RCAL (version 2.0)

glm.nreg: Non-regularied M-estimation for fitting generalized linear models

Description

This function implements non-regularizd M-estimation for fitting generalized linear models with continuous or binary responses, including maximum likelihood, calibrated estimation, and covariate-balancing estimation in the latter case of fitting propensity score models.

Usage

glm.nreg(y, x, iw = NULL, loss = "cal", init = NULL)

Arguments

y

An \(n\) x \(1\) response vector.

x

An \(n\) x \(p\) matix of covariates, excluding a constant.

iw

An \(n\) x \(1\) weight vector.

loss

A loss function used, which can be specified as "gaus" for continuous responses, or "ml", "cal", or "bal" for binary responses.

init

A \((p+1)\) x \(1\) vector of initial values (the intercept and coefficients).

Value

coef

The \((p+1)\) x \(1\) vector of estimated intercept and coefficients.

fit

The \(n\) x \(1\) vector of fitted values.

conv

Logical; 1 if loss="gaus" for continuous responses or convergence is obtained within 1000 iterations by glm with loss="ml" or trust with loss="cal" or "bal" for binary responses.

Details

Least squares estimation is implemented by calling lm for continuous responses (loss="gaus"). For binary responses, maximum likelihood estimation (loss="ml") is implemented by calling glm. Calibrated estimation (loss="cal") is implemented by using a trust-region algorithm in the R package trust to minimize the calibration loss, i.e., (6) in Tan (2020). Covariate-balancing estimation (loss="bal") in Imai and Ratkovic (2014) is implemented by using trust to minimize (36) in Tan (2020a).

References

Imai, K. and Ratkovic, M. (2014) Covariate balancing propensity score, Journal of the Royal Statistical Society, Ser. B, 76, 243-263.

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

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)

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

ps.ml <- glm.nreg(y=tr, x=x2, loss="ml")
check.ml <- mn.ipw(x2, tr, ps.ml$fit)
check.ml

ps.cal <- glm.nreg(y=tr, x=x2, loss="cal")
check.cal <- mn.ipw(x2, tr, ps.cal$fit)
check.cal  # should be numerically 0

ps.bal <- glm.nreg(y=tr, x=x2, loss="bal")
check.bal <- mn.ipw(x2, tr, ps.bal$fit)
check.bal

# }