## STATIS, a method for analysing K-tables

### Description

performs a STATIS analysis of a `ktab` object.

### Usage

```statis(X, scannf = TRUE, nf = 3, tol = 1e-07)
## S3 method for class 'statis':
plot(x, xax = 1, yax = 2, option = 1:4, ...)
## S3 method for class 'statis':
print(x, ...)
```

### Arguments

 `X` an object of class 'ktab' `scannf` a logical value indicating whether the number of kept axes for the compromise should be asked `nf` if `scannf` FALSE, an integer indicating the number of kept axes for the compromise `tol` a tolerance threshold to test whether the distance matrix is Euclidean : an eigenvalue is considered positive if it is larger than `-tol*lambda1` where `lambda1` is the largest eigenvalue `x` an object of class 'statis' `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 dispayed `...` further arguments passed to or from other methods

### Value

`statis` returns a list of class 'statis' containing :
 `\$RV` a matrix with the all RV coefficients `RV.eig` a numeric vector with all the eigenvalues `RV.coo` a data frame with the array scores `tab.names` a vector of characters with the names of the arrays `\$RV.tabw` a numeric vector with the array weigths `nf` an integer indicating the number of kept axes `rank` an integer indicating the rank of the studied matrix `C.li` a data frame with the row coordinates `C.Co` a data frame with the column coordinates `C.T4` a data frame with the principal vectors (for each table) `TL` a data frame with the factors (not used) `TC` a data frame with the factors for Co `T4` a data frame with the factors for T4

Daniel Chessel

### References

Lavit, C. (1988) Analyse conjointe de tableaux quantitatifs, Masson, Paris.

Lavit, C., Escoufier, Y., Sabatier, R. and Traissac, P. (1994) The ACT (Statis method). Computational Statistics and Data Analysis, 18, 97–119.

### Examples

```data(jv73)
kta1 <- ktab.within(withinpca(jv73\$morpho, jv73\$fac.riv, scann = FALSE))
statis1 <- statis(kta1, scann = FALSE)
plot(statis1)

dudi1 <- dudi.pca(jv73\$poi, scann = FALSE, scal = FALSE)
wit1 <- within(dudi1, jv73\$fac.riv, scann = FALSE)
kta3 <- ktab.within(wit1)
data(jv73)
statis3 <- statis(kta3, scann = FALSE)
plot(statis3)

s.arrow(statis3\$C.li, cgrid = 0)

kplot(statis3, traj = TRUE, arrow = FALSE, unique = TRUE,
clab = 0, csub = 3, cpoi = 3)
statis3
```

### Worked out examples

```
> ### Name: statis
> ### Title: STATIS, a method for analysing K-tables
> ### Aliases: statis print.statis plot.statis
> ### Keywords: multivariate
>
> ### ** Examples
>
> data(jv73)
> kta1 <- ktab.within(withinpca(jv73\$morpho, jv73\$fac.riv, scann = FALSE))
> statis1 <- statis(kta1, scann = FALSE)
> plot(statis1)
```
```>
> dudi1 <- dudi.pca(jv73\$poi, scann = FALSE, scal = FALSE)
> wit1 <- within(dudi1, jv73\$fac.riv, scann = FALSE)
> kta3 <- ktab.within(wit1)
> data(jv73)
> statis3 <- statis(kta3, scann = FALSE)
> plot(statis3)
```
```>
> s.arrow(statis3\$C.li, cgrid = 0)
```
```>
> kplot(statis3, traj = TRUE, arrow = FALSE, unique = TRUE,
+     clab = 0, csub = 3, cpoi = 3)
> statis3
STATIS Analysis
class:statis
table number: 12
row number: 19   total column number: 92

**** Interstructure ****

eigen values: 5.337 1.525 1.294 1.037 0.6419 ...
\$RV       matrix       12      12     RV coefficients
\$RV.eig   vector       12       eigenvalues
\$RV.coo   data.frame   12      4    array scores
\$tab.names    vector       12        array names
\$RV.tabw  vector       12      array weigths

RV coefficient
Doubs    Drugeon Dessoubre   Allaine    Audeux  Cusancin
Doubs     1.0000000
Drugeon   0.4214976 1.00000000
Dessoubre 0.5560554 0.09888345 1.0000000
Allaine   0.4162722 0.33016274 0.4264883 1.0000000
Audeux    0.5275275 0.09998470 0.7460391 0.3923156 1.0000000
Cusancin  0.2648507 0.14357569 0.4098816 0.6750590 0.4465916 1.0000000
Loue      0.4396741 0.31081167 0.2031117 0.3872305 0.1128074 0.3069628
Lison     0.4181009 0.07442131 0.4814447 0.2312130 0.3968212 0.3982919
Furieuse  0.2782714 0.18165914 0.4089889 0.3844109 0.3291450 0.6693345
Cuisance  0.4196404 0.22095719 0.4596960 0.4881191 0.3045202 0.5962413
Doulonnes 0.2183520 0.06715160 0.4014573 0.2401718 0.3781006 0.2987118
Clauge    0.4599651 0.51530332 0.2912210 0.4142577 0.2568859 0.2351574
Loue     Lison  Furieuse  Cuisance Doulonnes Clauge
Doubs
Drugeon
Dessoubre
Allaine
Audeux
Cusancin
Loue      1.0000000
Lison     0.3597613 1.0000000
Furieuse  0.3862660 0.5209446 1.0000000
Cuisance  0.6487130 0.6310371 0.7768327 1.0000000
Doulonnes 0.3005171 0.5346002 0.4748992 0.5445763 1.0000000
Clauge    0.5192117 0.2895775 0.3259230 0.4934249 0.3310817      1

**** Compromise ****

eigen values: 2.012 0.903 0.5025 0.3003 0.2282 ...

\$nf: 3 axis-components saved
\$rank: 19
data.frame nrow ncol content
\$C.li      19   3    row coordinates
\$C.Co      92   3    column coordinates
\$C.T4      48   3    principal vectors (each table)
\$TL        228  2    factors (not used)
\$TC        92   2    factors for Co
\$T4        48   2    factors for T4

>
>
>
>
```