rrvglm.control: Control Function for rrvglm()

Description

Algorithmic constants and parameters for running rrvglm are set using this function.

Usage

rrvglm.control(Rank = 1, Algorithm = c("alternating", "derivative"), Corner = TRUE, Uncorrelated.latvar = FALSE, Wmat = NULL, Svd.arg = FALSE, Index.corner = if (length(str0))  head((1:1000)[-str0], Rank) else 1:Rank, Ainit = NULL, Alpha = 0.5, Bestof = 1, Cinit = NULL, Etamat.colmax = 10, sd.Ainit = 0.02, sd.Cinit = 0.02, str0 = NULL, noRRR = ~1, Norrr = NA, noWarning = FALSE, trace = FALSE, Use.Init.Poisson.QO = FALSE,  checkwz = TRUE, Check.rank = TRUE, Check.cm.rank = TRUE, wzepsilon = .Machine$double.eps^0.75, ...)

Arguments

Rank

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.

Algorithm

Character string indicating what algorithm is to be used. The default is the first one.

Corner

Logical indicating whether corner constraints are to be used. This is one method for ensuring a unique solution. If TRUE, Index.corner specifies the $R$ rows of the constraint matrices that are use as the corner constraints, i.e., they hold an order-$R$ identity matrix.

Uncorrelated.latvar

Logical indicating whether uncorrelated latent variables are to be used. This is normalization forces the variance-covariance matrix of the latent variables to be diag(Rank), i.e., unit variance and uncorrelated. This constraint does not lead to a unique solution because it can be rotated.

Wmat

Yet to be done.

Svd.arg

Logical indicating whether a singular value decomposition of the outer product is to computed. This is another normalization which ensures uniqueness. See the argument Alpha below.

Index.corner

Specifies the $R$ rows of the constraint matrices that are used for the corner constraints, i.e., they hold an order-$R$ identity matrix.

Alpha

The exponent in the singular value decomposition that is used in the first part: if the SVD is $ U %*% D %*% t(V) $ then the first and second parts are $ U %*% D^Alpha$ and $D^(1-Alpha) %*% t(V)$ respectively. A value of 0.5 is `symmetrical'. This argument is used only when Svd.arg=TRUE.

Bestof

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.

Ainit, Cinit

Initial A and C matrices which may speed up convergence. They must be of the correct dimension.

Etamat.colmax

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.

str0

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.

sd.Ainit, sd.Cinit

Standard deviation of the initial values for the elements of A and C. These are normally distributed with mean zero. This argument is used only if Use.Init.Poisson.QO = FALSE.

noRRR

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 $x2$. The $x1$ variables constitute the $\bold{B}1$ matrix in Yee and Hastie (2003). Those $x2$ 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.

Norrr

Defunct. Please use noRRR. Use of Norrr will become an error soon.

trace

Logical indicating if output should be produced for each iteration.

Use.Init.Poisson.QO

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.

checkwz

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.

noWarning, Check.rank, Check.cm.rank

Same as vglm.control. Ignored for VGAM 0.9-7 and higher.

wzepsilon

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 valt.control.

Value

A list with components matching the input names. Some error checking is done, but not much.

Details

VGAM supports three normalizations to ensure a unique solution. Of these, only corner constraints will work with summary of RR-VGLM objects.

References

Yee, T. W. and Hastie, T. J. (2003) Reduced-rank vector generalized linear models. Statistical Modelling, 3, 15--41.

Examples

Run this code

## Not run: 
# set.seed(111)
# pneumo <- transform(pneumo, let = log(exposure.time),
#                             x3 = runif(nrow(pneumo)))  # x3 is random noise
# fit <- rrvglm(cbind(normal, mild, severe) ~ let + x3,
#               multinomial, data = pneumo, Rank = 1, Index.corner = 2)
# constraints(fit)
# vcov(fit)
# summary(fit)
# ## End(Not run)

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