#'
#' Function to calculate QICb
#'
#' @param model Model of class geeglm
#'
#' @author Lindesay Scott-Hayward, University of St Andrews
#'
#' @export
#'
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~#
#~~~~~~~~~~~~~~~ QICb ~~~~~~~~~~~~~~~~~~~~~~
# function to calculate a quasi version of a bic
# data inputs:
# data: vector of data
# fits: vector of fitted values from a model
# k: number of parameters estimated (length(coefficients))
# n: number of data points
QICb<-function(model){
data<-model$y
fits<-fitted(model)
k<-length(model$coeff)
n<-length(data)
if(model$family$family=='poisson' | model$family$family=='quasipoisson'){
ql<-sum(data*log(fits) - fits)
}
if(model$family$family=='binomial' | model$family$family=='quasibinomial'){
ql<-sum(data*(log(fits/(1-fits))) + log(1-fits))
}
if(model$family$family=='gaussian'){
ql <- -1/2 * sum((data - fits)^2)
}
-2*ql + k*log(n)
}
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