acat {VGAM} | R Documentation

## Ordinal Regression with Adjacent Categories Probabilities

### Description

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

### Usage

    acat(link = "loge", earg = list(),
         parallel = FALSE, reverse = FALSE, zero = NULL)

### Arguments

In the following, 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.

`link` | Link function applied to the ratios of the adjacent categories probabilities. See `Links` for more choices.
`earg` | List. Extra argument for the link function. See `earg` in `Links` for general information.
`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,...,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}.

### Details

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`.

### Warning

No check is made to verify that the response is ordinal; 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. (2002) Categorical Data Analysis, 2nd ed. New York: Wiley.

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

Documentation accompanying the VGAM package at http://www.stat.auckland.ac.nz/~yee contains further information and examples.

### See Also

`cumulative`, `cratio`, `sratio`, `multinomial`, `pneumo`.

### Examples

    pneumo = transform(pneumo, let=log(exposure.time))
    (fit = vglm(cbind(normal,mild,severe) ~ let, acat, pneumo))
    coef(fit, matrix=TRUE)
    constraints(fit)
    model.matrix(fit)

[Package VGAM version 0.7-9 Index]