| grc {VGAM} | R Documentation |
Fits a Goodman's RC Association Model to a matrix of counts
grc(y, Rank = 1, Index.corner = 2:(1 + Rank),
Structural.zero = 1, summary.arg = FALSE, h.step = 1e-04, ...)
y |
A matrix of counts. Output from table() is acceptable;
it is converted into a matrix.
Note that y must be at least 3 by 3.
|
Rank |
An integer in the range
{1,...,min(nrow(y), ncol(y))}.
This is the dimension of the fit.
|
Index.corner |
A vector of Rank integers.
These are used to store the Rank by Rank
identity matrix in the
A matrix; corner constraints are used.
|
Structural.zero |
An integer in the range {1,...,min(nrow(y), ncol(y))},
specifying the row that is used as the structural zero.
|
summary.arg |
Logical. If TRUE, a summary is returned.
If TRUE, y may be the output (fitted
object) of grc().
|
h.step |
A small positive value that is passed into
summary.rrvglm(). Only used when summary.arg=TRUE. |
... |
Arguments that are passed into rrvglm.control().
|
Goodman's RC association model can fit a reduced-rank approximation
to a table of counts. The log of each cell mean is decomposed as an
intercept plus a row effect plus a column effect plus a reduced-rank
part. The latter can be collectively written A %*% t(C),
the product of two `thin' matrices.
Indeed, A and C have Rank columns.
By default, the first column and row of the interaction matrix
A %*% t(C) is chosen
to be structural zeros, because Structural.zero=1.
This means the first row of A are all zeros.
This function uses options()$contrasts to set up the row and
column indicator variables.
An object of class "grc", which currently is the same as
an "rrvglm" object.
This function temporarily creates a permanent data frame called
.grc.df, which used to be needed by summary.rrvglm().
Then .grc.df is deleted before exiting the function. If an
error occurs, then .grc.df may be present in the workspace.
This function sets up variables etc. before calling rrvglm().
The ... is passed into rrvglm.control(), meaning, e.g.,
Rank=1 is default. Seting trace=TRUE may be useful for
monitoring convergence.
Using criterion="coefficients" can result in slow convergence.
If summary=TRUE, then y can be a "grc" object,
in which case a summary can be returned. That is,
grc(y, summary=TRUE) is equivalent to
summary(grc(y)).
Thomas W. Yee
Goodman, L. A. (1981) Association models and canonical correlation in the analysis of cross-classifications having ordered categories. Journal of the American Statistical Association, 76, 320–334.
Yee, T. W. and Hastie, T. J. (2003) Reduced-rank vector generalized linear models. Statistical Modelling, 3, 15–41.
Documentation accompanying the VGAM package at http://www.stat.auckland.ac.nz/~yee contains further information about the setting up of the indicator variables.
rrvglm,
rrvglm.control,
rrvglm-class,
summary.grc,
auuc.
# Some undergraduate student enrolments at the University of Auckland in 1990 data(auuc) g1 = grc(auuc, Rank=1) fitted(g1) summary(g1) g2 = grc(auuc, Rank=2, Index.corner=c(2,5)) fitted(g2) summary(g2)