ate.regu.path: Model-assisted inference for average treatment effects along...
In RCAL: Regularized Calibrated Estimation

Description Usage Arguments Details Value References Examples

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).

1 2	ate.regu.path(fold, nrho = NULL, rho.seq = NULL, y, tr, x, ploss = "cal", yloss = "gaus", off = NULL, ...)

`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`.

See Details for ate.regu.cv.

`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.

Tan, Z. (2020a) Regularized calibrated estimation of propensity scores with model misspecification and high-dimensional data, Biometrika, 107, 137<e2><80><93>158.

Tan, Z. (2020b) Model-assisted inference for treatment effects using regularized calibrated estimation with high-dimensional data, Annals of Statistics, 48, 811<e2><80><93>837.

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