Partial Triadic Analysis of a K-tables

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 \(\cos^2\) 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

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.

Author

Pierre Bady pierre.bady@univ-lyon1.fr
Anne-Béatrice Dufour anne-beatrice.dufour@univ-lyon1.fr

Examples

data(meaudret)
wit1 <- withinpca(meaudret$env, meaudret$design$season, 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
#> Partial Triadic Analysis
#> 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                  
#>  $T4        16   2    factors for Tax Tcomp            
#> 
plot(pta1)
#> Error in s.corcircle(dfxy = pta1$RV.coo, xax = 1, yax = 2, plot = FALSE,     storeData = TRUE, pos = -3, psub = list(text = "Interstructure",         position = "topleft"), pbackground = list(box = FALSE),     plabels = list(cex = 1.25)): non convenient selection for dfxy (can not be converted to dataframe)