sratio {VGAM} | R Documentation

## Ordinal Regression with Stopping Ratios

### Description

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

### Usage

    sratio(link = "logitlink", parallel = FALSE, reverse = FALSE,
           zero = NULL, whitespace = FALSE)

### Arguments

`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>=j]) for j=1,…,M. If `reverse` is `TRUE`, then eta_j = logit(P[Y=j+1|Y<=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.
`whitespace` | See `CommonVGAMffArguments` for information.

### Details

In this help file the response Y is assumed to be a factor with ordered values 1,2,…,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])`.

### Value

An object of class `"vglmff"` (see `vglmff-class`). The object is used by modelling functions such as `vglm`, `rrvglm` and `vgam`.

### Warning

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

### 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.

### Author(s)

Thomas W. Yee

### References

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

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

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

`cratio`, `acat`, `cumulative`, `multinomial`, `margeff`, `pneumo`, `logitlink`, `probitlink`, `clogloglink`, `cauchitlink`.

### Examples

    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)

[Package VGAM version 1.1-1 Index]