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Multinomial logistic regression values

`pihat = mnrval(B,X)`

```
[pihat,dlow,dhi]
= mnrval(B,X,stats)
```

```
[pihat,dlow,dhi]
= mnrval(B,X,stats,Name,Value)
```

`yhat = mnrval(B,X,ssize)`

```
[yhat,dlow,dhi]
= mnrval(B,X,ssize,stats)
```

```
[yhat,dlow,dhi]
= mnrval(B,X,ssize,stats,Name,Value)
```

returns
the predicted probabilities for the multinomial logistic regression
model with predictors, `pihat`

= mnrval(`B`

,`X`

)`X`

, and the coefficient estimates, `B`

.

`pihat`

is an *n*-by-*k* matrix
of predicted probabilities for each multinomial category. `B`

is
the vector or matrix that contains the coefficient estimates returned
by `mnrfit`

. And `X`

is
an *n*-by-*p* matrix which contains *n* observations
for *p* predictors.

`mnrval`

automatically includes a constant
term in all models. Do not enter a column of 1s in `X`

.

`[`

also
returns 95% error bounds on the predicted probabilities, `pihat`

,`dlow`

,`dhi`

]
= mnrval(`B`

,`X`

,`stats`

)`pihat`

,
using the statistics in the structure, `stats`

, returned
by `mnrfit`

.

The lower and upper confidence bounds for `pihat`

are `pihat`

minus `dlow`

and `pihat`

plus `dhi`

,
respectively. Confidence bounds are nonsimultaneous and only apply
to the fitted curve, not to new observations.

`[`

returns
the predicted probabilities and 95% error bounds on the predicted
probabilities `pihat`

,`dlow`

,`dhi`

]
= mnrval(`B`

,`X`

,`stats`

,`Name,Value`

)`pihat`

, with additional options specified
by one or more `Name,Value`

pair arguments.

For example, you can specify the model type, link function, and the type of probabilities to return.

`[`

also
computes 95% error bounds on the predicted counts `yhat`

,`dlow`

,`dhi`

]
= mnrval(`B`

,`X`

,`ssize`

,`stats`

)`yhat`

,
using the statistics in the structure, `stats`

, returned
by `mnrfit`

.

The lower and upper confidence bounds for `yhat`

are `yhat`

minus `dlo`

and `yhat`

plus `dhi`

,
respectively. Confidence bounds are nonsimultaneous and they apply
to the fitted curve, not to new observations.

`[`

returns
the predicted category counts and 95% error bounds on the predicted
counts `yhat`

,`dlow`

,`dhi`

]
= mnrval(`B`

,`X`

,`ssize`

,`stats`

,`Name,Value`

)`yhat`

, with additional options specified
by one or more `Name,Value`

pair arguments.

For example, you can specify the model type, link function, and the type of predicted counts to return.

[1] McCullagh, P., and J. A. Nelder. *Generalized
Linear Models*. New York: Chapman & Hall, 1990.

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