```
# NOT RUN {
# Example 1: apple tree data (Bliss and Fisher, 1953)
appletree <- data.frame(y = 0:7, w = c(70, 38, 17, 10, 9, 3, 2, 1))
fit <- vglm(y ~ 1, negbinomial(deviance = TRUE), data = appletree,
weights = w, crit = "coef") # Obtain the deviance
fit <- vglm(y ~ 1, negbinomial(deviance = TRUE), data = appletree,
weights = w, half.step = FALSE) # Alternative method
summary(fit)
coef(fit, matrix = TRUE)
Coef(fit) # For intercept-only models
deviance(fit) # NB2 only; needs 'crit = "coef"' & 'deviance = TRUE' above
# Example 2: simulated data with multiple responses
# }
# NOT RUN {
ndata <- data.frame(x2 = runif(nn <- 200))
ndata <- transform(ndata, y1 = rnbinom(nn, mu = exp(3+x2), size = exp(1)),
y2 = rnbinom(nn, mu = exp(2-x2), size = exp(0)))
fit1 <- vglm(cbind(y1, y2) ~ x2, negbinomial, data = ndata, trace = TRUE)
coef(fit1, matrix = TRUE)
# }
# NOT RUN {
# Example 3: large counts implies SFS is used
# }
# NOT RUN {
ndata <- transform(ndata, y3 = rnbinom(nn, mu = exp(10+x2), size = exp(1)))
with(ndata, range(y3)) # Large counts
fit2 <- vglm(y3 ~ x2, negbinomial, data = ndata, trace = TRUE)
coef(fit2, matrix = TRUE)
head(fit2@weights) # Non-empty; SFS was used
# }
# NOT RUN {
# Example 4: a NB-1 to estimate a negative binomial with Var(Y) = phi0 * mu
nn <- 200 # Number of observations
phi0 <- 10 # Specify this; should be greater than unity
delta0 <- 1 / (phi0 - 1)
mydata <- data.frame(x2 = runif(nn), x3 = runif(nn))
mydata <- transform(mydata, mu = exp(2 + 3 * x2 + 0 * x3))
mydata <- transform(mydata, y3 = rnbinom(nn, mu = mu, size = delta0 * mu))
# }
# NOT RUN {
plot(y3 ~ x2, data = mydata, pch = "+", col = "blue",
main = paste("Var(Y) = ", phi0, " * mu", sep = ""), las = 1)
# }
# NOT RUN {
nb1 <- vglm(y3 ~ x2 + x3, negbinomial(parallel = TRUE, zero = NULL),
data = mydata, trace = TRUE)
# Extracting out some quantities:
cnb1 <- coef(nb1, matrix = TRUE)
mydiff <- (cnb1["(Intercept)", "loglink(size)"] -
cnb1["(Intercept)", "loglink(mu)"])
delta0.hat <- exp(mydiff)
(phi.hat <- 1 + 1 / delta0.hat) # MLE of phi
summary(nb1)
# Obtain a 95 percent confidence interval for phi0:
myvec <- rbind(-1, 1, 0, 0)
(se.mydiff <- sqrt(t(myvec) %*% vcov(nb1) %*% myvec))
ci.mydiff <- mydiff + c(-1.96, 1.96) * c(se.mydiff)
ci.delta0 <- ci.exp.mydiff <- exp(ci.mydiff)
(ci.phi0 <- 1 + 1 / rev(ci.delta0)) # The 95 percent conf. interval for phi0
Confint.nb1(nb1) # Quick way to get it
summary(glm(y3 ~ x2 + x3, quasipoisson, mydata))$disper # cf. moment estimator
# }
```

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