acat: Ordinal Regression with Adjacent Categories Probabilities

Description

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

Usage

acat(link = "loge", 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 $j=1,\ldots,M$. 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,...,$M$}.

whitespace

See CommonVGAMffArguments for information.

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.

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. (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/.

Examples

Run this code

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)

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