logitexp <- function(exposure = 1) 
{ linkfun <- function(mu) {            
                 eta <- if (any(exposure-mu <= 0)) log((mu)/abs(mu-exposure)) else log((mu)/(exposure-mu))
                      eta 
                       }

 linkinv <- function(eta) {
           thresh <- -log(.Machine$double.eps)
               eta <- pmin(thresh, pmax(eta, -thresh))
                      exposure*(exp(eta)/(1 + exp(eta)))
            }

mu.eta <- function(eta) 
     {
           thresh <- -log(.Machine$double.eps)
               res <- rep(.Machine$double.eps, length(eta))
            res[abs(eta) < thresh] <- ((exposure*exp(eta))/(1 + exp(eta))^2)[abs(eta) < thresh]
            res
           }
 
valideta <- function(eta) TRUE 
link <- paste("logexp(", exposure, ")", sep="") 
structure(list(linkfun = linkfun, linkinv = linkinv, mu.eta = mu.eta, 
              valideta = valideta, name = link), class = "link-glm") }