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# syn.nb2o.r Synthetic NB2 with offset
# Table 9.9: Hilbe, Negative Binomial Regression, 2 ed, Cambridge Univ Press
library(MASS)
x1 <- qnorm(runif(50000))
x2 <- qnorm(runif(50000))
off <- rep(1:5, each=10000, times=1)*100 # offset
loff <- log(off) # log of offset
xb<-2 + .75*x1 -1.25*x2 + loff # linear predictor
exb <-exp(xb) # inverse link
a <- .5 # assign value to alpha
ia <- 1/.5 # invert alpha
xg <- rgamma(n = 50000, shape = a, rate = a) # generate gamma variates w alpha
xbg <-exb*xg # mix Poisson and gamma variates
nbyo <- rpois(50000, xbg) # generate NB2 variates - w offset
nb2o <-glm.nb(nbyo ~ x1 + x2 + offset(loff)) # model NB2
summary(nb2o)
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