Normed within principal component analysis
withinpca.RdPerforms a normed within Principal Component Analysis.
Usage
withinpca(df, fac, scaling = c("partial", "total"),
scannf = TRUE, nf = 2)Arguments
- df
a data frame with quantitative variables
- fac
a factor partitioning the rows of df in classes
- scaling
a string of characters as a scaling option :
if "partial", the sub-table corresponding to each class is centred and normed.
If "total", the sub-table corresponding to each class is centred and the total table is then normed.- 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
Details
This functions implements the 'Bouroche' standardization. In a first
step, the original variables are standardized (centred and normed). Then, a second
transformation is applied according to the value of the scaling
argument. For "partial", variables are standardized in each sub-table
(corresponding to each level of the factor). Hence, variables have null
mean and unit variance in each sub-table. For "total", variables are
centred in each sub-table and then normed globally. Hence, variables
have a null mean in each sub-table and a global variance equal to one.
Value
returns a list of the sub-class within of class dudi. See wca
References
Bouroche, J. M. (1975) Analyse des données ternaires: la double analyse en composantes principales. Thèse de 3ème cycle, Université de Paris VI.
Author
Daniel Chessel
Anne-Béatrice Dufour anne-beatrice.dufour@univ-lyon1.fr
Examples
data(meaudret)
wit1 <- withinpca(meaudret$env, meaudret$design$season, scannf = FALSE, scaling = "partial")
kta1 <- ktab.within(wit1, colnames = rep(c("S1", "S2", "S3", "S4", "S5"), 4))
unclass(kta1)
#> $spring
#> S1 S2 S3 S4 S5
#> Temp -1.372813e+00 -0.3922323 -0.39223227 0.5883484 1.5689291
#> Flow -1.615156e+00 -0.4251482 -0.01830782 0.8157149 1.2428973
#> pH 2.041241e-01 -1.8371173 0.20412415 1.2247449 0.2041241
#> Cond 9.457838e-17 1.9069252 -0.47673129 -0.4767313 -0.9534626
#> Bdo5 -9.621078e-01 1.9351487 -0.41545565 -0.3061252 -0.2514600
#> Oxyd -6.364382e-01 1.9923283 -0.49808208 -0.4980821 -0.3597259
#> Ammo -7.376580e-01 1.9837018 -0.45854414 -0.4087024 -0.3787973
#> Nitr -5.281643e-01 -1.6155614 0.40389035 0.4038903 1.3359450
#> Phos -1.047323e+00 1.6189391 -1.06650488 0.1419449 0.3529441
#>
#> $summer
#> S1 S2 S3 S4 S5
#> Temp -1.1666667 -1.1666667 0.5000000 1.33333333 0.5000000
#> Flow -1.2683846 -0.7763389 -0.2296214 0.86381368 1.4105312
#> pH 0.9354143 -1.4031215 -0.7349684 -0.06681531 1.2694909
#> Cond -1.5297323 0.9448347 1.1697953 0.04499213 -0.6298898
#> Bdo5 -1.0875080 1.4231586 0.6175971 0.21481639 -1.1680641
#> Oxyd -0.7664063 1.9508524 -0.2786932 -0.20901990 -0.6967330
#> Ammo -1.1379075 1.3255250 0.8424990 0.07982640 -1.1099429
#> Nitr -0.8553618 -1.4868370 0.4936988 0.69462267 1.1538773
#> Phos -1.6393299 0.6112322 1.1546918 0.48335936 -0.6099535
#>
#> $autumn
#> S1 S2 S3 S4 S5
#> Temp -1.6035675 1.06904497 -0.26726124 1.06904497 -0.2672612
#> Flow -1.8766905 -0.08487545 0.66957300 0.95249116 0.3395018
#> pH 0.5619515 -1.31122014 -0.84292723 0.09365858 1.4985373
#> Cond -0.7012869 1.87009833 0.11688115 -0.35064344 -0.9350492
#> Bdo5 -0.6044785 1.97542987 -0.19199318 -0.57447961 -0.6044785
#> Oxyd -0.7363901 1.97092649 -0.23102435 -0.41151212 -0.5919999
#> Ammo -0.6470895 1.95761335 -0.09597377 -0.57374709 -0.6408030
#> Nitr -0.5674453 -1.62198962 1.13991221 0.83861383 0.2109089
#> Phos -1.1374069 1.70830946 0.47677844 -0.44686983 -0.6008112
#>
#> $winter
#> S1 S2 S3 S4 S5
#> Temp 0.5000000 0.5000000 0.500000000 0.5000000 -2.0000000
#> Flow -1.5362076 -0.4891485 0.003125549 1.4330644 0.5891661
#> pH -1.8864844 0.6859943 0.685994341 0.6859943 -0.1714986
#> Cond -0.9819805 0.9274260 1.472970759 -0.7092081 -0.7092081
#> Bdo5 -1.0927369 1.2659029 1.027053299 -0.1373385 -1.0628807
#> Oxyd -0.9763927 1.2666716 1.134726600 -0.4486128 -0.9763927
#> Ammo -1.1833898 1.0449484 1.310452499 -0.3584306 -0.8135805
#> Nitr -1.9709202 0.4077766 0.577683516 0.2378697 0.7475904
#> Phos -1.0886790 0.4133145 1.744869109 -0.4175755 -0.6519291
#>
#> $lw
#> [1] 1 1 1 1 1 1 1 1 1
#>
#> $cw
#> [1] 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
#> [20] 0.2
#>
#> $blo
#> spring summer autumn winter
#> 5 5 5 5
#>
#> $TL
#> T L
#> 1 spring Temp
#> 2 spring Flow
#> 3 spring pH
#> 4 spring Cond
#> 5 spring Bdo5
#> 6 spring Oxyd
#> 7 spring Ammo
#> 8 spring Nitr
#> 9 spring Phos
#> 10 summer Temp
#> 11 summer Flow
#> 12 summer pH
#> 13 summer Cond
#> 14 summer Bdo5
#> 15 summer Oxyd
#> 16 summer Ammo
#> 17 summer Nitr
#> 18 summer Phos
#> 19 autumn Temp
#> 20 autumn Flow
#> 21 autumn pH
#> 22 autumn Cond
#> 23 autumn Bdo5
#> 24 autumn Oxyd
#> 25 autumn Ammo
#> 26 autumn Nitr
#> 27 autumn Phos
#> 28 winter Temp
#> 29 winter Flow
#> 30 winter pH
#> 31 winter Cond
#> 32 winter Bdo5
#> 33 winter Oxyd
#> 34 winter Ammo
#> 35 winter Nitr
#> 36 winter Phos
#>
#> $TC
#> T C
#> 1 spring S1
#> 2 spring S2
#> 3 spring S3
#> 4 spring S4
#> 5 spring S5
#> 6 summer S1
#> 7 summer S2
#> 8 summer S3
#> 9 summer S4
#> 10 summer S5
#> 11 autumn S1
#> 12 autumn S2
#> 13 autumn S3
#> 14 autumn S4
#> 15 autumn S5
#> 16 winter S1
#> 17 winter S2
#> 18 winter S3
#> 19 winter S4
#> 20 winter S5
#>
#> $T4
#> T 4
#> 1 spring 1
#> 2 spring 2
#> 3 spring 3
#> 4 spring 4
#> 5 summer 1
#> 6 summer 2
#> 7 summer 3
#> 8 summer 4
#> 9 autumn 1
#> 10 autumn 2
#> 11 autumn 3
#> 12 autumn 4
#> 13 winter 1
#> 14 winter 2
#> 15 winter 3
#> 16 winter 4
#>
#> $call
#> ktab.within(dudiwit = wit1, colnames = rep(c("S1", "S2", "S3",
#> "S4", "S5"), 4))
#>
#> $tabw
#> spring summer autumn winter
#> 0.25 0.25 0.25 0.25
#>
# See pta
plot(wit1)
#> Error in s.arrow(dfxy = wit1$c1, xax = 1, yax = 2, plot = FALSE, storeData = TRUE, pos = -3, psub = list(text = "Loadings"), plabels = list( cex = 1.25)): non convenient selection for dfxy (can not be converted to dataframe)