estfun {ivtools}

Computes the estimating function sum for "ivmod" objects, fitted with estmethod="g".

Description

estfun computes the estimating function H(\psi) for a "ivmod" object, fitted with estmethod="g", for a range of values of \psi. The estfun is not implemented for "ivah" objects, since G-estimation in additive hazards models is based on a recursive estimation technique, and not standard estimating equations.

Usage

estfun(object, lower, upper, step)

Arguments

object

an object of class "ivmod", fitted with estmethod="g".

lower

an optional vector of lower values for \psi. Defaults to \psi-0.5.

upper

an optional vector of upper values for \psi. Defaults to \psi+0.5.

step

an optional vector of steps between lower and upper. Defaults to 0.01 for each element of \psi.

Details

estfun may be useful for visual inspection of the estimating function, to make sure that a solution to the estimating equation

H(\psi)=0

was found, see ‘Examples’. For the i:th element of \psi, the estimating function sum is computed for a range of values within (lower[i], upper[i]), at the G-estimate of the remaining elements of \psi.

Value

An object of class "estfun" is a list containing

f

a named list of matricies; one matrix for each element of \psi. The first column of the i:th matrix contains the values for the i:th element of \psi at which the estimating function sum is computed, the second column contains the values of the estimating function sum.

est

the G-estimate of \psi.

Author(s)

Arvid Sjolander.

References

Burgess S, Granell R, Palmer TM, Sterne JA, Didelez V. (2014). Lack of identification in semiparametric instrumental variable models with binary outcomes. American Journal of Epidemiology 180(1), 111-119.

Vansteelandt S., Bowden J., Babanezhad M., Goetghebeur E. (2011). On instrumental variables estimation of causal odds ratios. Statistical Science 26(3), 403-422.

Examples

set.seed(9)

##Note: the parameter values in the examples below are chosen to make 
##Y0 independent of Z, which is necessary for Z to be a valid instrument.

n <- 1000
psi0 <- 0.5
psi1 <- 0.2

##---Example 1: linear model and interaction between X and L---

L <- rnorm(n)
Z <- rnorm(n, mean=L)
X <- rnorm(n, mean=Z)
m0 <- X-Z+L 
Y <- rnorm(n, mean=psi0*X+psi1*X*L+m0)
data <- data.frame(L, Z, X, Y)

#G-estimation
fitZ.L <- glm(formula=Z~L, data=data)
fitIV <- ivglm(estmethod="g", X="X", Y="Y", fitZ.L=fitZ.L, data=data, 
  formula=~L, link="identity")
summary(fitIV)
H <- estfun(fitIV)
plot(H)

##---Example 2: logistic model and no covariates--- 

Z <- rbinom(n, 1, 0.5)
X <- rbinom(n, 1, 0.7*Z+0.2*(1-Z)) 
m0 <- plogis(1+0.8*X-0.39*Z)
Y <- rbinom(n, 1, plogis(psi0*X+log(m0/(1-m0)))) 
data <- data.frame(Z, X, Y)

#G-estimation
fitZ.L <- glm(formula=Z~1, data=data)
fitY.LZX <- glm(formula=Y~X+Z+X*Z, family="binomial", data=data)
fitIV <- ivglm(estmethod="g", X="X", fitZ.L=fitZ.L, fitY.LZX=fitY.LZX, 
  data=data, link="logit")
summary(fitIV)
H <- estfun(fitIV)
plot(H)