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)