######################################################################
#  R function for fitting a binomial regression with a log link,
#  using Fisher scoring.
######################################################################
log.binomial<-function(x,y,n,maxits=20,eps=1e-10,beta.start){
   if( missing(beta.start) ){
      emp.log<-log((y+.5)/(n+1)) # add 1/2 success, 1/2 failure
      newbeta<-lsfit(x,emp.log,intercept=F)$coef}
   else{newbeta<-beta.start}
   iter<-0
   converged<-F
   while( (!converged) & (iter<maxits) ){
      iter<-iter+1
      cat(iter); cat("...")
      beta<-newbeta
      pi<-as.vector(exp(x%*%beta))
      mu<-n*pi
      u<-diag(1/(1-pi))
      w<-diag(n*pi/(1-pi))
      xtwx<-t(x)%*%w%*%x
      xtwxinv<-solve(xtwx)
      newbeta<-beta + xtwxinv%*%t(x)%*%u%*%(y-mu)
      converged<-all(abs(newbeta-beta)<eps)}
   cat("\n")
   pi<-exp(x%*%newbeta)
   loglik<-sum( y*log(pi) + (n-y)*log(1-pi) )
   result<-list(beta=newbeta, cov.beta=xtwxinv, iter=iter, 
      converged=converged, loglik=loglik)
   result}