#' getD
#'
#' Takes betas and x.matrix and returns matrix of partial derivatives dmu/dbeta
#' @param betas p vector of regression parameters
#' @param x.matrix nxp matrix of covariates
#' @param link link between xbeta and the mean, identify for normal, logit for logistic, Gammalog for gamma (should work)
#' @return matrix of partial derivatives dmu/dbeta
getD<-function(betas, x.matrix, link){
if(link=="identity") return(x.matrix)
if(link=="logit"){
p=length(betas)
D<-x.matrix
logit<-x.matrix %*% betas
pi<-exp(logit)/((1+exp(logit))^2)
for(i in 1:p){
D[,i]<-x.matrix[,i]*pi
}
}
if(link %in% c("Gammalog", "Poissonlog")){
p=length(betas)
D<-x.matrix
mu_i<-exp(x.matrix%*%betas)
for(i in 1:p){
D[,i]<-x.matrix[,i]*mu_i
}
}
return(D)
}
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