CCA {clim.pact} | R Documentation

## Canonical correlation analysis

### Description

Applies a canonical correlation analysis (CCA) to two data sets. The CCA here can be carried out in two different ways: i) an `svd` based approach (after Bretherton et al. (1992), J. Clim. Vol 5, p. 541, also documented in Benestad (1998): "Evaluation of Seasonal Forecast Potential for Norwegian Land Temperatures and Precipitation using CCA", DNMI KLIMA Report 23/98 at http://met.no/english/r_and_d_activities/publications/1998.html) or ii) a covariance-eigenvalue approach (after Wilks, 1995, "Statistical methods in the Atmospheric Sciences", Academic Press, p. 401).

The analysis can also be applied to either EOFs or fields.

Note: the analysis has sometimes been somewhat unstable, returning inconsistent results. The recommendation is to use EOFs and SVD option.

### Usage

    CCA(x1,x2,SVD=TRUE,plot=TRUE,main="CCA",sub="",test=FALSE,i.eofs=1:8,LINPACK=TRUE)
    testCCA(method="CCA",reconstr=FALSE,mode=1,test=TRUE,LINPACK=TRUE,SVD=TRUE,n.pc=4,synthetic=TRUE)

### Arguments

`x1` | A field or an eof object.
`x2` | A field or an eof object.
`SVD` | Flag: determine which approach to use: SVD or eigenfunction-based alogithm.
`plot` | Flag: plot the diagnostics.
`test` | Flag: test by reconstructing one series (leading EOF or a grid-box series).
`i.eofs` | Which EOFs to include (only when the input is given as eof objects).
`LINPACK` | 'TRUE': svd; 'FALSE':La.svd
`main` | main title (see `link{plot}`).
`sub` | subtitle (see `link{plot}`).
`method` | Which method to test: CCA or MVR.
`reconstr` | For the test-reconstruction of fields.
`mode` | Test for a particular EOF pattern/mode - the other modes are randomized.
`n.pc` | Number of principal components to include.
`synthetic` | Construct artificial test data from a random number generator and cosine series.

### Value

A CCA object: a list containing a.m, b.m, u.k, v.k, and r, describing the Canonical Correlation variates, patterns and correlations. a.m and b.m are the patterns and u.k and v.k the vectors (time evolution).)

### Author(s)

R.E. Benestad

### Examples

    ## Not run:
    data(DNMI.t2m)
    data(DNMI.slp)
    eof.1 <- EOF(DNMI.t2m,mon=1)
    eof.2 <- EOF(DNMI.slp,mon=1)
    cca <- CCA(eof.1,eof.2)
    # Testing routine:
    testCCA()
    ## End(Not run)

[Package clim.pact version 2.2-1 Index]