RCAL (version 2.0)

ate.regu.path: 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.

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.

Details

See Details for ate.regu.cv.

References

Tan, Z. (2020a) Regularized calibrated estimation of propensity scores with model misspecification and high-dimensional data, Biometrika, 107, 137<U+2013>158.

Tan, Z. (2020b) Model-assisted inference for treatment effects using regularized calibrated estimation with high-dimensional data, Annals of Statistics, 48, 811<U+2013>837.

Examples

# NOT RUN {
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
# }
# NOT RUN {
# }