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# p.reg.ml.r
# Poisson optimization
# Ch 6.2.1 : Hilbe, Negative Binomial Regression, 2 ed, Cambridge Univ Press
set.seed(3357)
b <- c(5, 1, 0.5) ## Population parameters
n <- 10000
X <- cbind(1, rnorm(n), rnorm(n)) ## Design matrix
y <- rpois(n = n, lambda = X %*% b)
p.reg.ml <- function(b.hat, X, y) { ## Joint Conditional LL
sum(dpois(y, lambda = X %*% b.hat, log = TRUE))
}
p.0 <- lm.fit(X, y)$coef ## Obtain initial estimates
fit <- optim(p.0, ## Maximize JCLL
p.reg.ml,
X = X,
y = y,
control = list(fnscale = -1),
hessian = TRUE
)
stderr <- sqrt(diag(solve(-fit$hessian))) ## Asymptotic SEs
poiresults <- data.frame(fit$par, stderr)
poiresults
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