# Detailed estimator comparison¶

Estimator

Treatment
Type
Requires
Instrument
Delivers Conf.
Intervals
Linear
Treatment
Linear
Heterogeneity
Mulitple
Outcomes
Multiple
Treatments
High-Dimensional
Features

NonparametricTwoStageLeastSquares

Any

Yes

Yes

Assumed

Yes

Yes

DeepIV

Any

Yes

Yes

Yes

SparseLinearDML

Any

Yes

Yes

Assumed

Yes

Yes

Yes

SparseLinearDRLearner

Categorical

Yes

Projected

Yes

Yes

LinearDML

Any

Yes

Yes

Assumed

Yes

Yes

LinearDRLearner

Categorical

Yes

Projected

Yes

CausalForestDML

Any

Yes

Yes

Yes

Yes

Yes

ForestDRLearner

Categorical

Yes

Yes

Yes

DMLOrthoForest

Any

Yes

Yes

Yes

Yes

DROrthoForest

Categorical

Yes

Yes

Yes

metalearners

Categorical

Yes

Yes

Yes

DRLearner

Categorical

Yes

Yes

DML

Any

Yes

Assumed

Yes

Yes

Yes

NonParamDML

1-d/Binary

Yes

Yes

Yes

Treatment Type

Some estimators can only estimate effects of particular kinds of treatments. Discrete treatments can be described by a finite number of comprehensive categories (for example, group A received a 10% discount on product 1, group B received a 10% discount on product 2, group C received no discounts). Binary treatments are a special case of discrete treatments with only two categories. Continuous treatments can take on any value along the number line (for example, minutes of exercise per week).

Requires Instrument

Some estimators identify the causal effect of a treatment by considering only a subset of the variation in treatment intensity that is conditionally random given other data features. This subset of the variation is driven by an instrument, which is usually some kind of randomization (i.e. an earlier experiment or a lottery). See the Instrumental Variable Regression section for more information on picking a good instrument.

Delivers Confidence Intervals

Many estimators can deliver analytic confidence intervals for the final treatment effects. These confidence intervals correctly adjust for the reuse of data across multiple stages of estimation. EconML cannot deliver analytic confidence intervals in cases where this multi-stage estimation is too complex or for estimators such as the MetaLearners that trade honest confidence intervals for model selection and regularization. In these cases it is still possible to get bootstrap confidence intervals, but this process is slow and may not be statistically valid.

Linear Treatment

Some estimators impose the assumption that the outcome is a linear function of the treatment. These estimators can also estimate a non-linear relationship between a treatment and the outcome if the structure of the relationship is known and additively separable (for example, the linear function could include both treatment and treatment-squared for continuous treatments). These linear functions can also include specified interactions between treatments. However, these estimators cannot estimate a fully flexible non-parametric relationship between treatments and the outcome (for example, the relationship cannot be modeled by a forest).

Linear Heterogeneity

The CATE function determines how the size of a user’s response to the treatment varies by user features. Some estimators impose the assumption that effect size is a linear function of user features. A few models estimate a more flexible relationship between effect size and user features and then project that flexible function onto a linear model. This second approach delivers a better-fitting linear approximation of a non-linear relationship, but is less efficient in cases where you are confident assuming the true relationship is linear. Finally, some estimation models allow a fully flexible relationship between effect size and user features with no linearity structure.

Multiple Outcomes

Some estimation models allow joint estimation of the effects of treatment(s) on multiple outcomes. Other models only accommodate a single outcome.

Multiple Treatments

Some estimation models allow joint estimation of the effects of multiple treatments on outcome(s). Other models only accommodate a single treatment.

High-Dimensional Features

Many estimators only behave well with a small set of specified features, X, that affect the size of a user’s response to the treatment. If you do not already know which few features might reasonably affect the user’s response, use one of our sparse estimators that can handle large feature sets and penalize them to discover the features that are most correlated with treatment effect heterogeneity.