# pingouin.mediation_analysis¶

pingouin.mediation_analysis(data=None, x=None, m=None, y=None, covar=None, alpha=0.05, n_boot=500, seed=None, return_dist=False)

Mediation analysis using a bias-correct non-parametric bootstrap method.

Parameters
datapandas.DataFrame

Dataframe.

xstr

Column name in data containing the predictor variable. The predictor variable must be continuous.

mstr or list of str

Column name(s) in data containing the mediator variable(s). The mediator(s) can be continuous or binary (e.g. 0 or 1). This function supports multiple parallel mediators.

ystr

Column name in data containing the outcome variable. The outcome variable must be continuous.

covarNone, str, or list

Covariate(s). If not None, the specified covariate(s) will be included in all regressions.

alphafloat

Significance threshold. Used to determine the confidence interval, $$\text{CI} = [\alpha / 2 ; 1 - \alpha / 2]$$.

n_bootint

Number of bootstrap iterations for confidence intervals and p-values estimation. The greater, the slower.

seedint or None

Random state seed.

return_distbool

If True, the function also returns the indirect bootstrapped beta samples (size = n_boot). Can be plotted for instance using seaborn.distplot() or seaborn.kdeplot() functions.

Returns
statspandas.DataFrame

Mediation summary:

• 'path': regression model

• 'coef': regression estimates

• 'se': standard error

• 'CI[2.5%]': lower confidence interval

• 'CI[97.5%]': upper confidence interval

• 'pval': two-sided p-values

• 'sig': statistical significance

Notes

Mediation analysis [1] is a “statistical procedure to test whether the effect of an independent variable X on a dependent variable Y (i.e., X → Y) is at least partly explained by a chain of effects of the independent variable on an intervening mediator variable M and of the intervening variable on the dependent variable (i.e., X → M → Y)” [2].

The indirect effect (also referred to as average causal mediation effect or ACME) of X on Y through mediator M quantifies the estimated difference in Y resulting from a one-unit change in X through a sequence of causal steps in which X affects M, which in turn affects Y. It is considered significant if the specified confidence interval does not include 0. The path ‘X –> Y’ is the sum of both the indirect and direct effect. It is sometimes referred to as total effect.

A linear regression is used if the mediator variable is continuous and a logistic regression if the mediator variable is dichotomous (binary). Multiple parallel mediators are also supported.

This function will only work well if the outcome variable is continuous. It does not support binary or ordinal outcome variable. For more advanced mediation models, please refer to the lavaan or mediation R packages, or the PROCESS macro for SPSS.

The two-sided p-value of the indirect effect is computed using the bootstrap distribution, as in the mediation R package. However, the p-value should be interpreted with caution since it is not constructed conditioned on a true null hypothesis [3] and varies depending on the number of bootstrap samples and the random seed.

Note that rows with missing values are automatically removed.

Results have been tested against the R mediation package and this tutorial https://data.library.virginia.edu/introduction-to-mediation-analysis/

References

1

Baron, R. M. & Kenny, D. A. The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. J. Pers. Soc. Psychol. 51, 1173–1182 (1986).

2

Fiedler, K., Schott, M. & Meiser, T. What mediation analysis can (not) do. J. Exp. Soc. Psychol. 47, 1231–1236 (2011).

3

Hayes, A. F. & Rockwood, N. J. Regression-based statistical mediation and moderation analysis in clinical research: Observations, recommendations, and implementation. Behav. Res. Ther. 98, 39–57 (2017).

Code originally adapted from https://github.com/rmill040/pymediation.

Examples

1. Simple mediation analysis

>>> from pingouin import mediation_analysis, read_dataset
>>> df = read_dataset('mediation')
>>> mediation_analysis(data=df, x='X', m='M', y='Y', alpha=0.05,
...                    seed=42)
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  0.083313  0.000000e+00  0.219818   0.537654  Yes

1. Return the indirect bootstrapped beta coefficients

>>> stats, dist = mediation_analysis(data=df, x='X', m='M', y='Y',
...                                  return_dist=True)
>>> print(dist.shape)
(500,)

1. Mediation analysis with a binary mediator variable

>>> mediation_analysis(data=df, x='X', m='Mbin', y='Y', seed=42).round(3)
path   coef     se   pval  CI[2.5%]  CI[97.5%]  sig
0  Mbin ~ X -0.021  0.116  0.857    -0.248      0.206   No
1  Y ~ Mbin -0.135  0.412  0.743    -0.952      0.682   No
2     Total  0.396  0.111  0.001     0.176      0.617  Yes
3    Direct  0.396  0.112  0.001     0.174      0.617  Yes
4  Indirect  0.002  0.050  0.960    -0.072      0.146   No

1. Mediation analysis with covariates

>>> mediation_analysis(data=df, x='X', m='M', y='Y',
...                    covar=['Mbin', 'Ybin'], seed=42).round(3)
path   coef     se   pval  CI[2.5%]  CI[97.5%]  sig
0     M ~ X  0.559  0.097  0.000     0.367      0.752  Yes
1     Y ~ M  0.666  0.086  0.000     0.495      0.837  Yes
2     Total  0.420  0.113  0.000     0.196      0.645  Yes
3    Direct  0.064  0.110  0.561    -0.155      0.284   No
4  Indirect  0.356  0.086  0.000     0.209      0.553  Yes

1. Mediation analysis with multiple parallel mediators

>>> mediation_analysis(data=df, x='X', m=['M', 'Mbin'], y='Y',
...                    seed=42).round(3)
path   coef     se   pval  CI[2.5%]  CI[97.5%]  sig
0          M ~ X  0.561  0.094  0.000     0.374      0.749  Yes
1       Mbin ~ X -0.005  0.029  0.859    -0.063      0.052   No
2          Y ~ M  0.654  0.086  0.000     0.482      0.825  Yes
3       Y ~ Mbin -0.064  0.328  0.846    -0.715      0.587   No
4          Total  0.396  0.111  0.001     0.176      0.617  Yes
5         Direct  0.040  0.110  0.721    -0.179      0.258   No
6     Indirect M  0.356  0.085  0.000     0.215      0.538  Yes
7  Indirect Mbin  0.000  0.010  0.952    -0.017      0.025   No