VGAM (version 1.0-6)

cratio: Ordinal Regression with Continuation Ratios

Description

Fits a continuation ratio logit/probit/cloglog/cauchit/... regression model to an ordered (preferably) factor response.

Usage

cratio(link = "logit", parallel = FALSE, reverse = FALSE, zero = NULL,
       whitespace = FALSE)

Arguments

link

Link function applied to the \(M\) continuation ratio probabilities. See Links for more choices.

parallel

A logical, or formula specifying which terms have equal/unequal coefficients.

reverse

Logical. By default, the continuation ratios used are \(\eta_j = logit(P[Y>j|Y \geq j])\) for \(j=1,\dots,M\). If reverse is TRUE, then \(\eta_j = logit(P[Y<j+1|Y\leq j+1])\) 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,…,\(M\)}. The default value means none are modelled as intercept-only terms.

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 \(1,2,\dots,M+1\), so that \(M\) is the number of linear/additive predictors \(\eta_j\).

There are a number of definitions for the continuation ratio in the literature. To make life easier, in the VGAM package, we use continuation ratios and stopping ratios (see sratio). Stopping ratios deal with quantities such as logit(P[Y=j|Y>=j]).

References

Agresti, A. (2013) Categorical Data Analysis, 3rd ed. Hoboken, NJ, USA: Wiley.

McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models, 2nd ed. London: Chapman & Hall.

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

sratio, acat, cumulative, multinomial, margeff, pneumo, logit, probit, cloglog, cauchit.

Examples

# NOT RUN {
pneumo <- transform(pneumo, let = log(exposure.time))
(fit <- vglm(cbind(normal, mild, severe) ~ let,
             cratio(parallel = TRUE), data = pneumo))
coef(fit, matrix = TRUE)
constraints(fit)
predict(fit)
predict(fit, untransform = TRUE)
margeff(fit)
# }