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Suppose that I have a regression model: $$ y=\beta+\beta_{1}T+\beta_{2}M+\epsilon $$ and $$ M=\alpha+\alpha_{1}T+v $$ In this model, $y$ is the outcome variable, $T$ is treatment, and $M$ is the mediating variable. In the terminilogy of mediation analysis, we have that the \textbf{causal mediation }effect is defined as $\alpha_{1}\beta_{2}$. Using OLS on these two models, we obtain an estimate of this effect as $\hat{\alpha}_{1}\hat{\beta}_{2}$. Although getting the point estimate is straightforward, how would we obtain the standard error of this effect, that is $SE\left(\hat{\alpha}_{1}\hat{\beta}_{2}\right)$?

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  • $\begingroup$ What data did you use? Of importance is whether you used the same responses in both procedures. $\endgroup$
    – whuber
    May 2 at 18:14
  • $\begingroup$ Same responses- just different models for $y$. $\endgroup$
    – ChinG
    May 2 at 18:30
  • $\begingroup$ Please edit your post to indicate that, because it has a huge influence on any correct solution. But it makes one wonder: you seem to be asking for the product of estimates of two contradictory models. How do you intend to interpret that?? $\endgroup$
    – whuber
    May 2 at 18:45
  • $\begingroup$ @whuber I Have modified the problem to more accurately suit what I have in mind. $\endgroup$
    – ChinG
    May 6 at 16:26

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