dmlmt

Double Machine Learning for Multiple Treatments

This code implements the Double Machine Learning approach (Chernozhukov et al., 2018) for multiple treatments following Farrell (2015). With modifications for sensitivity analysis and balancing checks as described and applied in Knaus (2018). The cross-validated Post-Lasso is based on the glmnet package.

Example

The following example shows how the analysis works for a binary treatment variable. The data are taken from the hdm package that is described in Chernozhukov, Hansen, & Spindler (2016).

# Download current version from Github
library(devtools)
install_github(repo="MCKnaus/dmlmt")
library(dmlmt)

# Get data
library(hdm)
data(pension)
Y = pension$tw; D = pension$p401
# Only main effects (toy example)
X = model.matrix(~ -1 + i2 + i3 + i4 + i5 + i6 + i7 + a2 + a3 + a4 + a5 +
                fsize + hs + smcol + col + marr + twoearn + db + pira + hown, data = pension)
## Consider also interactions if you have some time
# X = model.matrix(~ -1 + (i2 + i3 + i4 + i5 + i6 + i7 + a2 + a3 + a4 + a5 +
#                    fsize + hs + smcol + col + marr + twoearn + db + pira + hown)^2, data = pension)

Basic analysis

Binary treatment

The following code shows how to estimate the basic average potential outcomes and treatment effect. Following the analysis in Knaus (2018) all nuisance paramteres are estimated using cross-validated Post-Lasso.

stand_pl_bin <- dmlmt(X,D,Y)

One alternative is to use normal Lasso instead of Post-Lasso. This is usually much faster because it does not require to solve a full logistic and OLS model at each considered Lambda.

stand_l_bin <- dmlmt(X,D,Y,pl=FALSE)

Multiple treament

For expository purposes create a third treatment by randomly splitting the control group.

D_mult <- D
D_mult[runif(length(D))*(1-D)>0.5] <- 2
table(D_mult)

Run the analysis with the multiple treatment.

stand_pl_mult <- dmlmt(X,D_mult,Y)
stand_l_mult <- dmlmt(X,D_mult,Y,pl=FALSE)

Extended analysis as proposed in Knaus (2018)

Run the analysis also for 1SE, 0.5SE, 0.5SE+ and 1SE+ rules to select the Lambda and calculate the weights for balancing checks.

se_rules <- c(-1,-.5,.5,1)

# Binary
ext_pl_bin <- dmlmt(X,D,Y,se_rule=se_rules,w=TRUE)

# Example how to plot the results
df <- data.frame(SE_rule = factor(colnames(ext_pl_bin$SE_rule[[1]])
                                  ,levels = colnames(ext_pl_bin$SE_rule[[1]]))
                 ,coef = ext_pl_bin$SE_rule[[1]][1,],se = ext_pl_bin$SE_rule[[2]][1,])
j <- ggplot(df, aes(SE_rule, coef, ymin = coef-se, ymax = coef+se)) +
             geom_errorbar() + geom_point()

# Example how to check balancing with the package of your choice, e.g. cobalt
library(cobalt)
balance <- bal.tab(as.data.frame(X), treat = D,weights=ext_pl_bin$weights,method = "weighting",
                    s.d.denom = "pooled", disp.v.ratio = TRUE, disp.ks = TRUE, un = TRUE)
plot <- love.plot(balance,abs = TRUE, line=TRUE, var.order="unadjusted")

# Multiple
ext_pl_mult <- dmlmt(X,D_mult,Y,se_rule=se_rules,w=TRUE)

Using other machine learners for nuisance parameters

The package allows to create predictions for the nuisance parameters from any machine learner of choice and to calculate the potential outcomes and average treatment effects. For example with random forests:

library(grf)

# Initialize nuisance matrices
values <- sort(unique(D_mult))
ps_mat <- t_mat <- y_mat <- matrix(NA,length(Y),length(values))

# Get nuisance parameter predictions
for (tr in 1:length(values)){
  t_mat[,tr] <- as.numeric(D_mult == values[tr])
  rf_p <- regression_forest(X,t_mat[,tr])
  ps_mat[,tr] <- predict(rf_p, X)$predictions
  rf_y <- regression_forest(X[t_mat[,tr] == 1,],Y[t_mat[,tr] == 1])
  y_mat[,tr] <- predict(rf_y, X)$predictions
}

# Calculate generalized p-score and enforce common support
rf_gps <- gps_cs(ps_mat,t_mat)

# Potential outcomes
rf_PO <- PO_dmlmt(t_mat,Y,y_mat,rf_gps$p,cs_i=rf_gps$cs)
# ATE
rf_ATE <- TE_dmlmt(rf_PO$mu,rf_gps$cs)

References

Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W., & Robins, J. (2018). Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21(1), C1-C68.

Chernozhukov, V., Hansen, C., & Spindler, M. (2016). High-Dimensional Metrics in R. arXiv:1603.01700

Farrell, M. H. (2015). Robust inference on average treatment effects with possibly more covariates than observations. Journal of Econometrics, 189(1), 1-23.

Knaus, M. C. (2018). A Double Machine Learning Approach to Estimate the Effects of Musical Practice on Student's Skills, arXiv