# cratio

##### Ordinal Regression with Continuation Ratios

Fits a continuation ratio logit/probit/cloglog/cauchit/... regression model to an ordered (preferably) factor response.

- Keywords
- models, regression

##### Usage

```
cratio(link = "logit", parallel = FALSE, reverse = FALSE, zero = NULL,
whitespace = FALSE)
```

##### Arguments

- link
Link function applied to the \(M\) continuation ratio probabilities. See

`Links`

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

- reverse
Logical. By default, the continuation ratios used are \(\eta_j = logit(P[Y>j|Y \geq j])\) for \(j=1,\dots,M\). If

`reverse`

is`TRUE`

, then \(\eta_j = logit(P[Y<j+1|Y\leq j+1])\) 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,…,\(M\)}. The default value means none are modelled as intercept-only terms.

- whitespace
See

`CommonVGAMffArguments`

for information.

##### Details

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

There are a number of definitions for the *continuation ratio*
in the literature. To make life easier, in the VGAM package,
we use *continuation* ratios and *stopping* ratios
(see `sratio`

).
Stopping ratios deal with quantities such as
`logit(P[Y=j|Y>=j])`

.

##### 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 a
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.

McCullagh, P. and Nelder, J. A. (1989)
*Generalized Linear Models*, 2nd ed. London: Chapman & Hall.

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

`sratio`

,
`acat`

,
`cumulative`

,
`multinomial`

,
`margeff`

,
`pneumo`

,
`logit`

,
`probit`

,
`cloglog`

,
`cauchit`

.

##### Examples

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

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