For the second misidentification, we regressed Y1 on all of the variables in the system using the base LM command in R (illustrated in the Figure below). This was replicated 10,000 times – using R-loops – while randomly varying the effects for each causal pathway between the constructs in the network excluding the direct effect of X1 on Y1 (true direct causal effect = 1.00; N = 10,000; R-Code).
As illustrated in the figure below, the misidentification of the structural association where Y1 was regressed on X1, as well as all of the variables in the system, produced an average slope coefficient of b = -.757. This suggests that a 1 point increase in X1 directly causes a -.757 decrease in Y1, on average. Moreover, none of the 10,000 replications produced an estimate suggesting that a 1 point increase X1 resulted in an increased score on Y1. This observed direct effects were all in the opposite direction of the true direct casual effect of X1 on Y1, where a 1 point increase in X1 directly causes a 1 point increase Y1. As such, the misidentification of the structural network in the manner identified above flipped the sign of the direct causal effects of X1 on Y1.
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