late.regu.path {RCAL}

Model-assisted inference for local average treatment effects along regularization paths

Description

This function implements model-assisted inference for local average treatment effects (LATEs) using regularized calibrated estimation along regularization paths for instrument propensity score (IPS) estimation, while based on cross validation for the treatment and outcome regressions.

Usage

late.regu.path(fold, nrho = NULL, rho.seq = NULL, y, tr, iv, fx, gx, hx,
  arm = 2, d1 = NULL, d2 = NULL, ploss = "cal", yloss = "gaus",
  off = NULL, ...)

Arguments

fold

A vector of length 3, with the second and third components giving the fold number for cross validation in the treatment and outcome regressions respectively. The first component is not used.

nrho

A vector of length 3 giving the number of tuning parameters in a regularization path for IPS estimation and that in cross validation for the treatment and outcome regressions.

rho.seq

A list of two vectors giving the tuning parameters for IPS estimation (first vector), treatment (second vector) and outcome (third vector) regressions.

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).

iv

An n x 1 vector of instruments (0 or 1).

fx

An n x p matix of covariates, used in the instrument propensity score model.

gx

An n x q_1 matix of covariates, used in the treatment regression models. In theory, gx should be a subvector of gx, hence p\leq q_1.

hx

An n x q_2 matix of covariates, used in the outcome regression models. In theory, hx should be a subvector of gx, hence p\leq q_2.

arm

An integer 0, 1 or 2 indicating whether \theta_0, \theta_1 or both are computed; see Details for late.aipw.

d1

Degree of truncated polynomials of fitted values from treatment regression to be included as regressors in the outcome regression (NULL: no adjustment, 0: piecewise constant, 1: piecewise linear etc.).

d2

Number of knots of fitted values from treatment regression to be included as regressors in the outcome regression, with knots specified as the i/(d2+1)-quantiles for i=1,...,d2.

ploss

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

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

ips

A list of 2 objects, giving the results from fitting the IPS models by glm.regu.path for iv=0 (first) and iv=1 (second).

mfp

A list of 2 matrices of fitted instrument propensity scores, along the IPS regularization path, for iv=0 (first matrix) and iv=1 (second matrix).

tps

A list of 2 lists of objects for iv=0 (first) and iv=1 (second), where each object gives the results from fitting the treatment regression models by glm.regu.cv for an IPS tuning parameter.

mft

A list of 2 matrices of fitted treatment regression models based on cross validation, along the IPS regularization path, for iv=0 (first matrix) and iv=1 (second matrix).

or

A list of 4 lists of objects for iv=0, tr=0 (first), iv=0, tr=1 (second), iv=1, tr=0 (third) and iv=1, tr=1 (fourth), containing the results from fitting the outcome regression models by glm.regu.cv.

mfo

A list of 4 matrices of fitted outcome regression models based on cross validation, along the IPS regularization path, for iv=0, tr=0 (first), iv=0, tr=1 (second), iv=1, tr=0 (third) and iv=1, tr=1 (fourth). Two matrices are set to NA if arm=0 or 1.

est

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

rho

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

References

Sun, B. and Tan, Z. (2020) High-dimensional model-assisted inference for local average treatment effects with instrumental variables, arXiv:2009.09286.

Examples

data(simu.iv.data)
n <- dim(simu.iv.data)[1]
p <- dim(simu.iv.data)[2]-3

y <- simu.iv.data[,1]
tr <- simu.iv.data[,2]
iv <- simu.iv.data[,3]
x <- simu.iv.data[,3+1:p]
x <- scale(x)


late.path.rcal <- late.regu.path(fold=5*c(0,1,1), nrho=(1+10)*c(1,1,1), rho.seq=NULL,
                   y, tr, iv, fx=x, gx=x, hx=x, arm=2, d1=1, d2=3, ploss="cal", yloss="gaus")


late.path.rcal$est