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# Generic synthetic NB-C model
# Table 10.9, Hilbe, J.M., Negative Binomial Regression, 2nd ed.
# Cambridge Univ Press nbc_syn.r
require(MASS)
nbc_syn <- function(nobs = 50000,
alpha = 1.15,
xv = c(-1.5, -1.25, -.1)) {
q <- length(xv) - 1
X <- cbind(1, matrix(runif(nobs * q), ncol = q))
xb <- X %*% xv
a <- alpha
mu <- 1/((exp(-xb)-1)*a)
p <- 1/(1+a*mu)
r <- 1/a
nbcy <- rnbinom(nobs, size=r, prob = p)
out <- data.frame(cbind(nbcy, X[,-1]))
names(out) <- c("nbcy", paste("x", 1:q, sep=""))
return(out)
}
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