In each bootstrap iteration, you want to do something like
range <- 1:100 # this could be any substantively meaningful range
p <- predict(glm.out, newdata = data.frame(CL=range), "response")
range[match(TRUE,p>.5)] # predicted probability of 50% maturity
where you specify a range of values of CL to whatever precision you need. Then calculate the predicted probability of maturity at each of those levels. Then find the threshold value in the range where the predicted probability cross 0.5. This is the statistic it sounds like you want to bootstrap.
You also don't need the boot
to do this. If you define a function that samples and outputs that statistic as its result, you can just do replicate(1000, myfun)
to get your bootstrap distribution, as follows:
myfun <- function(){
srows <- sample(1:nrow(LowerChatham),nrow(LowerChatham),TRUE)
glm.out <- (Mature ~ CL, family=binomial(link=logit), data=LowerChatham[srows,])
range <- 1:100 # this could be any substantively meaningful range
p <- predict(glm.out, newdata = data.frame(CL=range), "response")
return(range[match(TRUE,p>.5)]) # predicted probability of 50% maturity
}
bootdist <- replicate(1000, myfun()) # your distribution
quantile(unlist(bootdist),c(.025,.975)) # 95% CI