ate.regu.path {RCAL}

Model-assisted inference for average treatment effects along regularization paths

Description

This function implements model-assisted inference for average treatment effects, using regularized calibrated estimation along regularization paths for propensity score (PS) estimation while based on cross validation for outcome regression (OR).

Usage

ate.regu.path(fold, nrho = NULL, rho.seq = NULL, y, tr, x, ploss = "cal",
  yloss = "gaus", off = NULL, ...)

Arguments

fold

A vector of length 2, with the second component giving the fold number for cross validation in outcome regression. The first component is not used.

nrho

A vector of length 2 giving the number of tuning parameters in a regularization path for PS estimation and that in cross validation for OR.

rho.seq

A list of two vectors giving the tuning parameters for propensity score estimation (first vector) and outcome regression (second vector).

y

An n x 1 vector of observed outcomes.

tr

An n x 1 vector of treatment indicators (=1 if treated or 0 if untreated).

x

An n x p matix of covariates, used in both propensity score and outcome regression models.

ploss

A loss function used in propensity score estimation (either "ml" or "cal").

yloss

A loss function used in outcome regression (either "gaus" for continuous outcomes or "ml" for binary outcomes).

off

A 2 x 1 vector of offset values (e.g., the true values in simulations) used to calculate the z-statistics from augmented IPW estimation.

...

Additional arguments to glm.regu.cv and glm.regu.path.

Details

See Details for ate.regu.cv.

Value

ps

A list of 2 objects, giving the results from fitting the propensity score model by glm.regu.path for untreated (first) and treated (second).

mfp

A list of 2 matrices of fitted propensity scores, along the PS regularization path, for untreated (first matrix) and treated (second matrix).

or

A list of 2 lists of objects for untreated (first) and treated (second), where each object gives the results from fitting the outcome regression model by glm.regu.cv for a PS tuning parameter.

mfo

A list of 2 matrices of fitted values from outcome regression based on cross validation, along the PS regularization path, for untreated (first matrix) and treated (second matrix).

est

A list containing the results from augmented IPW estimation by ate.aipw.

rho

A vector of tuning parameters leading to converged results in propensity score estimation.

References

Tan, Z. (2020a) Regularized calibrated estimation of propensity scores with model misspecification and high-dimensional data, Biometrika, 107, 137–158.

Tan, Z. (2020b) Model-assisted inference for treatment effects using regularized calibrated estimation with high-dimensional data, Annals of Statistics, 48, 811–837.

Examples

data(simu.data)
n <- dim(simu.data)[1]
p <- dim(simu.data)[2]-2

y <- simu.data[,1]
tr <- simu.data[,2]
x <- simu.data[,2+1:p]
x <- scale(x)

ate.path.rcal <- ate.regu.path(fold=5*c(0,1), nrho=(1+10)*c(1,1), rho.seq=NULL, y, tr, x, 
                               ploss="cal", yloss="gaus")
ate.path.rcal$est