VGAM (version 1.1-9)

acat: 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, thresholds = c("unconstrained", "equidistant",
     "symmetric1", "symmetric0"), Treverse = reverse,
     Tref = if (Treverse) "M" else 1, whitespace = FALSE)

Value

An object of class "vglmff"

(see vglmff-class). The object is used by modelling functions such as vglm,

rrvglm

and vgam.

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,...,\(M\)}. See CommonVGAMffArguments for more information.

thresholds, Treverse, Tref

See cumulative for information. These arguments apply to ordinal categorical regression models.

whitespace

See CommonVGAMffArguments for information.

Author

Thomas W. Yee

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.

Internally, deriv3 is called to perform symbolic differentiation and consequently this family function will struggle if \(M\) becomes too large. If this occurs, try combining levels so that \(M\) is effectively reduced. One idea is to aggregate levels with the fewest observations in them first.

References

Agresti, A. (2013). Categorical Data Analysis, 3rd ed. Hoboken, NJ, USA: Wiley.
Tutz, G. (2012). Regression for Categorical Data, Cambridge: Cambridge University Press.
Yee, T. W. (2010). The VGAM package for categorical data analysis. Journal of Statistical Software, 32, 1--34. tools:::Rd_expr_doi("10.18637/jss.v032.i10").

See Also

cumulative, cratio, sratio, multinomial, margeff, pneumo, budworm, deriv3.

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)