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 = "loglink", 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,…,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,…,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`.

### 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 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.

### 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: 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

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

### Examples

    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)

[Package VGAM version 1.1-1 Index]