pcaivortho {ade4} | R Documentation

## Principal Component Analysis with respect to orthogonal instrumental variables

### Description

performs a Principal Component Analysis with respect to orthogonal instrumental variables.

### Usage

    pcaivortho(dudi, df, scannf = TRUE, nf = 2)
    ## S3 method for class 'pcaivortho'
    summary(object, ...)

### 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
`object` | an object of class `pcaiv`
`...` | further arguments passed to or from other methods

### Value

an object of class 'pcaivortho' 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 axis of `dudi$tab` on PAP
`ls` | a data frame with the projection of lines of `dudi$tab` on PPA
`li` | a data frame `dudi$ls` with the predicted values by X
`l1` | a data frame with the Constraint Principal Components (CPC)
`co` | a data frame with the inner product between the CPC and Y
`param` | a data frame containing a summary

### Author(s)

Daniel Chessel
Anne-Béatrice Dufour anne-beatrice.dufour@univ-lyon1.fr
Stéphane Dray stephane.dray@univ-lyon1.fr

### References

Rao, C. R. (1964) The use and interpretation of principal component analysis in applied research. Sankhya, A 26, 329–359.
Sabatier, R., Lebreton J. D. and Chessel D. (1989) Principal component analysis with instrumental variables as a tool for modelling composition data. In R. Coppi and S. Bolasco, editors. Multiway data analysis, Elsevier Science Publishers B.V., North-Holland, 341–352

### Examples

    ## Not run:
    data(avimedi)
    cla <- avimedi$plan$reg:avimedi$plan$str
    # simple ordination
    coa1 <- dudi.coa(avimedi$fau, scan = FALSE, nf = 3)
    # within region
    w1 <- wca(coa1, avimedi$plan$reg, scan = FALSE)
    # no region the same result
    pcaivnonA <- pcaivortho(coa1, avimedi$plan$reg, scan = FALSE)
    summary(pcaivnonA)
    # region + strate
    interAplusB <- pcaiv(coa1, avimedi$plan, scan = FALSE)

    if(adegraphicsLoaded()) {
      g1 <- s.class(coa1$li, cla, psub.text = "Sans contrainte", plot = FALSE)
      g21 <- s.match(w1$li, w1$ls, plab.cex = 0, psub.text = "Intra Région", plot = FALSE)
      g22 <- s.class(w1$li, cla, plot = FALSE)
      g2 <- superpose(g21, g22)
      g31 <- s.match(pcaivnonA$li, pcaivnonA$ls, plab.cex = 0, psub.tex = "Contrainte Non A",
        plot = FALSE)
      g32 <- s.class(pcaivnonA$li, cla, plot = FALSE)
      g3 <- superpose(g31, g32)
      g41 <- s.match(interAplusB$li, interAplusB$ls, plab.cex = 0, psub.text = "Contrainte A + B",
        plot = FALSE)
      g42 <- s.class(interAplusB$li, cla, plot = FALSE)
      g4 <- superpose(g41, g42)
      G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))

    } else {
      par(mfrow = c(2, 2))
      s.class(coa1$li, cla, sub = "Sans contrainte")
      s.match(w1$li, w1$ls, clab = 0, sub = "Intra Région")
      s.class(w1$li, cla, add.plot = TRUE)
      s.match(pcaivnonA$li, pcaivnonA$ls, clab = 0, sub = "Contrainte Non A")
      s.class(pcaivnonA$li, cla, add.plot = TRUE)
      s.match(interAplusB$li, interAplusB$ls, clab = 0, sub = "Contrainte A + B")
      s.class(interAplusB$li, cla, add.plot = TRUE)
      par(mfrow = c(1,1))
    }
    ## End(Not run)

[Package ade4 version 1.7-13 Index]