[API Documentation]: DoubleMLData

[dirknbr]

Describe the issue related to the API documentation

DoubleMLData does allow more than 1 treatment variable but I cannot see which model does actually allow more than one treatment variable/model.

Suggested alternative or fix

No response

[SvenKlaassen]

Hi @dirknbr,

The partially linear model DoubleMLPLR allows for more than one treatment variable.

Generally, I think one should be careful with multiple treatments as there might be different controls for $X$ for different treatments. Per default with e.g. two treatments $D_1$ and $D_2$, the treatment $D_2$ is used as control variable when estimating the effect of $D_1$ and vice versa.
Usually, I would recommend to fit multiple models for each treatment seperately.

[dirknbr]

Are you sure, the docs say the below, so it expects a single estimator?

ml_m (estimator implementing fit() and predict()) – A machine learner implementing fit() and predict() methods (e.g. sklearn.ensemble.RandomForestRegressor) for the nuisance function
. For binary treatment variables
(with values 0 and 1), a classifier implementing fit() and predict_proba() can also be specified. If sklearn.base.is_classifier() returns True, predict_proba() is used otherwise predict().

[JanTeichertKluge]

Hi @dirknbr,

You're correct, the ml_m parameter expects only a single estimator. If you provide multiple treatments, this estimator will automatically be copied and used separately for each treatment variable. Therefore, it's currently not possible to specify distinct estimators tailored specifically for each treatments within the same PLR model. As a result, mixing categorical and continuous treatments isn't supported at this time. If you have categorical treatments, ensure the chosen estimator supports classification (predict_proba()), or stick to regression estimators (predict()) for continuous treatments.

But as @SvenKlaassen has already said, we would recommend fitting several models for each treatment individually.

[SvenKlaassen]

I will close this issue as this is the intended behavior.

[kkckk1110]

Hi @SvenKlaassen, I wonder the rationale behind "fit multiple models for each treatment seperately". I am not quite familiar in DML. In trational econometrics, we usually estimate each independent variables in a single linear regression. Could you kindly inform the justification for this method, or provide some references? Thanks a lot!

[JanTeichertKluge]

Hi @kkckk1110,

that has practical reasons according to the implementation rather than theoretical reasons. If you use a single instance of e.g. DoubleMLPLR for a model with multiple treatment variables, you have to accept simplifications. As noted above, this simplification affects the choice of ML models for estimating the nuisance elements with regard to the treatments. It is not possible to use, for example, a boosted tree algorithm for $D_1$ and a linear model for $D_2$. Furthermore, the choice of covariates can only be specified for all treatments simultaneously (only $X$ or $[X, D_2]$ as covariates for estimating $m_{0, D_1}$?).

The solution would be to use seperate instances for each treatment and concatenate the doubleml.DoubleMLFramework objects for valid simultanous inference. It contains a scaled version of the score function which is used to construct confidence intervals.

You can find more information about that in the docs.

Best
Jan

[SvenKlaassen]

I agree with @JanTeichertKluge.
Generally, specifying separate models for each treatment requires you to actually set controls for each treatment variable separately. If you are estimating multiple treatment variables in a single linear regression, this makes some implicit assumptions on the functional form and the underlying causal structure (DAG).