constraints {VGAM} | R Documentation |
Returns the constraint matrices of objects in the VGAM package.
constraints(object, ...)
object |
Some VGAM object, for example, having
class vglmff-class .
|
... |
Other possible arguments. |
Constraint matrices describe the relationship of coefficients/component functions of a particular explanatory variable between the linear/additive predictors in VGLM/VGAM models. For example, they may be all different (constraint matrix is the identity matrix) or all the same (constraint matrix has one column and has unit values).
VGLMs and VGAMs have constraint matrices which are known. The class of RR-VGLMs have constraint matrices which are unknown and are to be estimated.
This extractor function returns a list comprising of constraint matrices—one for each column of the LM model matrix, and in that order. The list is labelled with the variable names. Each constraint matrix has M rows, where M is the number of linear/additive predictors, and whose rank is equal to the number of columns. A model with no constraints at all has an order M identity matrix as each variable's constraint matrix.
In all VGAM family functions zero=NULL
means
none of the linear/additive predictors are modelled as
intercepts-only.
Other arguments found in certain VGAM family functions
which affect constraint matrices include
parallel
and exchangeable
.
The constraints
argument in vglm
and vgam
allows constraint matrices to
be inputted. If so, then constraints(fit)
should
return the same as the input.
The xij
argument does not affect constraint matrices; rather,
it allows each row of the constraint matrix to be multiplied by a
specified vector.
T. W. Yee
Yee, T. W. and Wild, C. J. (1996) Vector generalized additive models. Journal of the Royal Statistical Society, Series B, Methodological, 58, 481–493.
Yee, T. W. and Hastie, T. J. (2003) Reduced-rank vector generalized linear models. Statistical Modelling, 3, 15–41.
http://www.stat.auckland.ac.nz/~yee contains additional information.
VGLMs are described in vglm-class
;
RR-VGLMs are described in rrvglm-class
.
Arguments such as zero
and parallel
found in many VGAM
family functions are a way of creating/modifying constraint
matrices conveniently, e.g., see zero
.
See CommonVGAMffArguments
for more information.
# Fit the proportional odds model pneumo = transform(pneumo, let=log(exposure.time)) (fit = vglm(cbind(normal, mild, severe) ~ let, cumulative(parallel=TRUE, reverse=TRUE), pneumo)) coef(fit, matrix=TRUE) constraints(fit) # Parallel assumption results in this # Fit a rank-1 stereotype (RR-multinomial logit) model data(car.all) fit = rrvglm(Country ~ Width + Height + HP, multinomial, car.all, Rank=1) constraints(fit) # All except the first are the A matrix