# acat

##### Ordinal Regression with Adjacent Categories Probabilities

Fits an adjacent categories regression model to an ordered (preferably) factor response.

- Keywords
- models, regression

##### Usage

```
acat(link = "loge", parallel = FALSE, reverse = FALSE,
zero = NULL, whitespace = FALSE)
```

##### Arguments

- link
Link function applied to the ratios of the adjacent categories probabilities. See

`Links`

for more choices.- parallel
A logical, or formula specifying which terms have equal/unequal coefficients.

- reverse
Logical. By default, the linear/additive predictors used are \(\eta_j = \log(P[Y=j+1]/P[Y=j])\) for \(j=1,\ldots,M\). If

`reverse`

is`TRUE`

then \(\eta_j = \log(P[Y=j]/P[Y=j+1])\) will be used.- zero
An integer-valued vector specifying which linear/additive predictors are modelled as intercepts only. The values must be from the set {1,2,…,\(M\)}.

- whitespace
See

`CommonVGAMffArguments`

for information.

##### Details

In this help file the response \(Y\) is assumed to be a factor with ordered values \(1,2,\ldots,M+1\), so that \(M\) is the number of linear/additive predictors \(\eta_j\).

By default, the log link is used because the ratio of two probabilities is positive.

##### Value

An object of class `"vglmff"`

(see `vglmff-class`

).
The object is used by modelling functions such as `vglm`

,
`rrvglm`

and `vgam`

.

##### Note

The response should be either a matrix of counts (with row sums that are
all positive), or an ordered factor. In both cases, the `y`

slot returned
by `vglm`

/`vgam`

/`rrvglm`

is the matrix of counts.

For a nominal (unordered) factor response, the multinomial logit model
(`multinomial`

) is more appropriate.

Here is an example of the usage of the `parallel`

argument.
If there are covariates `x1`

, `x2`

and `x3`

, then
`parallel = TRUE ~ x1 + x2 -1`

and ```
parallel = FALSE ~
x3
```

are equivalent. This would constrain the regression coefficients
for `x1`

and `x2`

to be equal; those of the intercepts and
`x3`

would be different.

##### Warning

No check is made to verify that the response is ordinal if the
response is a matrix;
see `ordered`

.

##### References

Agresti, A. (2013)
*Categorical Data Analysis*,
3rd ed. Hoboken, NJ, USA: Wiley.

Simonoff, J. S. (2003)
*Analyzing Categorical Data*,
New York: Springer-Verlag.

Yee, T. W. (2010)
The VGAM package for categorical data analysis.
*Journal of Statistical Software*,
**32**, 1--34.
http://www.jstatsoft.org/v32/i10/.

##### See Also

##### Examples

```
# NOT RUN {
pneumo <- transform(pneumo, let = log(exposure.time))
(fit <- vglm(cbind(normal, mild, severe) ~ let, acat, data = pneumo))
coef(fit, matrix = TRUE)
constraints(fit)
model.matrix(fit)
# }
```

*Documentation reproduced from package VGAM, version 1.0-4, License: GPL-3*