. 2018 Mar 18;15(3):247–256. doi: 10.1177/1740774518760300

Table 1.

Bias predictions for three different estimators of causal mediation effects.^a

Process involving baseline measures	Parameter restrictionsin data generating model (Figure 1)	(A) Postapproach	(B) Changescore approach	(C) ANCOVAapproach
Model 1: Only $M_{0}$ observed common cause	$c_{1} \neq 0; c_{2} \neq 0$ $l_{2} = 0; d_{2} = 0$	Biased	Biased	Asymptotically unbiased
Model 2: Only $Y_{0}$ observed common cause	$d_{1} \neq 0; d_{2} \neq 0$ $l_{2} = 0; c_{1} = 0$	Biased	Biased	Asymptotically unbiased
Model 3: Only $M_{0}$ observed common cause and not predictive of $M_{1} - M_{0}$	$c_{1} = 0; c_{2} \neq 0$ $l_{2} = 0; d_{2} = 0$	Biased	Asymptotically unbiased	Asymptotically unbiased
Model 4: Only $Y_{0}$ observed common cause and not predictive of $M_{1} - M_{0}$	$d_{1} \neq 0; d_{2} = 0$ $l_{2} = 0; c_{1} = 0$	Biased	Asymptotically unbiased	Asymptotically unbiased
Model 5: Only V common cause of baseline levels, assuming $M_{0}$ not predictive of $M_{1} - M_{0}$ and $Y_{0}$ not predictive of $Y_{2} - Y_{0}$	$l_{1} \neq 0; l_{2} \neq 0$ $c_{1} = 0; d_{1} = 0$	Biased	Biased	Asymptotically unbiased
Model 6: Only V common cause of baseline levels, assuming $M_{0}$ not predictive of $M_{1} - M_{0}$ and $Y_{0}$ not predictive of $M_{1} - M_{0}$	$l_{1} \neq 0; l_{2} \neq 0$ $c_{1} = 0; d_{2} = 0$	Biased	Asymptotically unbiased	Asymptotically unbiased

ANCOVA: analysis of covariance

The target effect can be estimated without bias by either approach. Biases refer to estimators of the natural direct and indirect effects.