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)

### 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

### 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 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.
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:
    par(mfrow = c(2,2))
    data(avimedi)
    cla <- avimedi$plan$reg:avimedi$plan$str

    # simple ordination
    coa1 <- dudi.coa(avimedi$fau, scan = FALSE, nf = 3)
    s.class(coa1$li, cla, sub = "Sans contrainte")

    # within region
    w1 <- within(coa1, avimedi$plan$reg, scan = FALSE)
    s.match(w1$li, w1$ls, clab = 0, sub = "Intra Région")
    s.class(w1$li, cla, add.plot = TRUE)

    # no region the same result
    pcaivnonA <- pcaivortho(coa1, avimedi$plan$reg, scan = FALSE)
    s.match(pcaivnonA$li, pcaivnonA$ls, clab = 0,
        sub = "Contrainte Non A")
    s.class(pcaivnonA$li, cla, add.plot = TRUE)

    # region + strate
    interAplusB <- pcaiv(coa1, avimedi$plan, scan = FALSE)
    s.match(interAplusB$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)

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