| CCorA {vegan} | R Documentation |
Canonical correlation analysis, following Brian McArdle's unpublished graduate course notes, plus improvements to allow the calculations in the case of very sparse and collinear matrices.
CCorA(Y, X, stand.Y=FALSE, stand.X=FALSE, nperm = 0, ...) ## S3 method for class 'CCorA': biplot(x, xlabs, which = 1:2, ...)
Y |
left matrix. |
X |
right matrix. |
stand.Y |
logical; should Y be standardized? |
stand.X |
logical; should X be standardized? |
nperm |
numeric; Number of permutations to evaluate the significance of Pillai's trace |
x |
CCoaR result object |
xlabs |
Row labels. The default is to use row names, NULL
uses row numbers instead, and NA suppresses plotting row names
completely |
which |
1 plots Y reseults, and
2 plots X1 results |
... |
Other arguments passed to functions. biplot.CCorA
passes graphical arguments to biplot and
biplot.default, CCorA currently ignores extra
arguments. |
Canonical correlation analysis (Hotelling 1936) seeks linear
combinations of the variables of Y that are maximally
correlated to linear combinations of the variables of X. The
analysis estimates the relationships and displays them in graphs.
Algorithmic notes:
S12 %*% inv(S22) %*% t(S12) %*% inv(S11).
Its trace is Pillai's trace statistic.
solve is avoided. Computation of inverses
is done by SVD (svd) in most cases.
qr).
The biplot function can produce two biplots, each for the left
matrix and right matrix solutions. The function passes all arguments to
biplot.default, and you should consult its help page for
configuring biplots.
Function CCorA returns a list containing the following components:
Pillai |
Pillai's trace statistic = sum of canonical eigenvalues. |
EigenValues |
Canonical eigenvalues. They are the squares of the canonical correlations. |
CanCorr |
Canonical correlations. |
Mat.ranks |
Ranks of matrices Y and X1 (possibly after
controlling for X2). |
RDA.Rsquares |
Bimultivariate redundancy coefficients (R-squares) of RDAs of Y|X1 and X1|Y. |
RDA.adj.Rsq |
RDA.Rsquares adjusted for n and number of
explanatory variables. |
AA |
Scores of Y variables in Y biplot. |
BB |
Scores of X1 variables in X1 biplot. |
Cy |
Object scores in Y biplot. |
Cx |
Object scores in X1 biplot. |
Pierre Legendre, Departement de Sciences Biologiques, Universite de Montreal. Implemented in vegan with the help of Jari Oksanen.
Hotelling, H. 1936. Relations between two sets of variates. Biometrika 28: 321-377.
# Example using random numbers mat1 <- matrix(rnorm(60),20,3) mat2 <- matrix(rnorm(100),20,5) CCorA(mat1, mat2) # Example using intercountry life-cycle savings data, 50 countries data(LifeCycleSavings) pop <- LifeCycleSavings[, 2:3] oec <- LifeCycleSavings[, -(2:3)] out <- CCorA(pop, oec) out biplot(out, xlabs = NA)