acat: 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

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 CommonVGAMffArguments for more 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 $j=1,\ldots,M$. 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,...,$M$}.

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.

Details

In this help file the response $Y$ is assumed to be a factor with ordered values $1,2,\ldots,M+1$, 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.

References

Agresti, A. (2002) Categorical Data Analysis, 2nd ed. New York: 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/.

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

Examples

Run this code

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)

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