## Within-Class Analysis

### Description

Performs a particular case of an Orthogonal Principal Component Analysis with respect to Instrumental Variables (orthopcaiv), in which there is only a single factor as covariable.

### Usage

```within(dudi, fac, scannf = TRUE, nf = 2)
## S3 method for class 'dudi'
wca(x, fac, scannf = TRUE, nf = 2, ...)
```

### Arguments

 `dudi` a duality diagram, object of class `dudi` obtained from the functions `dudi.coa`, `dudi.pca`,... `x` a duality diagram, object of class `dudi` from one of the functions `dudi.coa`, `dudi.pca`,... `fac` a factor partitioning the rows of `dudi\$tab` in classes `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 `...` further arguments passed to or from other methods

### Value

Returns a list of the sub-class `within` in the class `dudi`

 `tab` a data frame containing the transformed data (substraction of the class mean) `call` the matching call `nf` number of kept axes `rank` the rank of the analysis `ratio` percentage of within-class inertia `eig` a numeric vector containing the eigenvalues `lw` a numeric vector of row weigths `cw` a numeric vector of column weigths `tabw` a numeric vector of class weigths `fac` the factor defining the classes `li` data frame row coordinates `l1` data frame row normed scores `co` data frame column coordinates `c1` data frame column normed scores `ls` data frame supplementary row coordinates `as` data frame inertia axis onto within axis

### Note

To avoid conflict names with the `base:::within` function, the function `within` is now deprecated and will be removed. Use the generic `wca` function instead.

### Author(s)

Daniel Chessel
Anne B Dufour anne-beatrice.dufour@univ-lyon1.fr

### References

Benzécri, J. P. (1983) Analyse de l'inertie intra-classe par l'analyse d'un tableau de correspondances. Les Cahiers de l'Analyse des données, 8, 351–358.

Dolédec, S. and Chessel, D. (1987) Rythmes saisonniers et composantes stationnelles en milieu aquatique I- Description d'un plan d'observations complet par projection de variables. Acta Oecologica, Oecologia Generalis, 8, 3, 403–426.

### Examples

```data(meaudret)
pca1 <- dudi.pca(meaudret\$env, scan = FALSE, nf = 4)
wit1 <- wca(pca1, meaudret\$design\$site, scan = FALSE, nf = 2)

g1 <- s.traject(pca1\$li, meaudret\$design\$site, psub.text = "Principal Component Analysis",
plines.lty = 1:nlevels(meaudret\$design\$site), psub.cex = 1.5, plot = FALSE)
g2 <- s.traject(wit1\$li, meaudret\$design\$site,
psub.text = "Within site Principal Component Analysis",
plines.lty = 1:nlevels(meaudret\$design\$site), psub.cex = 1.5, plot = FALSE)
g3 <- s.corcircle (wit1\$as, plot = FALSE)
G <- ADEgS(list(g1, g2, g3), layout = c(2, 2))

} else {
par(mfrow = c(2, 2))
s.traject(pca1\$li, meaudret\$design\$site, sub = "Principal Component Analysis", csub = 1.5)
s.traject(wit1\$li, meaudret\$design\$site, sub = "Within site Principal Component Analysis",
csub = 1.5)
s.corcircle (wit1\$as)
par(mfrow = c(1,1))
}
plot(wit1)
```