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# nb.reg.ml.r
# Synthetic MLE Negative Binomial NB2 data and model
# Table 9.11: Hilbe, Negative Binomial Regression, 2 ed, Cambridge Univ Press
# with assistance of: Andrew Robinson, University of Melbourne, Australia
#
set.seed(85132)
b <- c(5, 2, 3, 0.5) ## Population parameters
n <- 10000
X <- cbind(rlnorm(n), rlnorm(n)) ## Design matrix
y <- rnbinom(n = n, ## Choice of parameterization
mu = b[1] + b[2] * X[,1],
size = b[3] + b[4] * X[,2])
nb.reg.ml <- function(b.hat, X, y) { ## JCLL
sum(dnbinom(y,
mu = b.hat[1] + b.hat[2] * X[,1],
size = b.hat[3] + b.hat[4] * X[,2],
log = TRUE))
}
p.0 <- c(1,1,1,1) ## initial estimates
fit <- optim(p.0, ## Maximize the JCLL
nb.reg.ml,
X = X,
y = y,
control = list(fnscale = -1),
hessian = TRUE
)
stderr <- sqrt(diag(solve(-fit$hessian))) ## Asymptotic SEs
nbresults <- data.frame(fit$par, stderr)
nbresults
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