RCAL (version 2.0)

mn.regu.path: Model-assisted inference for population means along a regularization path

Description

This function implements model-assisted inference for population means with missing data, using regularized calibrated estimation along a regularization path for propensity score (PS) estimation while based on cross validation for outcome regression (OR).

Usage

mn.regu.path(fold, nrho = NULL, rho.seq = NULL, y, tr, x, ploss = "cal",
  yloss = "gaus", off = 0, ...)

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 outcomes with missing data.

tr

An \(n\) x \(1\) vector of non-missing indicators (=1 if y is observed or 0 if y is missing).

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

An offset value (e.g., the true value in simulations) used to calculate the z-statistic from augmented IPW estimation.

...

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

Value

ps

A list containing the results from fitting the propensity score model by glm.regu.path.

fp

The matrix of fitted propensity scores, column by column, along the PS regularization path.

or

A list of objects, each giving the results from fitting the outcome regression model by glm.regu.cv for a PS tuning parameter.

fo

The matrix of fitted values from outcome regression based on cross validation, column by column, along the PS regularization path.

est

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

rho

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

Details

See Details for mn.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)

# missing data
y[tr==0] <- NA

mn.path.rcal <- mn.regu.path(fold=5*c(0,1), nrho=(1+10)*c(1,1), y=y, tr=tr, x=x, 
                             ploss="cal", yloss="gaus")
mn.path.rcal$est
# }
# NOT RUN {
# }