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, ...)
```

A `nnet`

object with additional components:

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

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

- AIC
the AIC for this fit.

- Hessian
(if

`Hess`

is true).- model
(if

`model`

is true).

- 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`

`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.

`nnet`

```
oc <- options(contrasts = c("contr.treatment", "contr.poly"))
library(MASS)
example(birthwt)
(bwt.mu <- multinom(low ~ ., bwt))
options(oc)
```

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