Algorithmic constants and parameters for
running rrvglm are set using this
function.
Doubly constrained RR-VGLMs (DRR-VGLMs) are
also catered for.
rrvglm.control(Rank = 1, Corner = TRUE,
Index.corner = head(setdiff(seq(length(str0) +
Rank), str0), Rank), noRRR = ~ 1, str0 = NULL,
Crow1positive = NULL, trace = FALSE, Bestof = 1,
H.A.thy = list(), H.C = list(),
Ainit = NULL, Cinit = NULL, sd.Cinit = 0.02,
Algorithm = "alternating", Etamat.colmax = 10,
noWarning = FALSE, Use.Init.Poisson.QO = FALSE,
checkwz = TRUE, Check.rank = TRUE, Check.cm.rank = TRUE,
wzepsilon = .Machine$double.eps^0.75, ...)A list with components matching the input names. Some error checking is done, but not much.
The numerical rank \(R\) of the
model. Must be an element from the set
{1,2,...,min(\(M\),p2)}.
Here, the vector of explanatory
variables x is partitioned into
(x1, x2), which is of dimension
p1+p2. The variables making
up x1 are given by the terms in
noRRR argument, and the rest of the
terms comprise x2.
Logical indicating whether corner
constraints are to be used.
Strongly recommended as the only
method for fitting RR-VGLMs and
DRR-VGLMs.
This is one
method for ensuring a unique solution
and the availability of standard errors.
If TRUE then Index.corner
specifies the position of the corner
constraints.
Also used by DRR-VGLMs, and this is
known as RCCs (see below).
Specifies the \(R\) rows of
the corner constraints, e.g., they hold an
order-\(R\) identity matrix for RR-VGLMs.
The default are the first \(R\) positive
integers that exclude str0.
For DRR-VGLMs one needs
to have (restricted) corner constraints.
Then argument str0 will be ignored.
If there are structural zeros then they
should be built into the constraint matrices
(see H.A.thy).
Formula giving terms that are not
to be included in the reduced-rank
regression. That is, noRRR
specifes which explanatory variables
are in the x1 vector of
rrvglm, and the rest go into
x2.
I will write x1 as \(x_1\)
and x2 as \(x_2\) hereafter.
The \(x_1\) variables
constitute the \(\bold{B}_1\)
matrix in Yee and Hastie (2003). Those
\(x_2\) variables which are subject
to the reduced-rank regression correspond
to the \(\bold{B}_2\)
matrix. Set noRRR = NULL for the
reduced-rank regression to be applied to
every explanatory variable including the
intercept.
Integer vector specifying which rows of the
estimated constraint matrices (A)
are to be all zeros. These are called
structural zeros. Must not have
any common value with Index.corner,
and be a subset of the vector 1:M.
The default, str0 = NULL, means no
structural zero rows at all.
This argument is ignored by DRR-VGLMs.
Currently this argument has no effect.
In the future, it may be a
logical vector of length Rank
(recycled if necessary): are
the elements of the first
row of \(C\) positive?
Because of corner constraints (diag(Rank))
this argument currently must be NULL.
Having a logical vector would mean some of the diagonals
might be \(1\) and others \(-1\).
Logical indicating if output should be produced for each iteration.
Integer. The best of Bestof
models fitted is returned. This argument
helps guard against local solutions by
(hopefully) finding the global solution
from many fits. The argument works only
when the function generates its own initial
value for C, i.e., when C
is not passed in as initial values.
Lists.
DRR-VGLMs are Doubly constrained
RR-VGLMs where A has
Rank
constraint matrices
(one for each column)
in a list called H.A.thy,
and C has a
constraint matrix for each row,
i.e., for each explanatory
variable making up it.
The class
"drrvglm" may arise for such models.
So H.C
should be a named list of \(p_2\)
constraint matrices,
each one for a different row of C,
i.e., \(p_2\) is the number of variables
making up the latent variable.
Note that if H.C has
names then
matching is done with that,
and the components of H.C
are reordered if they are not sorted
according to the terms in formula.
If they are not named, then
their order is used,
for example, H.C[[1]]
and H.C[[2]] are taken as
the constraint matrices for the first two
variables of the latent variable(s).
Character string indicating what algorithm is
to be used. The default is the first one.
The choice "derivative" has been
withdrawn in VGAM 1.1-10.
Initial A and C matrices which may speed up convergence. They must be of the correct dimension.
Standard deviation of the initial values
for the elements of C.
These are normally distributed with
mean zero. This argument is used only if
Use.Init.Poisson.QO = FALSE.
Positive integer, no smaller than
Rank. Controls the amount of
memory used by .Init.Poisson.QO().
It is the maximum number of columns allowed
for the pseudo-response and its weights.
In general, the larger the value, the
better the initial value. Used only if
Use.Init.Poisson.QO = TRUE.
Logical indicating whether the
.Init.Poisson.QO() should be used
to obtain initial values for the C.
The function uses a new method that can
work well if the data are Poisson counts
coming from an equal-tolerances QRR-VGLM
(CQO). This option is less realistic for
RR-VGLMs compared to QRR-VGLMs.
logical indicating whether the diagonal
elements of the working weight matrices
should be checked whether they are
sufficiently positive, i.e., greater than
wzepsilon. If not, any values less
than wzepsilon are replaced with
this value.
Same as vglm.control.
Ignored for VGAM 0.9-7 and higher.
Small positive number used to test whether the diagonals of the working weight matrices are sufficiently positive.
Variables in ... are passed into
vglm.control.
If the derivative algorithm is used
then ... are also passed into
rrvglm.optim.control;
and if the alternating algorithm is
used then ... are also passed into
valt0.control.
In the above, \(R\) is the Rank and
\(M\) is the number of linear predictors.
Thomas W. Yee
VGAM supported three normalizations
to ensure a unique solution.
But currently,
only corner constraints will work with
summary of RR-VGLM
and DRR-VGLM objects.
Update during late-2023/early-2024:
with ongoing work implementing
the "drrvglm" class, there may
be disruption and changes to other
normalizations. However, corner
constraints should be fully supported
and have the greatest priority.
Yee, T. W. and Hastie, T. J. (2003). Reduced-rank vector generalized linear models. Statistical Modelling, 3, 15--41.
rrvglm,
rrvglm-class,
summary.drrvglm,
rrvglm.optim.control,
vglm,
vglm.control,
TypicalVGAMfamilyFunction,
CM.qnorm,
cqo.
if (FALSE) {
set.seed(111)
pneumo <- transform(pneumo, let = log(exposure.time),
x3 = runif(nrow(pneumo))) # Unrelated
fit <- rrvglm(cbind(normal, mild, severe) ~ let + x3,
multinomial, pneumo, Rank = 1, Index.corner = 2)
constraints(fit)
vcov(fit)
summary(fit)
}
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