ccr12.coef | R Documentation |
Computes the first squared canonical correlation. The maximization of this criterion is equivalent to the maximization of the Roy first root.
ccr12.coef(mat, H, r, indices,
tolval=10*.Machine$double.eps, tolsym=1000*.Machine$double.eps)
mat |
the Variance or Total sums of squares and products matrix for the full data set. |
H |
the Effect description sums of squares and products matrix (defined in the same way as the |
r |
the Expected rank of the H matrix. See the |
indices |
a numerical vector, matrix or 3-d array of integers giving the indices of the variables in the subset. If a matrix is specified, each row is taken to represent a different k-variable subset. If a 3-d array is given, it is assumed that the third dimension corresponds to different cardinalities. |
tolval |
the tolerance level to be used in checks for
ill-conditioning and positive-definiteness of the 'total' and
'effects' (H) matrices. Values smaller than |
tolsym |
the tolerance level for symmetry of the
covariance/correlation/total matrix and for the effects ( |
Different kinds of statistical methodologies are considered within the framework, of a multivariate linear model:
X = A \Psi + U
where X
is the (nxp) data matrix of
original variables, A
is a known (nxp) design matrix,
\Psi
an (qxp) matrix of unknown parameters and U
an (nxp)
matrix of residual vectors.
The ccr_1^2
index is related to the traditional test statistic
(the Roy first root) and measures the contribution of each subset to
an Effect characterized by the violation of a linear hypothesis of the form
C \Psi = 0
, where C
is a known cofficient matrix
of rank r. The Roy first root is the first eigen value of HE^{-1}
, where
H
is the Effect matrix and E
is the Error matrix.
The index ccr_1^2
is related to the Roy first root
(\lambda_1
) by:
ccr_1^2 =\frac{\lambda_1}{1+\lambda_1}
The fact that indices
can be a matrix or 3-d array allows for
the computation of the ccr_1^2
values of subsets produced
by the search
functions anneal
, genetic
,
improve
and
anneal
(whose output option $subsets
are
matrices or 3-d arrays), using a different criterion (see the example
below).
The value of the ccr_1^2
coefficient.
## 1) A Linear Discriminant Analysis example with a very small data set.
## We considered the Iris data and three groups,
## defined by species (setosa, versicolor and virginica).
data(iris)
irisHmat <- ldaHmat(iris[1:4],iris$Species)
ccr12.coef(irisHmat$mat,H=irisHmat$H,r=2,c(1,3))
## [1] 0.9589055
## ---------------------------------------------------------------
## 2) An example computing the value of the ccr1_2 criteria for two
## subsets produced when the anneal function attempted to optimize
## the zeta_2 criterion (using an absurdly small number of iterations).
zetaresults<-anneal(irisHmat$mat,2,nsol=2,niter=2,criterion="zeta2",
H=irisHmat$H,r=2)
ccr12.coef(irisHmat$mat,H=irisHmat$H,r=2,zetaresults$subsets)
## Card.2
##Solution 1 0.9526304
##Solution 2 0.9558787
## ---------------------------------------------------------------
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