rcc {integrOmics} | R Documentation |
The function performs the regularized extension of the Canonical Correlation Analysis to seek correlations between two data matrices.
rcc(X, Y, lambda1 = 0, lambda2 = 0, ...)
X |
numeric matrix or data frame (n times p), the observations on the X variables.
NA s are allowed. |
Y |
numeric matrix or data frame (n times q), the observations on the Y variables.
NA s are allowed. |
lambda1, lambda2 |
a not negative real. The regularization parameter for the X and
Y data. Defaults to lambda1=lambda2=0 . |
... |
not used currently. |
The main purpose of Canonical Correlations Analysis (CCA) is the exploration of sample correlations between two sets of variables X and Y observed on the same individuals (experimental units) whose roles in the analysis are strictly symmetric.
The cancor
function performs the core of computations
but additional tools are required to deal with data sets highly
correlated (nearly collinear), data sets with more variables
than units by example.
The rcc
function, the regularized version of CCA,
is one way to deal with this problem by
including a regularization step in the computations of CCA.
Such a regularization in this context
was first proposed by Vinod (1976), then developped by Leurgans et al. (1993).
It consists in the regularization of the empirical covariances matrices of
X and Y by adding a multiple of the matrix identity, that is,
Cov(X)+ λ_1 I and Cov(Y)+ λ_2 I.
When lambda1=0
and lambda2=0
, rcc
perform classic
CCA, if posible.
rcc
was implemented to allows
the use of data missing.
rcc
returns a object of class "rcc"
, a list that
contains the following components:
X |
the original X data. |
Y |
the original Y data. |
lambda |
a vector containing the regularization parameters. |
cor |
a vector containing the canonical correlations. |
loadings |
list containing the estimated loadings for the X and Y canonical variates. |
variates |
list containing the canonical variates. |
names |
list containing the names to be used for individuals and variables. |
Sébastien Déjean and Ignacio González.
Leurgans, S. E., Moyeed, R. A. and Silverman, B. W. (1993). Canonical correlation analysis when the data are curves. Journal of the Royal Statistical Society. Series B 55, 725-740.
Vinod, H. D. (1976). Canonical ridge and econometrics of joint production. Journal of Eco-no-me-trics 6, 129-137.
summary
, estim.regul
,
plot.rcc
, plotIndiv
,
plotVar
, cim
## Classic CCA data(linnerud) X <- linnerud$exercise Y <- linnerud$physiological linn.res <- rcc(X, Y) ## Regularized CCA data(nutrimouse) X <- nutrimouse$lipid Y <- nutrimouse$gene nutri.res <- rcc(X, Y, lambda1 = 0.064, lambda2 = 0.008)