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)