Misidentification 1: Bivariate Regression of Y on X

This post was updated on 1/15/2021.

A problem was identified in the specification of the seed for the structural model (i.e., Lavaan seed command) in the initial loop. It appears that the sample command does not explore the full distribution of potential values. As such, the seed in the updated code now equals runif(1,0,1000000000). I apologize for the error in the initial code.

For the first misidentification, we regressed Y₁ on X₁ (no control variables included) using the base LM command in R (illustrated in the Figure 1). 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 a bivariate structural association where Y₁ was only regressed on X₁ produced an average slope coefficient of b = 27.768. This suggests that a 1 point increase in X₁ directly causes a 27.768 increase in Y₁, on average. This is a large departure from the true direct casual effect of X₁ on Y₁ (1.00). As such, the misidentification of the structural network in the manner identified above upwardly biased the direct causal effects of X₁ on Y₁.