Coinertia analysis between two groups of numerical variables

`coiPCA(Xa, Xb, row.w = NULL, ncp = 5)`

## Arguments

- Xa
data frame with the first group of numerical variables

- Xb
data frame with the second group of numerical variables

- row.w
numeric vector of row weights. If NULL (default), a vector of 1 for uniform row weights is used.

- ncp
number of dimensions kept in the results (by default 5)

## Details

Coinertia analysis aims at capturing the structure common to two groups of variables. With groups of numerical variables, it is equivalent to Tucker's inter-battery analysis.
It consists in the following steps :
1. Variables in Xa and Xb are centered and scaled
2. Computation of the covariance matrix t(Xa).Xb
3. PCA of the matrix

## Value

An object of class `PCA`

from `FactoMineR`

package, with an additional item :

- RV
the RV coefficient between the two groups of variabels

## References

Tucker, L.R. (1958) An inter-battery method of factor analysis. *Psychometrika*, 23-2, 111-136.

Dolédec, S. and Chessel, D. (1994) Co-inertia analysis: an alternative method for studying species-environment relationships. *Freshwater Biology*, 31, 277–294.

## Examples

```
library(FactoMineR)
data(decathlon)
# variables of results for each sport
Xa <- decathlon[,1:10]
# rank and points variables
Xb <- decathlon[,11:12]
# coinertia analysis
res <- coiPCA(Xa, Xb)
# plot of variables in Xa
plot(res, choix = "ind")
# plot of variables in Xb
plot(res, choix = "var")
# RV coefficient
res$RV
#> [1] 0.09265003
```