late.nreg {RCAL}

Model-assisted inference for local average treatment effects without regularization

Description

This function implements model-assisted inference for local average treatment effects, using non-regularized calibrated estimation.

Usage

late.nreg(y, tr, iv, fx, gx, hx, arm = 2, d1 = NULL, d2 = NULL,
  ploss = "cal", yloss = "gaus", off = NULL)

Arguments

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.

hx

An n x q_2 matix of covariates, used in the outcome regression models.

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.

Details

For ploss="cal", calibrated estimation of the instrument propensity score (IPS) and weighted likelihood estimation of the treatment and outcome regression models are performed, similarly as in Sun and Tan (2020), but without regularization. See also Details for mn.nreg.

Value

ips

A list containing the results from fitting the instrument propensity score models by glm.nreg.

mfp

An n x 2 matrix of fitted instrument propensity scores for iv=0 (first column) and iv=1 (second column).

tps

A list containing the results from fitting the treatment regression models by glm.nreg.

mft

An n x 2 matrix of fitted treatment regression models for iv=0 (first column) and iv=1 (second column).

or

A list containing the results from fitting the outcome regression models by glm.nreg.

mfo

An n x 4 matrix of fitted outcome regression models for for iv=0, tr=0 (first column), iv=0, tr=1 (second column), iv=1, tr=0 (third column) and iv=1, tr=1 (fourth column). Two columns are set to NA if arm=0 or 1.

est

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

References

Tan, Z. (2006) Regression and weighting methods for causal inference using instrumental variables, Journal of the American Statistical Association, 101, 1607–1618.

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)

# include only 10 covariates
x2 <- x[,1:10]

late.cal <- late.nreg(y, tr, iv, fx=x2, gx=x2, hx=x2, arm=2, d1=1, d2=3,
                       ploss="cal", yloss="gaus")

matrix(unlist(late.cal$est), ncol=2, byrow=TRUE, 
dimnames=list(c("ipw", "or", "est", "var", "ze", 
 "late.est", "late.var", "late.ze"), c("theta1", "theta0")))