User-defined link function for glmer for known-fate survival modeling

Question

A common situation in ecology is a survival model with a binary outcome (0=die, 1=survive) where individuals (for this example think of individual nesting attempts by birds)

Answer 1

You need to use a more recent version of the lme4 package, e.g. the 1.0-4 version that has just gone up on CRAN. Earlier versions did not allow user-specified link functions.

Also, note that the code you posted above is not what appears in recent versions of ?family, where the (obsolete) .Call("logit_mu_eta", eta, PACKAGE = "stats") is replaced by a pure-R implementation:

logexp <- function(days = 1)
     {
         linkfun <- function(mu) qlogis(mu^(1/days))
         linkinv <- function(eta) plogis(eta)^days
         mu.eta <- function(eta) days * plogis(eta)^(days-1) * binomial()$mu_eta
         valideta <- function(eta) TRUE
         link <- paste0("logexp(", days, ")")
         structure(list(linkfun = linkfun, linkinv = linkinv,
                        mu.eta = mu.eta, valideta = valideta, name = link),
                   class = "link-glm")
     }

The link you specified above, http://rpubs.com/bbolker/4082 , does in fact have an example of such a model (but it does require a recent version of lme4).