Estimating and Interpreting Correlations between Disturbances and Residual Path Coefficients in Nonrecursive (and Recursive) Causal Models

In: American journal of political science: AJPS, Band 22, Heft 2, S. 444-474

Abstract

Explored are the estimation & meaning, in both recursive & (especially) nonrecursive causal models, of two kinds of parameters that describe the disturbances: correlations between the disturbances of different structural equations & residual path coefficients. Presented is a straightforward & statistically consistent method of calculating estimates of both types of parameters -- a method applicable to any identified model in which these parameters appear, whether nonrecursive or recursive. The interpretation of both kinds of parameters is discussed. In the case of correlations between disturbances, the caveat is that a high value can occur even when the factors responsible for the correlation are not truly worthy of note & a low value can occur even when they are. For this reason, estimated correlations between disturbances should always be juxtaposed with estimates of the strength of the disturbances involved. For residual path coefficients, the caveat is that in nonrecursive structures, unlike in recursive structures, their estimators do not represent the proportion of variance in a dependent variable that the model leaves unexplained. Appendixes. Modified HA.