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

```
sratio(link = "logitlink", parallel = FALSE, reverse = FALSE,
zero = NULL, thresholds = c("unconstrained", "equidistant",
"symmetric1", "symmetric0"), Treverse = reverse,
Tref = if (Treverse) "M" else 1, whitespace = FALSE)
```

An object of class `"vglmff"`

(see `vglmff-class`

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

,

`rrvglm`

and `vgam`

.

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

`Links`

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

- reverse
Logical. By default, the stopping 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
Can be 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. See

`CommonVGAMffArguments`

for information.- thresholds, Treverse, Tref
See

`cumulative`

for information. These arguments apply to ordinal categorical regression models.- whitespace
See

`CommonVGAMffArguments`

for information.

Thomas W. Yee

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

.

Boersch-Supan (2021) considers a sparse data set
(called `budworm`

)
and the numerical problems encountered when
fitting models such as
`cratio`

,
`sratio`

,
`cumulative`

.
Although improvements to links such as
`clogloglink`

have been made,
currently these family functions have not been
properly adapted to handle sparse data as well as they could.

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 (see `cratio`

)
and *stopping* ratios.
Continuation ratios deal with quantities such as
`logitlink(P[Y>j|Y>=j])`

.

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

Boersch-Supan, P. H. (2021).
Modeling insect phenology using ordinal
regression and continuation ratio models.
*ReScience C*,
**7.1**, 1--14.
tools:::Rd_expr_doi("10.18637/jss.v032.i10").

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

Tutz, G. (2012).
*Regression for Categorical Data*,
Cambridge: Cambridge University Press.

Yee, T. W. (2010).
The VGAM package for categorical data analysis.
*Journal of Statistical Software*,
**32**, 1--34.
tools:::Rd_expr_doi("10.18637/jss.v032.i10").

`cratio`

,
`acat`

,
`cumulative`

,
`multinomial`

,
`margeff`

,
`pneumo`

,
`budworm`

,
`logitlink`

,
`probitlink`

,
`clogloglink`

,
`cauchitlink`

.

```
pneumo <- transform(pneumo, let = log(exposure.time))
(fit <- vglm(cbind(normal, mild, severe) ~ let,
sratio(parallel = TRUE), data = pneumo))
coef(fit, matrix = TRUE)
constraints(fit)
predict(fit)
predict(fit, untransform = TRUE)
```

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