Principal Component Analysis with Orthogonal Instrumental Variables

`PCAoiv(X, Z, row.w = NULL, ncp = 5)`

## Arguments

- X
data frame with only numeric variables

- Z
data frame of instrumental variables to be "partialled out"", which can be numeric or factors. It must have the same number of rows as `X`

.

- 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

Principal Component Analysis with Orthogonal Instrumental Variables consists in two steps :
1. Computation of one linear regression for each variable in `X`

, with this variable as response and all variables in `Z`

as explanatory variables.
2. Principal Component Analysis of the set of residuals from the regressions in 1.

## Value

An object of class `PCA`

from `FactoMineR`

package, and an additional item :

- ratio
the share of inertia not explained by the instrumental variables

.

## References

Bry X., 1996, *Analyses factorielles multiples*, Economica.

Lebart L., Morineau A. et Warwick K., 1984, *Multivariate Descriptive Statistical Analysis*, John Wiley and sons, New-York.)

## Examples

```
library(FactoMineR)
data(decathlon)
pcaoiv <- PCAoiv(decathlon[,1:10], decathlon[,12:13])
plot(pcaoiv, choix = "var", invisible = "quanti.sup")
```