```
# NOT RUN {
# Example 1: RR negative binomial with Var(Y) = mu + delta1 * mu^delta2
nn <- 1000 # Number of observations
delta1 <- 3.0 # Specify this
delta2 <- 1.5 # Specify this; should be greater than unity
a21 <- 2 - delta2
mydata <- data.frame(x2 = runif(nn), x3 = runif(nn))
mydata <- transform(mydata, mu = exp(2 + 3 * x2 + 0 * x3))
mydata <- transform(mydata,
y2 = rnbinom(nn, mu = mu, size = (1/delta1)*mu^a21))
plot(y2 ~ x2, data = mydata, pch = "+", col = 'blue', las = 1,
main = paste("Var(Y) = mu + ", delta1, " * mu^", delta2, sep = ""))
rrnb2 <- rrvglm(y2 ~ x2 + x3, negbinomial(zero = NULL),
data = mydata, trace = TRUE)
a21.hat <- (Coef(rrnb2)@A)["loglink(size)", 1]
beta11.hat <- Coef(rrnb2)@B1["(Intercept)", "loglink(mu)"]
beta21.hat <- Coef(rrnb2)@B1["(Intercept)", "loglink(size)"]
(delta1.hat <- exp(a21.hat * beta11.hat - beta21.hat))
(delta2.hat <- 2 - a21.hat)
# exp(a21.hat * predict(rrnb2)[1,1] - predict(rrnb2)[1,2]) # delta1.hat
summary(rrnb2)
# Obtain a 95 percent confidence interval for delta2:
se.a21.hat <- sqrt(vcov(rrnb2)["I(latvar.mat)", "I(latvar.mat)"])
ci.a21 <- a21.hat + c(-1, 1) * 1.96 * se.a21.hat
(ci.delta2 <- 2 - rev(ci.a21)) # The 95 percent confidence interval
Confint.rrnb(rrnb2) # Quick way to get it
# Plot the abundances and fitted values against the latent variable
plot(y2 ~ latvar(rrnb2), data = mydata, col = "blue",
xlab = "Latent variable", las = 1)
ooo <- order(latvar(rrnb2))
lines(fitted(rrnb2)[ooo] ~ latvar(rrnb2)[ooo], col = "orange")
# Example 2: stereotype model (reduced-rank multinomial logit model)
data(car.all)
scar <- subset(car.all,
is.element(Country, c("Germany", "USA", "Japan", "Korea")))
fcols <- c(13,14,18:20,22:26,29:31,33,34,36) # These are factors
scar[, -fcols] <- scale(scar[, -fcols]) # Standardize all numerical vars
ones <- matrix(1, 3, 1)
clist <- list("(Intercept)" = diag(3), Width = ones, Weight = ones,
Disp. = diag(3), Tank = diag(3), Price = diag(3),
Frt.Leg.Room = diag(3))
set.seed(111)
fit <- rrvglm(Country ~ Width + Weight + Disp. + Tank +
Price + Frt.Leg.Room,
multinomial, data = scar, Rank = 2, trace = TRUE,
constraints = clist, noRRR = ~ 1 + Width + Weight,
Uncor = TRUE, Corner = FALSE, Bestof = 2)
fit@misc$deviance # A history of the fits
Coef(fit)
biplot(fit, chull = TRUE, scores = TRUE, clty = 2, Ccex = 2,
ccol = "blue", scol = "orange", Ccol = "darkgreen", Clwd = 2,
main = "1=Germany, 2=Japan, 3=Korea, 4=USA")
# }
```

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