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Sample Splitting with Caret

Source: vignettes/sample_split_caret.Rmd
sample_split_caret.Rmd

We can train the model with the caret package (for further information about caret, see the original website). We use parallel computing to speed up the computation.

# parallel computing
library(doParallel)
cl <- makePSOCKcluster(5)
registerDoParallel(cl)

# stop after finishing the computation
stopCluster(cl)

The following example shows how to estimate the ITR with grandient boosting machine (GBM) using the caret package. Note that we have already loaded the data and specify the treatment, outcome, and covariates as shown in the Sample Splitting vignette. Since we are using the caret package, we need to specify the trainControl and/or tuneGrid arguments. The trainControl argument specifies the cross-validation method and the tuneGrid argument specifies the tuning grid. For more information about these arguments, please refer to the caret website.

We estimate the ITR with only one machine learning algorithm (GBM) and evaluate the ITR with the evaluate_itr() function. To compute PAPDp, we need to specify the algorithms argument with more than 2 machine learning algorithms.

library(evalITR)

# specify the trainControl method
fitControl <- caret::trainControl(
  method = "repeatedcv", # 3-fold CV
  number = 3, # repeated 3 times
  repeats = 3,
  search='grid',
  allowParallel = TRUE) # grid search

# specify the tuning grid
gbmGrid <- expand.grid(
  interaction.depth = c(1, 5, 9), 
  n.trees = (1:30)*50, 
  shrinkage = 0.1,
  n.minobsinnode = 20)

# estimate ITR
fit_caret <- estimate_itr(
  treatment = "treatment",
  form = user_formula,
  trControl = fitControl,
  data = star_data,
  algorithms = c("gbm"),
  budget = 0.2,
  split_ratio = 0.7,
  tuneGrid = gbmGrid,
  verbose = FALSE)
#> Evaluate ITR under sample splitting ...

# evaluate ITR
est_caret <- evaluate_itr(fit_caret)
#> Cannot compute PAPDp

We can extract the training model from caret and check the model performance. Other functions from caret can be applied to the training model.

# extract the final model
caret_model <- fit_caret$estimates$models$gbm
print(caret_model$finalModel)
#> A gradient boosted model with gaussian loss function.
#> 50 iterations were performed.
#> There were 53 predictors of which 36 had non-zero influence.

# check model performance
trellis.par.set(caretTheme()) # theme
plot(caret_model) 

# heatmap 
plot(
  caret_model, 
  plotType = "level",
  scales = list(x = list(rot = 90)))

Thesummary() function displays the following summary statistics: (1) population average prescriptive effect PAPE; (2) population average prescriptive effect with a budget constraint PAPEp; (3) population average prescriptive effect difference with a budget constraint PAPDp. This quantity will be computed with more than 2 machine learning algorithms); (4) and area under the prescriptive effect curve AUPEC. For more information about these evaluation metrics, please refer to Imai and Li (2021); (5) Grouped Average Treatment Effects GATEs. The details of the methods for this design are given in Imai and Li (2022).

# summarize estimates
summary(est_caret)
#> ── PAPE ────────────────────────────────────────────────────────────────────────
#>   estimate std.deviation algorithm statistic p.value
#> 1    -0.35           1.5       gbm     -0.24    0.81
#> 
#> ── PAPEp ───────────────────────────────────────────────────────────────────────
#>   estimate std.deviation algorithm statistic p.value
#> 1      1.6           1.3       gbm       1.2    0.21
#> 
#> ── PAPDp ───────────────────────────────────────────────────────────────────────
#> data frame with 0 columns and 0 rows
#> 
#> ── AUPEC ───────────────────────────────────────────────────────────────────────
#>   estimate std.deviation algorithm statistic p.value
#> 1     0.22           1.1       gbm      0.19    0.85
#> 
#> ── GATE ────────────────────────────────────────────────────────────────────────
#>   estimate std.deviation algorithm group statistic p.value upper lower
#> 1      105           109       gbm     1      0.96    0.34   -75   285
#> 2      -60           108       gbm     2     -0.56    0.58  -238   117
#> 3     -139           107       gbm     3     -1.30    0.19  -315    37
#> 4       64           108       gbm     4      0.59    0.55  -114   243
#> 5       51           109       gbm     5      0.47    0.64  -128   230

We plot the estimated Area Under the Prescriptive Effect Curve for the writing score across a range of budget constraints for the gradient boosting machine.

# plot the AUPEC 
plot(est_caret)