pcaiv {ade4} | R Documentation

## Principal component analysis with respect to instrumental variables

### Description

performs a principal component analysis with respect to instrumental variables.

### Usage

    pcaiv(dudi, df, scannf = TRUE, nf = 2)
    plot.pcaiv (x, xax = 1, yax = 2, ...)
    print.pcaiv (x, ...)

### Arguments

`dudi` | a duality diagram, object of class `dudi`
`df` | a data frame with the same rows
`scannf` | a logical value indicating whether the eigenvalues bar plot should be displayed
`nf` | if scannf FALSE, an integer indicating the number of kept axes
`x` | an object of class `pcaiv`
`xax` | the column number for the x-axis
`yax` | the column number for the y-axis
`...` | further arguments passed to or from other methods

### Value

returns an object of class `pcaiv`, sub-class of class `dudi`

`rank` | an integer indicating the rank of the studied matrix
`nf` | an integer indicating the number of kept axes
`eig` | a vector with the all eigenvalues
`lw` | a numeric vector with the row weigths (from `dudi`)
`cw` | a numeric vector with the column weigths (from `dudi`)
`Y` | a data frame with the dependant variables
`X` | a data frame with the explanatory variables
`tab` | a data frame with the modified array (projected variables)
`c1` | a data frame with the Pseudo Principal Axes (PPA)
`as` | a data frame with the Principal axes of `dudi$tab` on PPA
`ls` | a data frame with the projections of lines of `dudi$tab` on PPA
`li` | a data frame `dudi$ls` with the predicted values by X
`fa` | a data frame with the loadings (Constraint Principal Components as linear combinations of X
`l1` | data frame with the Constraint Principal Components (CPC)
`co` | a data frame with the inner products between the CPC and Y
`cor` | a data frame with the correlations between the CPC and X

### Author(s)

Daniel Chessel chessel@biomserv.univ-lyon1.fr

### References

Rao, C. R. (1964) The use and interpretation of principal component analysis in applied research. Sankhya, A 26, 329–359.
Obadia, J. (1978) L'analyse en composantes explicatives. Revue de Statistique Appliquée, 24, 5–28.
Lebreton, J. D., Sabatier, R., Banco G. and Bacou A. M. (1991) Principal component and correspondence analyses with respect to instrumental variables : an overview of their role in studies of structure-activity and species- environment relationships. In J. Devillers and W. Karcher, editors. Applied Multivariate Analysis in SAR and Environmental Studies, Kluwer Academic Publishers, 85–114

### Examples

    data(rhone)
    pca1 <- dudi.pca(rhone$tab, scan = FALSE, nf = 3)
    iv1 <- pcaiv(pca1, rhone$disch, scan = FALSE)
    iv1
    # iner inercum inerC inercumC ratio R2    lambda
    # 6.27 6.27    5.52  5.52     0.879 0.671 3.7
    # 4.14 10.4    4.74  10.3     0.984 0.747 3.54
    plot(iv1)

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