Propensity Score Model
In this example, the propensity score is known because the data is
from a randomized experiment. We don’t need to estimate a model for the
propensity score.
For CATEs on discrete moderators, this implies that our estimates
will simply be equivalent to AIPW estimators and will therefore inherit
unbiasedness. For continuous moderators, similarly, if the CATE
functions are smooth, we will attain consistency for recovering the true
function non-parametrically.
Outcome Model
We estimate the outcome (T-learner) plugin estimate using an ensemble
of machine learning models, including a wide array of model complexities
from linear models, GAMs, regularized regressions. In this example,
non-linear models are not included (due to runtime), but they could
easily be added by uncommenting the associated lines.
Each individual component of the model provides a list of
hyperparameters, over which a full cross-product is taken and all
resulting models are estimate. For instance, SL.glmnet
sweeps over one hyperparameter (the mixing parameters between ridge and
Lasso). A model with each of the hyper-parameter values will be
estimated and incorporated into the ensemble. Note that
SL.glmnet automatically tunes the regularization parameter
using cv.glmnet, so this is not included as a
hyperparameter.
Quantities of interest
Quantities of Interest determine how results are reported to the
user. You can think about this as determining, for instance how results
should be plotted in a resulting chart.
For simplicity, this example simply provides results in one of two
ways: - Discrete covariates are stratified and the conditional effect is
plotted at each distinct level of the covariate. - Continuous covariates
have the effect surface estimated using local-linear regression via
nprobust of Calonico, Cattaneo and Farrell (2018). See,
similarly, Kennedy, Ma, McHugh and Small (2017) for justification of
this approach. Results are obtained for a grid of 100 quantiles across
the domain of the covariate.
An additional quantity of interest provided is the variable
importance of a learned joint model of conditional effects (over all
covariates). The approach implemented is described in Williamson,
Gilbert, Carone and Simon (2020).
basic_config() %>%
add_known_propensity_score("ps") %>%
add_outcome_model("SL.glm.interaction") %>%
add_outcome_model("SL.glmnet", alpha = c(0, 1)) %>%
add_outcome_model("SL.glmnet.interaction", alpha = c(0, 1)) %>%
add_outcome_diagnostic("RROC") %>%
add_effect_model("SL.glm.interaction") %>%
add_effect_model("SL.glmnet", alpha = c(0, 1)) %>%
add_effect_model("SL.glmnet.interaction", alpha = c(0, 1)) %>%
add_effect_diagnostic("RROC") %>%
add_moderator("Stratified", x2, x3) %>%
add_moderator("KernelSmooth", x1, x4, x5) %>%
add_vimp(sample_splitting = FALSE) ->
hte_cfg
## Super Learner
## Version: 2.0-28.1
## Package created on 2021-05-04
