# nominal_test

##### Likelihood ratio tests of model terms in scale and nominal formulae

Add all model terms to scale and nominal formulae and perform
likelihood ratio tests. These tests can be viewed as goodness-of-fit
tests. With the logit link, `nominal_test`

provides likelihood
ratio tests of the proportional odds assumption. The `scale_test`

tests can be given a similar interpretation.

- Keywords
- models

##### Usage

`nominal_test(object, ...)`# S3 method for clm
nominal_test(object, scope, trace=FALSE, ...)

scale_test(object, ...)

# S3 method for clm
scale_test(object, scope, trace=FALSE, ...)

##### Arguments

- object
for the

`clm`

method an object of class`"clm"`

, i.e., the result of a call to`clm`

.- scope
a formula or character vector specifying the terms to add to scale or nominal. In

`nominal_test`

terms in scope already in`nominal`

are ignored. In`scale_test`

terms in scope already in`scale`

are ignored.In

`nominal_test`

the default is to add all terms from`formula`

(location part) and`scale`

that are not also in`nominal`

.In

`scale_test`

the default is to add all terms from`formula`

(location part) that are not also in`scale`

.- trace
if

`TRUE`

additional information may be given on the fits as they are tried.- …
arguments passed to or from other methods.

##### Details

The definition of AIC is only up to an additive constant because the likelihood function is only defined up to an additive constant.

##### Value

A table of class `"anova"`

containing columns for the change
in degrees of freedom, AIC, the likelihood ratio statistic and a
p-value based on the asymptotic chi-square distribtion of the
likelihood ratio statistic under the null hypothesis.

##### Examples

```
# NOT RUN {
## Fit cumulative link model:
fm <- clm(rating ~ temp + contact, data=wine)
summary(fm)
## test partial proportional odds assumption for temp and contact:
nominal_test(fm)
## no evidence of non-proportional odds.
## test if there are signs of scale effects:
scale_test(fm)
## no evidence of scale effects.
## tests of scale and nominal effects for the housing data from MASS:
if(require(MASS)) {
fm1 <- clm(Sat ~ Infl + Type + Cont, weights = Freq, data = housing)
scale_test(fm1)
nominal_test(fm1)
## Evidence of multiplicative/scale effect of 'Cont'. This is a breach
## of the proportional odds assumption.
}
# }
```

*Documentation reproduced from package ordinal, version 2019.12-10, License: GPL (>= 2)*