Constraint Matrices
Extractor function for the constraint matrices of objects in the VGAM package.
constraints(object, ...)
constraints.vlm(object, type = c("lm", "term"), all = TRUE, which,
matrix.out = FALSE, colnames.arg = TRUE,
rownames.arg = TRUE, ...)object |
Some VGAM object, for example, having
class |
type |
Character. Whether LM- or term-type constraints are to be returned.
The number of such matrices returned is equal to
|
all, which |
If |
matrix.out |
Logical. If |
colnames.arg, rownames.arg |
Logical. If |
... |
Other possible arguments such as |
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.
The extractor function
constraints()
returns a list comprising of
constraint matrices—usually one for each column of the
VLM 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.
For vglm and vgam objects,
feeding in type = "term" constraint matrices back
into the same model should work and give an identical model.
The default are the "lm"-type constraint matrices;
this is a list with one constraint matrix per column of
the LM matrix.
See the constraints argument of vglm,
and the example below.
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 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.
is.parallel,
is.zero,
trim.constraints.
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))
(fit1 <- vglm(cbind(normal, mild, severe) ~ sm.bs(let, 3),
cumulative(parallel = TRUE, reverse = TRUE), data = pneumo))
coef(fit1, matrix = TRUE)
constraints(fit1) # Parallel assumption results in this
constraints(fit1, type = "term") # Same as the default ("vlm"-type)
is.parallel(fit1)
# An equivalent model to fit1 (needs the type "term" constraints):
clist.term <- constraints(fit1, type = "term") # "term"-type constraints
# cumulative() has no 'zero' argument to set to NULL (a good idea
# when using the 'constraints' argument):
(fit2 <- vglm(cbind(normal, mild, severe) ~ sm.bs(let, 3), data = pneumo,
cumulative(reverse = TRUE), constraints = clist.term))
abs(max(coef(fit1, matrix = TRUE) -
coef(fit2, matrix = TRUE))) # Should be zero
# Fit a rank-1 stereotype (RR-multinomial logit) model:
fit <- rrvglm(Country ~ Width + Height + HP, multinomial, data = car.all)
constraints(fit) # All except the first are the estimated A matrixPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.