Mediation coefficients

[swank10009]

Hello,
I have a question about the output from pingouin's mediation_analysis. Shouldn't the 'Indirect' coefficient be the product of the coefficients from 'MX' and 'YM'? When I compare the output to that from the pyprocessmacro package, everything is the same except the stats for 'YM'. What is interesting is that 'Indirect' (the total indirect effects) is also the same, which suggests that the correct coefficient for 'YM' is being calculated. However, it doesn't seem like that is what is being returned.
Please let me know if I am misinterpreting something.
Thanks

[swank10009]

I have no idea why the text above was struck through. That was not intentional.

[raphaelvallat]

Hi,

Can you please provide example scripts and data with pingouin and pyprocessmacro? The calculation of the indirect coefficient in Pingouin is done here:

pingouin/pingouin/regression.py

Lines 952 to 968 in 5c5f61a

	def _point_estimate(X_val, XM_val, M_val, y_val, idx, n_mediator, mtype="linear", **logreg_kwargs):
	"""Point estimate of indirect effect based on bootstrap sample."""
	# Mediator(s) model (M(j) ~ X + covar)
	beta_m = []
	for j in range(n_mediator):
	if mtype == "linear":
	beta_m.append(linear_regression(X_val[idx], M_val[idx, j], coef_only=True)[1])
	else:
	beta_m.append(
	logistic_regression(X_val[idx], M_val[idx, j], coef_only=True, **logreg_kwargs)[1]
	)
	# Full model (Y ~ X + M + covar)
	beta_y = linear_regression(XM_val[idx], y_val[idx], coef_only=True)[2 : (2 + n_mediator)]
	# Point estimate
	return beta_m * beta_y

Please see this screenshot from Hayes and Rockwood 2017 for more details:

[swank10009]

Hello,
As is stated in the paragraph above from Hayes and Rockwood 2017, "...indirect effect is estimated as the product of regression coefficients a and b...".
Here is the code and output from pingouin:

Code:
import pingouin as pg; df = pg.read_dataset('mediation'); pg.mediation_analysis(data=df, x='X', m='M', y='Y', seed=42, alpha=0.05, n_boot=1000)

Output:
path coef se pval CI[2.5%] CI[97.5%] sig
0 M ~ X 0.561015 0.094480 4.391362e-08 0.373522 0.748509 Yes
1 Y ~ M 0.654173 0.085831 1.612674e-11 0.483844 0.824501 Yes
2 Total 0.396126 0.111160 5.671128e-04 0.175533 0.616719 Yes
3 Direct 0.039604 0.109648 7.187429e-01 -0.178018 0.257226 No
4 Indirect 0.356522 0.083984 0.000000e+00 0.218835 0.538517 Yes

In the output, the indirect path coefficients are 0.561015 and 0.654173, the product of which is 0.367. However, the total indirect coefficient is 0.35622.

Using pyprocessmacro:

Code:
from pyprocessmacro import Process; proc=Process(data=df, model=4, x='X', m=['M'], y='Y'); proc.summary()

Output:
***************************** OUTCOME MODELS ****************************

Outcome = Y
OLS Regression Summary

 R²  Adj. R²    MSE       F  df1  df2  p-value

0.3730 0.3534 2.6613 28.8524 2 97 0.0000

Coefficients

  coeff     se      t      p    LLCI   ULCI

Cons 1.9043 0.6055 3.1452 0.0022 0.7176 3.0909
X 0.0396 0.1096 0.3612 0.7187 -0.1753 0.2545
M 0.6355 0.1005 6.3212 0.0000 0.4385 0.8325

---

Outcome = M
OLS Regression Summary

 R²  Adj. R²    MSE       F  df1  df2  p-value

0.2646 0.2494 2.6868 35.2586 1 98 0.0000

Coefficients

       coeff     se      t      p   LLCI   ULCI

Cons 1.4995 0.5892 2.5450 0.0125 0.3447 2.6543
X 0.5610 0.0945 5.9379 0.0000 0.3758 0.7462

---

********************** DIRECT AND INDIRECT EFFECTS **********************

Direct effect of X on Y:

Effect SE t p LLCI ULCI
0.0396 0.1096 0.3612 0.7187 -0.1753 0.2545

Indirect effect of X on Y:

Effect Boot SE BootLLCI BootULCI
M 0.3565 0.0786 0.2191 0.5347

In the pyprocessmacro output, the indirect coefficients are 0.6355 and 0.5610, the product of which is 0.3565. This agrees to the total indirect effect shown at the bottom. It also agrees to the total indirect effect from pingouin (if you account for rounding). However, the coefficient for M in pingouin (0.654173) does not agree to that from pyprocessmacro (0.6355) and multiplying it by the other indirect coefficient does not agree to the total indirect effect. So, it seems like pingouin is calculating the correct coefficient for M (because the total indirect effect is correct), but the coefficient for M that is returned does not seem correct. I also tested output against cardiomoon's processR shiny app (https://cardiomoon.shinyapps.io/processR/). The app agrees to pyprocessmacro. Again, if I am just missing something, please let me know.

[raphaelvallat]

Hi,

Apologies about the delayed response. Thanks for the detailed post. So, if you look at the output of the pyprocessmacro the 0.6355 coefficient is the regression coefficient of Y ~ M in a full model that also includes X, i.e. Y ~ M + X

This is the same coefficient that Pingouin uses to calculate the indirect effect, here:

pingouin/pingouin/regression.py

Lines 952 to 968 in 7923141

	def _point_estimate(X_val, XM_val, M_val, y_val, idx, n_mediator, mtype="linear", **logreg_kwargs):
	"""Point estimate of indirect effect based on bootstrap sample."""
	# Mediator(s) model (M(j) ~ X + covar)
	beta_m = []
	for j in range(n_mediator):
	if mtype == "linear":
	beta_m.append(linear_regression(X_val[idx], M_val[idx, j], coef_only=True)[1])
	else:
	beta_m.append(
	logistic_regression(X_val[idx], M_val[idx, j], coef_only=True, **logreg_kwargs)[1]
	)
	# Full model (Y ~ X + M + covar)
	beta_y = linear_regression(XM_val[idx], y_val[idx], coef_only=True)[2 : (2 + n_mediator)]
	# Point estimate
	return beta_m * beta_y

However, the Y ~ M coefficient reported in the Pingouin output table is the univariate regression of M on Y, without the effect of X, which I believe is not reported by pyprocessmacro.

In other words, Pingouin agrees with pyprocessmacro and uses the same coefficient internally, however, it reports the univariate regression coefficient and not the coefficient from the full model.

Let me know if that answered your question. I think it'd be a good idea to make this more explicit in the documentation or code perhaps.

Thanks
Raphael