withinpca: Normed within principal component analysis

In ade4: Analysis of Ecological Data : Exploratory and Euclidean Methods in Environmental Sciences

Description

Performs 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 within

Author(s)

Daniel Chessel
Anne B Dufour [e-mail]

References

Bouroche, J. M. (1975) Analyse des données ternaires: la double analyse en composantes principales. Thèse de 3ème cycle, Université de Paris VI.

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)

# See pta
plot(wit1)

Example output

$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 

ade4 documentation built on May 2, 2019, 5:50 p.m.