Fits multinomial log-linear models via neural networks.

```
multinom(formula, data, weights, subset, na.action,
contrasts = NULL, Hess = FALSE, summ = 0, censored = FALSE,
model = FALSE, …)
```

formula

a formula expression as for regression models, of the form
`response ~ predictors`

. The response should be a factor or a
matrix with K columns, which will be interpreted as counts for each of
K classes.
A log-linear model is fitted, with coefficients zero for the first
class. An offset can be included: it should be a numeric matrix with K columns
if the response is either a matrix with K columns or a factor with K >= 2
classes, or a numeric vector for a response factor with 2 levels.
See the documentation of `formula()`

for other details.

data

an optional data frame in which to interpret the variables occurring
in `formula`

.

weights

optional case weights in fitting.

subset

expression saying which subset of the rows of the data should be used in the fit. All observations are included by default.

na.action

a function to filter missing data.

contrasts

a list of contrasts to be used for some or all of the factors appearing as variables in the model formula.

Hess

logical for whether the Hessian (the observed/expected information matrix) should be returned.

summ

integer; if non-zero summarize by deleting duplicate rows and adjust weights.
Methods 1 and 2 differ in speed (2 uses `C`

); method 3 also combines rows
with the same X and different Y, which changes the baseline for the
deviance.

censored

If Y is a matrix with `K`

columns, interpret the entries as one
for possible classes, zero for impossible classes, rather than as
counts.

model

logical. If true, the model frame is saved as component `model`

of the returned object.

…

additional arguments for `nnet`

A `nnet`

object with additional components:

the residual deviance, compared to the full saturated model (that explains individual observations exactly). Also, minus twice log-likelihood.

the (effective) number of degrees of freedom used by the model

the AIC for this fit.

(if `Hess`

is true).

(if `model`

is true).

`multinom`

calls `nnet`

. The variables on the rhs of
the formula should be roughly scaled to [0,1] or the fit will be slow
or may not converge at all.

Venables, W. N. and Ripley, B. D. (2002)
*Modern Applied Statistics with S.* Fourth edition. Springer.

```
# NOT RUN {
oc <- options(contrasts = c("contr.treatment", "contr.poly"))
library(MASS)
example(birthwt)
(bwt.mu <- multinom(low ~ ., bwt))
options(oc)
# }
```

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