# Effect analysis and causation in linear structural equation models

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## Abstract

This paper considers total and direct effects in linear structural equation models. Adopting a causal perspective that is implicit in much of the literature on the subject, the paper concludes that in many instances the effects do not admit the interpretations imparted in the literature. Drawing a distinction between concomitants and factors, the paper concludes that a concomitant has neither total nor direct effects on other variables. When a variable is a factor and one or more intervening variables are concomitants, the notion of a direct effect is not causally meaningful. Even when the notion of a direct effect is meaningful, the usual estimate of this quantity may be inappropriate. The total effect is usually interpreted as an equilibrium multiplier. In the case where there are simultaneity relations among the dependent variables in tghe model, the results in the literature for the total effects of dependent variables on other dependent variables are not equilibrium multipliers, and thus, the usual interpretation is incorrect. To remedy some of these deficiencies, a new effect, the total effect of a factor*X* on an outcome*Y*, holding a set of variables*F* constant, is defined. When defined, the total and direct effects are a special case of this new effect, and the total effect of a dependent variable on a dependent variable is an equilibrium multiplier.

### Key words

Causal analysis covariance structure analysis direct effect indirect effect structural equation models total effect## Preview

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### References

- Alwin, D. F., & Hauser, R. M. (1975). The decomposition of effects in path analysis.
*American Sociological Review, 40*, 37–47.Google Scholar - Bentler, P. M., & Freeman, E. H. (1983). Tests for stability in linear structural equation systems.
*Psychometrika, 48*, 143–145.Google Scholar - Bollen, K. A., (1987). Total, direct and indirect effects in structural equation models. In C. C. Clogg (Ed.),
*Sociological methodology, 1987*(pp. 37–69). Washinton, D. C.: American Sociological Association.Google Scholar - Brand, M. (1976). Introduction: Defining causes. In M. Brand (Ed.),
*The nature of causation*(pp. 1–44). Urbana, IL: University of Illinois Press.Google Scholar - Chow, G. C. (1975).
*Analysis and control of dynamic economic systems*. New York: Wiley.Google Scholar - Cook, T. D., & Campbell, D. T. (1979).
*Quasi-experimentation: Design and analysis issues for field settings*. Boston: Houghton Mifflin.Google Scholar - Cox, D. R., & Snell, E. J. (1981).
*Applied statistics*. London: Chapman and Hall.Google Scholar - Duncan, O. D. (1975).
*Introduction to structural equation models*. New York: Academic.Google Scholar - Fisher, F. M. (1970). A correspondence principle for simulataneous equation models.
*Econometrica, 38*, 73–92.Google Scholar - Fox, J. (1985). Effect analysis in structural equation models. II: Calculation of specific infirect effects.
*Sociological Methods and Research, 14*, 81–95.Google Scholar - Freedman, D. A. (1987). As others see us: A case study in path analysis.
*Journal of Educational Statistics, 12*, 101–129.Google Scholar - Freeman, E. H. (1982).
*The implementation of effect decomposition methods for two general structural covariance modeling systems*. Unpublished doctoral dissertation, Los Angeles: University of California, Los Angels, Department of Psychology.Google Scholar - Glymour, C. (1986). Statistics and metaphysics.
*Journal of the American Statitiscal Association, 81*, 964–966.Google Scholar - Goldberger, A. S. (1959).
*Impact multipliers and dynamic properties of the Klein-Goldberger model*. Amsterdam: North Holland.Google Scholar - Graff, J., & Schmidt, P. (1982). A general model for decomposition of effects. In K. G. Jöreskog & D. Sörbom (Eds.),
*Systems under indirect observation, Part 1*(pp. 131–148). Amsterdam: North Holland.Google Scholar - Graybill, F. A. (1983).
*Matrices with applications in statistics*. Belmont, CA: Wadsworth.Google Scholar - Harary, F. R., Norman, Z., & Cartwright, D. (1965).
*Structural models: An introduction to the theory of directed graphs*. New York: Wiley.Google Scholar - Holland, P. W. (1986). Statistics and causal inference.
*Journal of the American Statistical Association, 81*, 945–960.Google Scholar - Holland, P. W. (1988). Causal inference, path analysis, and recursive structural equations models. In C. C. Clogg (Ed.),
*Sociological Methodology, 1988*. (pp. 449–484). Washington, D. C.: American Sociological Association.Google Scholar - Hume, D. (1977).
*An enquiry concerning human understanding and A letter from a gentleman to his friend in Edinburgh*. Indianapolis: Hackett.Google Scholar - Hume, D. (1978).
*A treatise of human nature*. Cambridge: Oxford University Press.Google Scholar - Jöreskog, K. G., & Sörbom, D. (1989).
*LISREL 7: User's reference guide*. Mooresville, IN: Scientific Software.Google Scholar - Kerckhoff, A. C. (1974).
*Ambition and attainment*. Washigton, D. C.: Sociological Association.Google Scholar - Luenberger, D. C. (1979).
*Introduction to dynamic systems*. New York: Wiley.Google Scholar - Pratt, J. W., & Schlaifer, R. (1984). On the nature and discovery of structure.
*Journal of the American Statistical Association, 79*, 9–21.Google Scholar - Rozeboom, W. R. (1956). Mediation variables in scientific theory.
*Psychological Review, 63*, 249–264.Google Scholar - Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies.
*Journal of Educational Psychology, 66*, 688–701.Google Scholar - Rubin, D. B. (1978). Bayesian inference for causal effects: the role of randomization.
*The Annals of Statistics, 6*, 34–58.Google Scholar - Rubin, D. B. (1986). Comment: Which ifs have causal answers.
*Journal of the American Statistical Association, 81*, 961–962.Google Scholar - Salmon, W. C. (1984).
*Scientific explanation and the causal structure of the world*. Princeton, NJ: Princeton University Press.Google Scholar - Sobel, M. E. (1982). Asymptotic confidence intervals for indirect effects in structural equation models. In S. Leinhardt (Ed.),
*Sociological Methodology, 1982*(pp. 290–312). San Francisco: Jossey-Bass.Google Scholar - Sobel, M. E. (1986). Some new results on indirect effects and their standard errors in covariance structure analysis. In N. B. Tuma (Ed.),
*Sociological Methodology, 1986*(pp. 159–186). Washinton, D. C.: American Sociological Association.Google Scholar - Sobel, M. E. (1987). Direct and indirect effects in linear structural equation models.
*Sociological Methods and Research, 16*, 155–176.Google Scholar - Sobel, M. E., & Arminger, G. (1986). Platonic and operational true scores in covariance structure analysis: An invited comment on Bielby's ‘Arbitrary metrics in multiple indicator models of latent variables’.
*Sociological Methods and Research, 15*, 44–58.Google Scholar - Strotz, R. H., & Wold, H. O. A. (1960). Recursive vs. nonrecursive systems: An attempt at synthesis.
*Econometrica, 28*, 417–427.Google Scholar - Tinbergen, J. (1937).
*An econometric approach to business cycle problems*. Paris: Hermann.Google Scholar - Wheaton, B., Muthén, B., Alwin, D., & Summers, G. (1977). Assessing reliability and stability in panel models. In D. R. Heise (Ed.),
*Sociological Methodology, 1977*(pp. 84–136). San Francisco: Jossey-Bass.Google Scholar - Winer, B. J. (1971).
*Statistical Principles in experimental design*. New York: McGraw-Hill.Google Scholar