View source: R/family.categorical.R
acat  R Documentation 
Fits an adjacent categories regression model to an ordered (preferably) factor response.
acat(link = "loglink", parallel = FALSE, reverse = FALSE,
zero = NULL, thresholds = c("unconstrained", "equidistant",
"symmetric1", "symmetric0"), Treverse = reverse,
Tref = if (Treverse) "M" else 1, whitespace = FALSE)
link 
Link function applied to the ratios of the
adjacent categories probabilities.
See 
parallel 
A logical, or formula specifying which terms have equal/unequal coefficients. 
reverse 
Logical.
By default, the linear/additive predictors used are

zero 
An integervalued vector specifying which
linear/additive predictors are modelled as intercepts only.
The values must be from the set {1,2,..., 
thresholds, Treverse, Tref 
See 
whitespace 
See 
In this help file the response Y
is assumed to be a
factor with ordered values 1,2,\ldots,M+1
, so that
M
is the number of linear/additive predictors
\eta_j
.
By default, the log link is used because the ratio of
two probabilities is positive.
Internally, deriv3
is called to
perform symbolic differentiation and
consequently this family function will struggle if
M
becomes too large.
If this occurs, try combining levels so that
M
is effectively reduced.
One idea is to aggregate levels with the fewest observations
in them first.
An object of class "vglmff"
(see vglmffclass
).
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 an ordered 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.
Tutz, G. (2012).
Regression for Categorical Data,
Cambridge: Cambridge University Press.
Yee, T. W. (2010).
The VGAM package for categorical data analysis.
Journal of Statistical Software,
32, 1–34.
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v032.i10")}.
cumulative
,
cratio
,
sratio
,
multinomial
,
margeff
,
pneumo
,
budworm
,
deriv3
.
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)
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