Fits a continuation ratio logit/probit/cloglog/cauchit/... regression model to an ordered (preferably) factor response.
cratio(link = "logit", parallel = FALSE, reverse = FALSE, zero = NULL,
whitespace = FALSE)Link function applied to the \(M\) continuation ratio probabilities.
See Links for more choices.
A logical, or formula specifying which terms have equal/unequal coefficients.
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.
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.
See CommonVGAMffArguments for information.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
rrvglm
and vgam.
No check is made to verify that the response is ordinal if the
response is a matrix;
see ordered.
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]).
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/.
sratio,
acat,
cumulative,
multinomial,
margeff,
pneumo,
logit,
probit,
cloglog,
cauchit.
# 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)
# }
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