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loglog_link_private <-function( guessing, lapsing ) {
#
# THIS IS AN INTERNAL FUNCTION: USE LOGLOG_LINK INSTEAD
#
# Log-log link for use with GLM functions
#
# The guessing rate and lapsing rate are fixed, hence link is
# a function of only one variable.
#
# INPUT
#
# guessing - guessing rate
# lapsing - lapsing rate
#
# OUTPUT
#
# link - log-log link for use in all GLM functions
# LINK FUNCTIONS
# LOGLOG WITH LIMITS
# link
loglogFL<-function( mu, g, l ) {
mu <- pmax( pmin( l - .Machine$double.eps, mu) , g
+ .Machine$double.eps );
return( -log( -log( ( mu - g ) / ( l - g ) ) ) );
}
# derivative
loglogFD<-function( eta, g, l ) {
eta <- pmax( -log( -log( ( .Machine$double.eps ) / ( l - g ) ) ), eta );
eta <- pmin( -log( -log( 1 - .Machine$double.eps / ( l - g ) ) ), eta );
return( ( l - g ) * exp( -exp( -eta ) - eta ) );
}
# inverse link
loglogFI<-function( eta, g, l ) {
eta <- pmax( -log( -log( ( .Machine$double.eps ) / ( l - g ) ) ), eta );
eta <- pmin( -log( -log( 1 - .Machine$double.eps / ( l - g ) ) ), eta );
return( g + ( l - g ) * exp( -exp( -eta ) ) );
}
# User-defined link
linkuser <- function( guessing, lapsing ) {
linkl <- "loglogFL";
linkd <- "loglogFD";
linki <- "loglogFI";
linkfun <- function(mu) eval( call( linkl, mu, guessing, 1-lapsing ) );
linkinv <- function(eta) eval( call( linki, eta, guessing, 1-lapsing ) );
mu.eta <- function(eta) eval( call( linkd, eta, guessing, 1-lapsing ) );
link <- paste("loglog( ", "c(", guessing, ", ", 1-lapsing, ")", " )",
sep = "" );
structure(list(linkfun = linkfun, linkinv = linkinv,
mu.eta = mu.eta, name = link),
class = "link-glm" );
}
# MAIN PROGRAM
return( linkuser( guessing, lapsing ) );
}
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