multinomial(zero = NULL, parallel = FALSE, nointercept = NULL,
refLevel = "last", whitespace = FALSE)CommonVGAMffArguments for more details."vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
rrvglm
and vgam.
See CommonVGAMffArguments for more warnings.
The default model can be written
refLevel argument.
In almost all the literature, the constraint matrices
associated with this family of models are known. For
example, setting parallel = TRUE will make all
constraint matrices (except for the intercept) equal to
a vector of $M$ 1's. If the constraint matrices are
unknown and to be estimated, then this can be achieved by
fitting the model as a reduced-rank vector generalized
linear model (RR-VGLM; see rrvglm).
In particular, a multinomial logit model with unknown
constraint matrices is known as a stereotype
model (Anderson, 1984), and can be fitted with
rrvglm.
Yee, T. W. and Hastie, T. J. (2003) Reduced-rank vector generalized linear models. Statistical Modelling, 3, 15--41.
McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models, 2nd ed. London: Chapman & Hall.
Agresti, A. (2002) Categorical Data Analysis, 2nd ed. New York, USA: Wiley.
Hastie, T. J., Tibshirani, R. J. and Friedman, J. H. (2009) The Elements of Statistical Learning: Data Mining, Inference and Prediction, 2nd ed. New York, USA: Springer-Verlag.
Simonoff, J. S. (2003) Analyzing Categorical Data, New York, USA: Springer-Verlag.
Anderson, J. A. (1984) Regression and ordered categorical variables. Journal of the Royal Statistical Society, Series B, Methodological, 46, 1--30.
Tutz, G. (2012) Regression for Categorical Data, Cambridge University Press.
margeff,
cumulative,
acat,
cratio,
sratio,
dirichlet,
dirmultinomial,
rrvglm,
fill1,
Multinomial,
multilogit,
iris.
The author's homepage has further documentation about
categorical data analysis using # Example 1: fit a multinomial logit model to Edgar Anderson's iris data
data(iris)
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))) # Counts
fit <- vglm(ycounts ~ 1, multinomial)
head(fitted(fit)) # Proportions
fit@prior.weights # NOT recommended for extraction of 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(yfactor = gl(3, nn, labels = c("Control", "Trt1", "Trt2")),
x2 = runif(3 * nn))
myrefLevel <- with(dframe3, yfactor[12])
fit3a <- vglm(yfactor ~ x2, multinomial(refLevel = myrefLevel), dframe3)
fit3b <- vglm(yfactor ~ x2, multinomial(refLevel = 2), dframe3)
coef(fit3a, matrix = TRUE) # "Treatment1" is the reference level
coef(fit3b, matrix = TRUE) # "Treatment1" is the reference level
margeff(fit3b)
# Example 4: Fit a rank-1 stereotype model
fit4 <- rrvglm(Country ~ Width + Height + HP, multinomial, data = 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 # This has rank 1; = C %*% t(A)
# Classification (but watch out for NAs in some of the variables):
apply(fitted(fit4), 1, which.max) # Classification
colnames(fitted(fit4))[apply(fitted(fit4), 1, which.max)] # Classification
apply(predict(fit4, car.all, type = "response"), 1, which.max) # Ditto
# Example 5: The use of 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 0Run the code above in your browser using DataLab