By David A. Kenny
A normal creation to the subject of structural research that presumes no prior acquaintance with causal research. Assumes reader has a few familiarity with a number of regression and issue research.
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Additional resources for Correlation and Causality
There are three correlations and three free parameters, a, b, and c. The correlations are U12 = ab U13 = ac U23 = bc The parameters are then U12U13 a2 = U23 U12U23 b2 = U13 U U U12 13 23 c2 = This is a single-factor model where a, b, and c are factor loadings (cf. Duncan, 1972; Harmon, 1967). This model is more extensively discussed in Chapter 7. Chap ter 3 PRINCIPLES OF MODELING 53 STATISTICAL ESTIMATION, INFERENCE AND TESTING The discussion has been mainly restricted to the population by assuming that the population values of correlation coefficients are known.
Goldberger (1970) has shown that the statistically best solution is to use the least-squares solution and ignore any other solution. The least-squares solution is more efficient than a pooled solution. Thus, if the theory is correct, one should estimate the path coefficients by regression analysis yielding r12 as an estimate of a and r23 as an estimate of b. I would not argue for exactly this solution. It is possible that there is a specification error of a path from X1 to X3. If there is such a path, the estimate of the path from X2 to X3 will be distorted through this specification error.
In fact, it adds increased validity to the model by making an explicit prediction of a zero path. 2, if the model contains specification error by omitting either X1 or X3, the causal coefficients become misleading. 3. This bias is due to X1 being correlated with the disturbance since X3, which causes X4, is contained in the disturbance and is correlated with X1. 6. 2 Thus there is no bias in estimating the effect of a causal variable if either the omitted variable does not cause the endogenous variable or the regression of the omitted variable on the causal variable controlling for the remaining causal variables is zero.