| acat {VGAM} | R Documentation |
Fits an adjacent categories regression model to an ordered (preferably) factor response.
acat(link = "loge", 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 ratios of the
adjacent categories 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 linear/additive predictors used are
eta_j = log(P[Y=j+1]/P[Y=j])
for j=1,...,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}.
|
By default, the log link is used because the ratio of two probabilities is positive.
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.
Documentation accompanying the VGAM package at http://www.stat.auckland.ac.nz/~yee contains further information and examples.
cumulative,
cratio,
sratio,
multinomial,
pneumo.
data(pneumo) 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)