| % File src/library/stats/man/cancor.Rd |
| % Part of the R package, https://www.R-project.org |
| % Copyright 1995-2018 R Core Team |
| % Distributed under GPL 2 or later |
| |
| \name{cancor} |
| \title{Canonical Correlations} |
| \alias{cancor} |
| \usage{ |
| cancor(x, y, xcenter = TRUE, ycenter = TRUE) |
| } |
| \arguments{ |
| \item{x}{numeric matrix (\eqn{n \times p_1}{n * p1}), containing the |
| x coordinates.} |
| \item{y}{numeric matrix (\eqn{n \times p_2}{n * p2}), containing the |
| y coordinates.} |
| \item{xcenter}{logical or numeric vector of length \eqn{p_1}{p1}, |
| describing any centering to be done on the x values before the |
| analysis. If \code{TRUE} (default), subtract the column means. |
| If \code{FALSE}, do not adjust the columns. Otherwise, a vector |
| of values to be subtracted from the columns.} |
| \item{ycenter}{analogous to \code{xcenter}, but for the y values.} |
| } |
| \description{ |
| Compute the canonical correlations between two data matrices. |
| } |
| \details{ |
| The canonical correlation analysis seeks linear combinations of the |
| \code{y} variables which are well explained by linear combinations |
| of the \code{x} variables. The relationship is symmetric as |
| \sQuote{well explained} is measured by correlations. |
| } |
| \value{ |
| A list containing the following components: |
| \item{cor}{correlations.} |
| \item{xcoef}{estimated coefficients for the \code{x} variables.} |
| \item{ycoef}{estimated coefficients for the \code{y} variables.} |
| \item{xcenter}{the values used to adjust the \code{x} variables.} |
| \item{ycenter}{the values used to adjust the \code{x} variables.} |
| } |
| \references{ |
| Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988). |
| \emph{The New S Language}. |
| Wadsworth & Brooks/Cole. |
| |
| Hotelling H. (1936). |
| Relations between two sets of variables. |
| \emph{Biometrika}, \bold{28}, 321--327. |
| \doi{10.1093/biomet/28.3-4.321}. |
| |
| Seber, G. A. F. (1984). |
| \emph{Multivariate Observations}. |
| New York: Wiley. |
| Page\sspace{}506f. |
| } |
| \seealso{ |
| \code{\link{qr}}, \code{\link{svd}}. |
| } |
| \examples{\donttest{## signs of results are random |
| pop <- LifeCycleSavings[, 2:3] |
| oec <- LifeCycleSavings[, -(2:3)] |
| cancor(pop, oec) |
| |
| x <- matrix(rnorm(150), 50, 3) |
| y <- matrix(rnorm(250), 50, 5) |
| (cxy <- cancor(x, y)) |
| all(abs(cor(x \%*\% cxy$xcoef, |
| y \%*\% cxy$ycoef)[,1:3] - diag(cxy $ cor)) < 1e-15) |
| all(abs(cor(x \%*\% cxy$xcoef) - diag(3)) < 1e-15) |
| all(abs(cor(y \%*\% cxy$ycoef) - diag(5)) < 1e-15) |
| }} |
| \keyword{multivariate} |