```
# Example 1: fit a MLM to Edgar Anderson's iris data
data(iris)
if (FALSE) fit <- vglm(Species ~ ., multinomial, iris)
coef(fit, matrix = TRUE)
# Example 2a: a simple example
ycounts <- t(rmultinom(10, size = 20, prob = c(0.1, 0.2, 0.8)))
fit <- vglm(ycounts ~ 1, multinomial)
head(fitted(fit)) # Proportions
fit@prior.weights # NOT recommended for the prior weights
weights(fit, type = "prior", matrix = FALSE) # The better method
depvar(fit) # Sample proportions; same as fit@y
constraints(fit) # Constraint matrices
# Example 2b: Different reference level used as the baseline
fit2 <- vglm(ycounts ~ 1, multinomial(refLevel = 2))
coef(fit2, matrix = TRUE)
coef(fit , matrix = TRUE) # Easy to reconcile this output with fit2
# Example 3: The response is a factor.
nn <- 10
dframe3 <- data.frame(yfac = gl(3, nn, labels = c("Ctrl",
"Trt1", "Trt2")),
x2 = runif(3 * nn))
myrefLevel <- with(dframe3, yfac[12])
fit3a <- vglm(yfac ~ x2, multinomial(refLevel = myrefLevel), dframe3)
fit3b <- vglm(yfac ~ x2, multinomial(refLevel = 2), dframe3)
coef(fit3a, matrix = TRUE) # "Trt1" is the reference level
coef(fit3b, matrix = TRUE) # "Trt1" is the reference level
margeff(fit3b)
# Example 4: Fit a rank-1 stereotype model
fit4 <- rrvglm(Country ~ Width + Height + HP, multinomial, car.all)
coef(fit4) # Contains the C matrix
constraints(fit4)$HP # The A matrix
coef(fit4, matrix = TRUE) # The B matrix
Coef(fit4)@C # The C matrix
concoef(fit4) # Better to get the C matrix this way
Coef(fit4)@A # The A matrix
svd(coef(fit4, matrix = TRUE)[-1, ])$d # Has rank 1; = C %*% t(A)
# Classification (but watch out for NAs in some of the variables):
apply(fitted(fit4), 1, which.max) # Classification
# Classification:
colnames(fitted(fit4))[apply(fitted(fit4), 1, which.max)]
apply(predict(fit4, car.all, type = "response"),
1, which.max) # Ditto
# Example 5: Using the xij argument (aka conditional logit model)
set.seed(111)
nn <- 100 # Number of people who travel to work
M <- 3 # There are M+1 models of transport to go to work
ycounts <- matrix(0, nn, M+1)
ycounts[cbind(1:nn, sample(x = M+1, size = nn, replace = TRUE))] = 1
dimnames(ycounts) <- list(NULL, c("bus","train","car","walk"))
gotowork <- data.frame(cost.bus = runif(nn), time.bus = runif(nn),
cost.train= runif(nn), time.train= runif(nn),
cost.car = runif(nn), time.car = runif(nn),
cost.walk = runif(nn), time.walk = runif(nn))
gotowork <- round(gotowork, digits = 2) # For convenience
gotowork <- transform(gotowork,
Cost.bus = cost.bus - cost.walk,
Cost.car = cost.car - cost.walk,
Cost.train = cost.train - cost.walk,
Cost = cost.train - cost.walk, # for labelling
Time.bus = time.bus - time.walk,
Time.car = time.car - time.walk,
Time.train = time.train - time.walk,
Time = time.train - time.walk) # for labelling
fit <- vglm(ycounts ~ Cost + Time,
multinomial(parall = TRUE ~ Cost + Time - 1),
xij = list(Cost ~ Cost.bus + Cost.train + Cost.car,
Time ~ Time.bus + Time.train + Time.car),
form2 = ~ Cost + Cost.bus + Cost.train + Cost.car +
Time + Time.bus + Time.train + Time.car,
data = gotowork, trace = TRUE)
head(model.matrix(fit, type = "lm")) # LM model matrix
head(model.matrix(fit, type = "vlm")) # Big VLM model matrix
coef(fit)
coef(fit, matrix = TRUE)
constraints(fit)
summary(fit)
max(abs(predict(fit) - predict(fit, new = gotowork))) # Should be 0
```

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