Advertisement

Analysis of Covariance Structures Applied to Family Research and Theory

  • Alan C. Acock
  • Walter R. Schumm

Abstract

Family research uses an increasing storehouse of multivariate methods. A major stream in these developments involves the analysis of covariance structures (ACS). ACS subsumes a variety of seemingly distinct procedures including exploratory factor analysis, confirmatory factor analysis, measurement models, path analysis, regression analysis, some panel designs, multiple population comparisons, and structural equation modeling. During the 1980s, family scholars learned that multiple regression is only a special case of ACS.1 The 1990s should see a rapid increase in the use of ACS across a variety of theoretical and methodological perspectives.

Keywords

Covariance Structure Marital Satisfaction Asymptotic Covariance Matrix Panel Design Family Behavior 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Acock, A. C. (1979). Applications of LISREL in family research. Presented at the preconference Theory and Methods Workshop of the National Council on Family Relations. Philadelphia.Google Scholar
  2. Acock, A. C. (1989). Measurement error in secondary data analysis. In K. Namboodiri & R. G. Corwin (Eds.), Sociology of education and socialization (Vol. 8, pp. 201–230). Greenwich, CT: JAI Press.Google Scholar
  3. Acock, A. C., & Bengtson, V. L. (1980). Socialization and attribution processes: Actual vs. perceived similarity among parents and youth. Journal of Marriage and the Family, 43, 501–518.CrossRefGoogle Scholar
  4. Acock, A. C., & Edwards, J. N. (1982). Egalitarian sex role attitudes and female income. Journal of Marriage and the Family, 44, 581–590.CrossRefGoogle Scholar
  5. Anderson, J. C., & Gerbing, D. W. (1984). The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis. Psychometrika, 49, 155–173.CrossRefGoogle Scholar
  6. Bagozzi, R. P. (1980). Causal models in marketing. New York: Wiley.Google Scholar
  7. Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107, 238–246.CrossRefGoogle Scholar
  8. Blalock, H. M. (1964). Causal inference in nonexperimental research. Chapel Hill: University of North Carolina Press.Google Scholar
  9. Blalock, H. M. (1982). Conceptualization and measurement in the social sciences. Beverly Hills, CA: Sage.Google Scholar
  10. Block, R. D., & Bargmann, R. E. (1966). Analysis of covariance structures. Psychometrika, 31, 507–534.CrossRefGoogle Scholar
  11. Boomsma, A. (1982). The robustness of LISREL against small sample sizes in factor analysis models. In Systems under indirect observation: Causality, structure, prediction (Part I, pp. 275–319). Amsterdam: North-Holland.Google Scholar
  12. Boomsma, A. (1985). Nonconvergence, improper solutions, and starting values in lisrel maximum likelihood estimation. Psychometrika, 50, 229–242.CrossRefGoogle Scholar
  13. Breckler, S. J. (1990). Applications of covariance structure modeling in psychology: Cause for concern? Psychological Bulletin, 107, 260–273.CrossRefGoogle Scholar
  14. Child, D. (1970). The essentials of factor analysis. London: Holt, Rinehart, & Winston.Google Scholar
  15. Costner, H. L. (1969). Theory, deduction, and rules of correspondence. American Journal of Sociology, 75, 245–63.CrossRefGoogle Scholar
  16. Dillon, W. R., Kumar, A., & Mulani, N. (1987). Offending estimates in covariance structure analysis: Comments on the causes of and solutions to Heywood cases. Psychological Bulletin, 10, 126–135.CrossRefGoogle Scholar
  17. Feigl, H. (1970). The “Orthodox” view of theories: Remarks in defense as well as critique. In M. Radnor & S. Winokur (Eds.), Minnesota Studies in the Philosophy of Science (Vol. 4, pp. 3–16). Minneapolis: University of Minnesota Press.Google Scholar
  18. Gerbing, David W., & Anderson, J. C. (1987). Improper solutions in the analysis of covariance structures: Their interpretability and a comparison of alternative respecifications. Psychometrika, 52, 99–111.CrossRefGoogle Scholar
  19. Glenn, N. D. (1989, September). Unwarranted causal conclusions in the social sciences. ICPSR Bulletin, 1–2.Google Scholar
  20. Hayduk, L. A. (1987). Structural equation modeling with LISREL: Essentials and advances. Baltimore: John Hopkins University Press.Google Scholar
  21. Jöreskog, K G. (1973). A general method for estimating a linear structural equation system. In A. S. Goldberger & O. D. Duncan (Eds.), Structural equation models in the social sciences (85–112).Google Scholar
  22. Jöreskog, K. G., & Sörbom, D. (1988a). LISREL (2nd ed.). Mooresville, IN: Scientific Software.Google Scholar
  23. Jöreskog, K. G., & Sörbom, D. (1988b). PREUS: A program for multivariate data screening and data summarization (2nd ed.). Mooresville, IN: Scientific Software.Google Scholar
  24. Kaplan, A. (1964). The conduct of inquiry. San Francisco: Chandler.Google Scholar
  25. Long, J. S. (1983). Covariance structure models: An introduction to LISREL. Beverly Hills, CA: Sage.Google Scholar
  26. Mangen, D. J., Bengtson, V. L., & Landry, Jr., P. H. (1988). Measurement of intergenerational relations. Newbury Park, CA: Sage.Google Scholar
  27. Marsh, H. W., Balla, J. R., & McDonald, R. P. (1988). Goodness-of-fit indexes in confirmatory factor analysis: The effect of sample size. Psychological Bulletin, 103, 391–410.CrossRefGoogle Scholar
  28. McDonald, R. P., & Marsh, H. W. (1990). Choosing a multivariate model: Noncentrality and goodness of fit. Psychological Bulletin, 107, 247–255.CrossRefGoogle Scholar
  29. Pearson, K. (1901). On lines and planes of closest fit to systems of points in space. Philosophical Magazine.Google Scholar
  30. Simon, H. A. (1957). Models of man. New York: Wiley.Google Scholar
  31. Steiger, J. H. (1989). EzPath: Causal modeling, a supplementary module for SYSTAT and SYGRAPH. Evanston, IL: SYSTAT.Google Scholar
  32. Tukey, J. W. (1954). Causation, regression, and path analysis. In O. Kempthorne (Ed), Statistics and mathematics in biology (35–66).Google Scholar
  33. Wheaton, B., Buthen, B., Alwin, D., & Summers, G. (1977). Assessing reliability and stability in panel models. In D. R. Heise (Ed.), Sociological Methodology 1977 (84–136).Google Scholar
  34. Wright, S. (1921). Correlation and causation. Journal of Agricultural Research, 20, 557–58.Google Scholar
  35. Wright, S. (1960). The treatment of reciprocal interaction, with or without lag, in path analysis. Biometrics, 16, 423–45.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Alan C. Acock
    • 1
  • Walter R. Schumm
    • 2
  1. 1.Department of Human Development and Family SciencesOregon State UniversityCorvallis
  2. 2.Department of Human Development and Family StudiesKansas State UniversityManhattan

Personalised recommendations