# statsmodels.stats.mediation.Mediation¶

class statsmodels.stats.mediation.Mediation(outcome_model, mediator_model, exposure, mediator=None, moderators=None, outcome_fit_kwargs=None, mediator_fit_kwargs=None)[source]

Conduct a mediation analysis.

Parameters: outcome_model (statsmodels model) – Regression model for the outcome. Predictor variables include the treatment/exposure, the mediator, and any other variables of interest. mediator_model (statsmodels model) – Regression model for the mediator variable. Predictor variables include the treatment/exposure and any other variables of interest. exposure (string or (int, int) tuple) – The name or column position of the treatment/exposure variable. If positions are given, the first integer is the column position of the exposure variable in the outcome model and the second integer is the position of the exposure variable in the mediator model. If a string is given, it must be the name of the exposure variable in both regression models. mediator (string or int) – The name or column position of the mediator variable in the outcome regression model. If None, infer the name from the mediator model formula (if present). moderators (dict) – Map from variable names or index positions to values of moderator variables that are held fixed when calculating mediation effects. If the keys are index position they must be tuples (i, j) where i is the index in the outcome model and j is the index in the mediator model. Otherwise the keys must be variable names. outcome_fit_kwargs (dict-like) – Keyword arguments to use when fitting the outcome model. mediator_fit_kwargs (dict-like) – Keyword arguments to use when fitting the mediator model. a MediationResults object. (Returns) –

Notes

The mediator model class must implement get_distribution.

Examples

A basic mediation analysis using formulas:

>>> import statsmodels.api as sm
>>> probit = links.probit
>>> outcome_model = sm.GLM.from_formula("cong_mesg ~ emo + treat + age + educ + gender + income",
>>> mediator_model = sm.OLS.from_formula("emo ~ treat + age + educ + gender + income", data)
>>> med = Mediation(outcome_model, mediator_model, "treat", "emo").fit()
>>> med.summary()


A basic mediation analysis without formulas. This may be slightly faster than the approach using formulas. If there are any interactions involving the treatment or mediator variables this approach will not work, you must use formulas.

>>> import patsy
>>> outcome = np.asarray(data["cong_mesg"])
>>> outcome_exog = patsy.dmatrix("emo + treat + age + educ + gender + income", data,
...                              return_type='dataframe')
>>> probit = sm.families.links.probit
>>> outcome_model = sm.GLM(outcome, outcome_exog, family=sm.families.Binomial(link=probit()))
>>> mediator = np.asarray(data["emo"])
>>> mediator_exog = patsy.dmatrix("treat + age + educ + gender + income", data,
...                               return_type='dataframe')
>>> mediator_model = sm.OLS(mediator, mediator_exog)
>>> tx_pos = [outcome_exog.columns.tolist().index("treat"),
...           mediator_exog.columns.tolist().index("treat")]
>>> med_pos = outcome_exog.columns.tolist().index("emo")
>>> med = Mediation(outcome_model, mediator_model, tx_pos, med_pos).fit()
>>> med.summary()


A moderated mediation analysis. The mediation effect is computed for people of age 20.

>>> fml = "cong_mesg ~ emo + treat*age + emo*age + educ + gender + income",
>>> outcome_model = sm.GLM.from_formula(fml, data,
...                                      family=sm.families.Binomial())
>>> mediator_model = sm.OLS.from_formula("emo ~ treat*age + educ + gender + income", data)
>>> moderators = {"age" : 20}
>>> med = Mediation(outcome_model, mediator_model, "treat", "emo",
...                 moderators=moderators).fit()


References

Imai, Keele, Tingley (2010). A general approach to causal mediation analysis. Psychological Methods 15:4, 309-334. http://imai.princeton.edu/research/files/BaronKenny.pdf

Tingley, Yamamoto, Hirose, Keele, Imai (2014). mediation : R package for causal mediation analysis. Journal of Statistical Software 59:5. http://www.jstatsoft.org/v59/i05/paper

Methods

 fit([method, n_rep]) Fit a regression model to assess mediation.