# Logistical Exposure Link Function
# See Shaffer, T.  2004. A unifying approach to analyzing nest success. 
# Auk 121(2): 526-540.
library(MASS)
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) *
      .Call("logit_mu_eta", eta, PACKAGE = "stats")
    valideta <- function(eta) TRUE
    link <- paste("logexp(", days, ")", sep="")
    structure(list(linkfun = linkfun, linkinv = linkinv,
                   mu.eta = mu.eta, valideta = valideta, name = link),
              class = "link-glm")
}

#Example using chat data from Shaffer(2004).
nestdata<-read.table("http://data.prbo.org/tools/NestSurvival/chat.txt")
chat.glm.logexp<-glm(survive/trials~parastat+nest_ht*patsize,family=binomial(logexp(days=nestdata$expos)),data=nestdata)
# if you have MASS installed
library(MASS)
chat.step<-stepAIC(chat.glm.logexp,scope=list(upper=~parastat+nest_ht*patsize,lower=~1))
chat.step$anova
summary(chat.step)
#Not run:
# note this compares to following results from SAS :
#              Criteria For Assessing Goodness Of Fit
#
#    Criterion                 DF           Value        Value/DF
#    Deviance                 289        193.9987          0.6713
#    Scaled Deviance          289        193.9987          0.6713
#    Pearson Chi-Square       289        537.8609          1.8611
#    Scaled Pearson X2        289        537.8609          1.8611
#    Log Likelihood                      -96.9994
#    Algorithm converged.
#                       Analysis Of Parameter Estimates
#
#                                Standard Wald 95%   Chi-
#Parameter   DF  Estimate Error        Limits       Square Pr > ChiSq
##Intercept   1  2.6973   0.2769   2.1546  3.2399   94.92  <.0001
#parastat0    1 -1.0350   0.5201  -2.0544  -0.0155  3.96   0.0466
#parastat1    0  0.0000   0.0000   0.0000  0.0000     .      .
#patsizelarge 1  1.0844   0.5094   0.0861  2.0827   4.53   0.0333
#patsizesmall 0  0.0000   0.0000   0.0000  0.0000     .       .
#Scale        0  1.0000   0.0000   1.0000  1.0000
#
#NOTE: The scale parameter was held fixed.