I have fit a generalized additive model (GAM) using the mgcv package in R. My model has a dichotomous response variable and so i've used the binomial family link function. After creating the model I would like to do a little post-estimation inference above and beyond the plot.gam graphs.
I would like to take two x-values, for example, and calculate the risk ratio and 95% confidence intervals for that ratio. Obtaining the risk ratio seems fairly straightforward. I could transform the predictions into probabilities and simply divide the two probabilities corresponding to the x-values of interest in order to get the risk ratio. I am less certain how to get the confidence intervals.
In this link here: http://grokbase.com/t/r/r-help/125qbnw21a/r-mgcv-how-to-calculate-a-confidence-interval-of-a-ratio Simon Wood, the author of the mgcv package explained how to get the CIs for a log ratio using a poisson model. I'm uncertain how I would need to change the code to get the risk ratios and 95% CIs from my logistic model.
Here is a reproducible example provided by Simon Wood in the link above:
library(mgcv) ## simulate some data dat <- gamSim(1, n=1000, dist="poisson", scale=.25) ## fit log-linear model... b <- gam(y~s(x0)+s(x1)+s(x2)+s(x3), family=poisson, data=dat, method="REML") ## data at which predictions to be compared... pd <- data.frame(x0=c(.2,.3),x1=c(.5,.5),x2=c(.5,.5), x3=c(.5,.5)) ## log(E(y_1)/E(y_2)) = s(x_1) - s(x_2) Xp <- predict(b,newdata=pd,type="lpmatrix") ## ... Xp%*%coef(b) gives log(E(y_1)) and log(E(y_2)), ## so the required difference is computed as... diff <- (Xp[1,]-Xp[2,]) dly <- t(diff)%*%coef(b) ## required log ratio (diff of logs) se.dly <- sqrt(t(diff)%*%vcov(b)%*%diff) ## corresponding s.e. dly + c(-2,2)*se.dly ## 95%CI
Any help is greatly appreciated.