cratio {VGAM} | R Documentation |
Fits a continuation ratio logit/probit/cloglog/cauchit/... regression model to an ordered (preferably) factor response.
cratio(link = "logit", earg = list(), parallel = FALSE, reverse = FALSE, zero = NULL)
In the following, 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.
link |
Link function applied to the M continuation ratio probabilities.
See Links for more choices.
|
earg |
List. Extra argument for the link function.
See earg in Links for general information.
|
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 reverse is TRUE , then
eta_j=logit(P[Y<j+1|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}.
The default value means none are modelled as intercept-only terms.
|
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])
.
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;
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. (2002) Categorical Data Analysis, 2nd ed. New York: Wiley.
Simonoff, J. S. (2003) Analyzing Categorical Data, New York: Springer-Verlag.
McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models, 2nd ed. London: Chapman & Hall.
Documentation accompanying the VGAM package at http://www.stat.auckland.ac.nz/~yee contains further information and examples.
sratio
,
acat
,
cumulative
,
multinomial
,
pneumo
,
logit
,
probit
,
cloglog
,
cauchit
.
data(pneumo) pneumo = transform(pneumo, let=log(exposure.time)) (fit = vglm(cbind(normal,mild,severe) ~ let, cratio(parallel=TRUE), pneumo)) coef(fit, matrix=TRUE) constraints(fit) predict(fit) predict(fit, untransform=TRUE)