Finite Feedback Cycling in Structural Equation Models

Abstract

In models containing reciprocal effects, or longer causal loops, the usual effect estimates assume that any effect touching a loop initiates an infinite cycling of effects around that loop. The real world, in contrast, might permit only finite feedback cycles. I use a simple hypothetical model to demonstrate that if the world permits only a few effect cycles, many coefficient estimates are substantially biased. If the world permits additional partial-cycle use in addition to full cyclings around the causal loop, some of the effect estimates are proper, and a full set of proper effect estimates can be recovered by hand calculations involving the model total effects. If the world permits no additional partial-cycle use, it might not be possible to recover proper estimates from the usual output. It is not the equations representing the causal model, but rather the calculations of the covariance implications of the model, that change with limited cycling possibilities. Unfortunately, the features required to permit direct estimation of limited-cycle effects are not under user control in common structural equation programs, so estimation and detailed investigation of models with finite cycling of effects around feedback loops awaits new programming. To obtain unbiased estimates with limited causal cyclings, the researcher must continue to strive to specify the proper effect locations but must also attend to the number of full and partial causal cyclings permitted by the world. Determining the appropriate number of cycles is not a matter to be delegated to a statistician; it is something the researcher must attend to as a matter of substantive theory, methodology, and model interpretation.