# Computes the estimating function sum for `"ivmod"` objects, fitted with `estmethod="g"`. `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. ```r 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 $\psi$. ## Returns 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 $\psi$. ## 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. ## Author(s) Arvid Sjolander. ## Examples ```r 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) ```

estfun function