## Partial Triadic Analysis of a K-tables

### Description

performs a partial triadic analysis of a K-tables, using an object of class `ktab`.

### Usage

```pta(X, scannf = TRUE, nf = 2)
## S3 method for class 'pta':
plot(x, xax = 1, yax = 2, option = 1:4, ...)
## S3 method for class 'pta':
print(x, ...)
```

### Arguments

 `X` an object of class `ktab` where the arrays have 1) the same dimensions 2) the same names for columns 3) the same column weightings `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 'pta' `xax, yax` the numbers of the x-axis and the y-axis `option` an integer between 1 and 4, otherwise the 4 components of the plot are displayed `...` further arguments passed to or from other methods

### Value

returns a list of class 'pta', sub-class of 'dudi' containing :
 `RV` a matrix with the all RV coefficients `RV.eig` a numeric vector with the all eigenvalues (interstructure) `RV.coo` a data frame with the scores of the arrays `tab.names` a vector of characters with the array names `nf` an integer indicating the number of kept axes `rank` an integer indicating the rank of the studied matrix `tabw` a numeric vector with the array weights `cw` a numeric vector with the column weights `lw` a numeric vector with the row weights `eig` a numeric vector with the all eigenvalues (compromis) `cos2` a numeric vector with the cos² between compromise and arrays `tab` a data frame with the modified array `li` a data frame with the row coordinates `l1` a data frame with the row normed scores `co` a data frame with the column coordinates `c1` a data frame with the column normed scores `Tli` a data frame with the row coordinates (each table) `Tco` a data frame with the column coordinates (each table) `Tcomp` a data frame with the principal components (each table) `Tax` a data frame with the principal axes (each table) `TL` a data frame with the factors for Tli `TC` a data frame with the factors for Tco `T4` a data frame with the factors for Tax and Tcomp

### Author(s)

Anne B Dufour dufour@biomserv.univ-lyon1.fr

### References

Blanc, L., Chessel, D. and Dolédec, S. (1998) Etude de la stabilité temporelle des structures spatiales par Analyse d'une série de tableaux faunistiques totalement appariés. Bulletin Français de la Pêche et de la Pisciculture, 348, 1–21.

Thioulouse, J., and D. Chessel. 1987. Les analyses multi-tableaux en écologie factorielle. I De la typologie d'état à la typologie de fonctionnement par l'analyse triadique. Acta Oecologica, Oecologia Generalis, 8, 463–480.

### Examples

```data(meaudret)
wit1 <- withinpca(meaudret\$mil, meaudret\$plan\$dat, scan = FALSE,
scal = "partial")
kta1 <- ktab.within(wit1, colnames = rep(c("S1","S2","S3","S4","S5"), 4))
kta2 <- t(kta1)
pta1 <- pta(kta2, scann = FALSE)
pta1
plot(pta1)
```

### Worked out examples

```
> ### Name: pta
> ### Title: Partial Triadic Analysis of a K-tables
> ### Aliases: pta print.pta plot.pta
> ### Keywords: multivariate
>
> ### ** Examples
>
> data(meaudret)
> wit1 <- withinpca(meaudret\$mil, meaudret\$plan\$dat, scan = FALSE,
+     scal = "partial")
> kta1 <- ktab.within(wit1, colnames = rep(c("S1","S2","S3","S4","S5"), 4))
> kta2 <- t(kta1)
> pta1 <- pta(kta2, scann = FALSE)
> pta1
class:pta dudi
table number: 4
row number: 5   column number: 9

**** Interstructure ****

eigen values: 2.812 0.7541 0.2537 0.18
\$RV       matrix       4      4     RV coefficients
\$RV.eig   vector       4       eigenvalues
\$RV.coo   data.frame   4      4    array scores
\$tab.names    vector       4        array names

**** Compromise ****

eigen values: 17.2 7.298 0.6099 0.2008

\$nf: 2 axis-components saved
\$rank: 4

vector length mode    content
\$tabw  4      numeric array weights
\$cw    9      numeric column weights
\$lw    5      numeric row weights
\$eig   4      numeric eigen values
\$cos2  4      numeric cosine^2 between compromise and arrays

data.frame nrow ncol content
\$tab       5    9    modified array
\$li        5    2    row coordinates
\$l1        5    2    row normed scores
\$co        9    2    column coordinates
\$c1        9    2    column normed scores

**** Intrastructure ****

data.frame nrow ncol content
\$Tli       20   2    row coordinates (each table)
\$Tco       36   2    col coordinates (each table)
\$Tcomp     16   2    principal components (each table)
\$Tax       16   2    principal axis (each table)
\$TL        20   2    factors for Tli
\$TC        36   2    factors for Tco
\$T4        16   2    factors for Tax Tcomp

> plot(pta1)
```
```>
>
>
>
```