Ordinal Regression with Continuation Ratios
Fits a continuation ratio logit/probit/cloglog/cauchit/... regression model to an ordered (preferably) factor response.
cratio(link = "logitlink", parallel = FALSE, reverse = FALSE, zero = NULL,
whitespace = FALSE)link |
Link function applied to the M continuation ratio probabilities.
See |
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>=j]) for
j=1,…,M.
If |
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 |
In this help file the response Y is assumed to be a factor with ordered values 1,2,…,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
logitlink(P[Y=j|Y>=j]).
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.
The response should be either a matrix of counts
(with row sums that are all positive), or a
factor. In both cases, the y slot returned by
vglm/vgam/rrvglm is the matrix
of counts.
For a nominal (unordered) factor response, the
multinomial logit model (multinomial)
is more appropriate.
Here is an example of the usage of the parallel
argument. If there are covariates x1, x2
and x3, then parallel = TRUE ~ x1 + x2 -1
and parallel = FALSE ~ x3 are equivalent. This
would constrain the regression coefficients for x1
and x2 to be equal; those of the intercepts and
x3 would be different.
Thomas W. Yee
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. https://www.jstatsoft.org/v32/i10/.
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.