loglik.g {iWeigReg}

The calibrated objective function ("log-likelihood")

Description

This function computes the objective function, its gradient and its Hessian matrix for the calibrated likelihood estimator in Tan (2010), Biometrika.

Arguments

lam

A vector of parameters ("lambda").

tr

A vector of non-missing or treatment indicators.

h

A constraint matrix.

pr

A vector of fitted propensity scores.

g

A matrix of calibration variables.

Value

value

The value of the objective function.

gradient

The gradient of the objective function.

hessian

The Hessian matrix of the objective function.

References

Tan, Z. (2006) "A distributional approach for causal inference using propensity scores," Journal of the American Statistical Association, 101, 1619-1637.

Tan, Z. (2010) "Bounded, efficient and doubly robust estimation with inverse weighting," Biometrika, 97, 661-682.

Examples

data(KS.data)
attach(KS.data)
z=cbind(z1,z2,z3,z4)
x=cbind(x1,x2,x3,x4)

#logistic propensity score model, correct
ppi.glm <- glm(tr~z, family=binomial(link=logit))
p <- ppi.glm$fitted

#outcome regression model, misspecified
y.fam <- gaussian(link=identity)

eta1.glm <- glm(y ~ x, subset=tr==1, 
               family=y.fam, control=glm.control(maxit=1000))
eta1.hat <- predict.glm(eta1.glm, 
               newdata=data.frame(x=x), type="response")

#
g1 <- cbind(1,eta1.hat)
h <- cbind(p, (1-p)*g1)

loglik.g(lam=rep(0,dim(g1)[2]), tr=tr, h=h, pr=p, g=g1)