# estfun: Computes the estimating function sum for '"ivmod"' objects,... In ivtools: Instrumental Variables

## Description

`estfun` computes the estimating function H(ψ) for a `"ivmod"` object, fitted with `estmethod="g"`, for a range of values of ψ. 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

 `1` ```estfun(object, lower, upper, step) ```

## Arguments

 `object` an object of class `"ivmod"`, fitted with `estmethod="g"`. `lower` an optional vector of lower values for ψ. Defaults to ψ-0.5. `upper` an optional vector of upper values for ψ. Defaults to ψ+0.5. `step` an optional vector of steps between `lower` and `upper`. Defaults to 0.01 for each element of ψ.

## Details

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

H(ψ)=0

was found, see ‘Examples’. For the i:th element of ψ, 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 ψ.

## Value

An object of class `"estfun"` is a list containing

 `f` a named list of matricies; one matrix for each element of ψ. The first column of the i:th matrix contains the values for the i:th element of ψ at which the estimating function sum is computed, the second column contains the values of the estimating function sum. `est` the G-estimate of ψ.

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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42``` ```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) ```

ivtools documentation built on March 26, 2020, 7:14 p.m.