, W. L. (1973).Statistics for the social sciences (2nd ed.). NY: Holt, Rinehart and Winston, Inc.Google Scholar
  11. Heise, D. R. (1975).Causal analysis. NY: John Wiley & Sons.Google Scholar
  12. IMSL. (1980).International Mathematical and Statistical Libraries. Houston: IMSL, Inc.Google Scholar
  13. Jackson, D. N., & Chan, D. W. (1980). Maximum-likelihood estimation in common factor analysis: A cautionary note.Psychological Bulletin, 88, 502–508.Google Scholar
  14. Joreskog, K. G. (1966). Testing a simple structure hypothesis in factor analysis.Psychometrika, 31, 165–178.Google Scholar
  15. Joreskog, K. G. (1967). Some contributions to maximum likelihood factor analysis.Psychometrika, 32, 443–482.Google Scholar
  16. Joreskog, K. G. (1969). A general approach to confirmatory maximum likelihood factor analysis.Psychometrika, 34, 183–202.Google Scholar
  17. Joreskog, K. G. (1970). A general method for analysis of covariance structures.Biometrika, 57, 239–251.Google Scholar
  18. Joreskog, K. G. (1971). Statistical analysis of sets of congeneric tests.Psychometrika, 36, 109–133.Google Scholar
  19. Joreskog, K. G. (1978). Structural analysis of covariance and correlation matricPsychometrika, 43, 443–477.Google Scholar
  20. Joreskog, K. G., & Sorbom, D. (1978).LISREL: Analysis of linear structural relationships by the method of maximum likelihood (Version IV). Chicago: National Educational Resources, Inc.Google Scholar
  21. Joreskog, K. G., & Sorbom, D. (1981).LISREL: Analysis of linear structural relationships by the method of maximum likelihood (Version V). Chicago: National Educational Resources, Inc.Google Scholar
  22. Lawley, D. N., & Maxwell, A. E. (1971).Factor analysis as a statistical method. NY: American Elsevier Publishing Company, Inc.Google Scholar
  23. Learmouth, G. P. and Lewis, P. A. W. (November 1973).Statistical tests of some widely used and recently proposed uniform random number generators. (Report No. NPS55LW73111A). Monterey, CA: Naval Postgraduate School.Google Scholar
  24. Siegel, S. (1956).Nonparametric statistics for the behavioral sciences. NY: McGraw-Hill Book Company.Google Scholar
  25. Tucker, L. R., & Lewis, C. (1973). A reliability coefficient for maximum likelihood factor analysis.Psychometrika, 38, 1–10.Google Scholar
  26. van Driel, O. P. (1978). On various causes of improper solutions of maximum likelihood factor analysis.Psychometrika, 43, 225–243.Google Scholar

Copyright information

© The Psychometric Society 1984

Authors and Affiliations

  • James C. Anderson
    • 1
  • David W. Gerbing
    • 2
  1. 1.Department of Marketing AdministrationThe University of Texas at AustinUSA
  2. 2.Baylor UniversityUSA

Personalised recommendations