Michael E. Sobel
Michael E. Sobel. 1990. Effect analysis and causation in linear structural equation models Psychometrika 55(3): 495-515, DOI: 10.1007/BF02294763
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 the 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 factorX on an outcomeY, holding a set of variablesF 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
For helpful comments, I am grateful to G. Arminger, K. Bollen, W. Faris, R. M. Hauser, T. Petersen, three anonymous Psychometrikas reviewers, and the Editor. For computational assistance, I am grateful to B. D. Kim.