Decomposition of inertia (i.e. contributions) in multivariate methods

Computes the decomposition of inertia to measure the contributions of row and/or columns in multivariate methods

Usage

# S3 method for class 'dudi'
inertia(x, row.inertia = FALSE, col.inertia = FALSE, ...)
# S3 method for class 'inertia'
print(x, ...)
# S3 method for class 'inertia'
summary(object, sort.axis = 1, subset = 5, ...)

Arguments

x, object

a duality diagram, object of class dudi for inertia.dudi. An object of class inertia for the methods print and summary

row.inertia

if TRUE, returns the decomposition of inertia for the rows

col.inertia

if TRUE, returns the decomposition of inertia for the columns

sort.axis

the kept axis used to sort the contributions in decreasing order

subset

the number of rows and/or columns to display in the summary

...

further arguments passed to or from other methods

Value

An object of class inertia, i.e. a list containing :

tot.inertia

repartition of the total inertia between axes

row.contrib

contributions of the rows to the total inertia

row.abs

absolute contributions of the rows (i.e. decomposition per axis)

row.rel

relative contributions of the rows

row.cum

cumulative relative contributions of the rows (i.e. decomposition per row)

col.contrib

contributions of the columns to the total inertia

col.abs

absolute contributions of the columns (i.e. decomposition per axis)

col.rel

relative contributions of the columns

col.cum

cumulative relative contributions of the columns (i.e. decomposition per column)

nf

the number of kept axes

References

Lebart, L., Morineau, A. and Tabart, N. (1977) Techniques de la description statistique, méthodes et logiciels pour la description des grands tableaux, Dunod, Paris, 61–62.

Volle, M. (1981) Analyse des données, Economica, Paris, 89–90 and 118

Lebart, L., Morineau, L. and Warwick, K.M. (1984) Multivariate descriptive analysis: correspondence and related techniques for large matrices, John Wiley and Sons, New York.

Greenacre, M. (1984) Theory and applications of correspondence analysis, Academic Press, London, 66.

Rouanet, H. and Le Roux, B. (1993) Analyse des données multidimensionnelles, Dunod, Paris, 143–144.

Tenenhaus, M. (1994) Méthodes statistiques en gestion, Dunod, Paris, p. 160, 161, 166, 204.

Lebart, L., Morineau, A. and Piron, M. (1995) Statistique exploratoire multidimensionnelle, Dunod, Paris, p. 56,95-96.

Details

Contributions are printed in percentage and the sign is the sign of the coordinates

Author

Daniel Chessel
Stéphane Dray stephane.dray@univ-lyon1.fr
Anne-Béatrice Dufour anne-beatrice.dufour@univ-lyon1.fr

Examples

data(housetasks)
coa1 <- dudi.coa(housetasks, scann = FALSE)
res <- inertia(coa1, col = TRUE, row = FALSE)
res
#> Inertia information:
#> Call: inertia.dudi(x = coa1, row.inertia = FALSE, col.inertia = TRUE)
#> 
#> Decomposition of total inertia:
#>     inertia     cum  cum(%)
#> Ax1  0.5429  0.5429   48.69
#> Ax2  0.4450  0.9879   88.60
#> Ax3  0.1270  1.1149  100.00
#> 
#> Column contributions (%):
#>        Wife Alternating     Husband     Jointly 
#>       27.00       10.57       34.21       28.23 
#> 
#> Column absolute contributions (%):
#>               Axis1   Axis2
#> Wife        44.4620  10.312
#> Alternating  0.1037   2.783
#> Husband     54.2339  17.787
#> Jointly      1.2004  69.118
#> 
#> Signed column relative contributions:
#>               Axis1   Axis2
#> Wife         80.188  -15.24
#> Alternating   0.478  -10.51
#> Husband     -77.203  -20.75
#> Jointly      -2.071   97.73
#> 
#> Cumulative sum of column relative contributions (%):
#>               Axis1 Axis1:2 Axis3:3
#> Wife         80.188   95.43   4.568
#> Alternating   0.478   10.99  89.012
#> Husband      77.203   97.96   2.043
#> Jointly       2.071   99.80   0.200
summary(res)
#> 
#> Total inertia: 1.115
#> 
#> Projected inertia (%):
#>     Ax1     Ax2 
#>   48.69   39.91 
#> 
#> (Only 2 dimensions (out of 3) are shown)
#> 
#> 
#> Column absolute contributions (%):
#>               Axis1   Axis2
#> Husband     54.2339  17.787
#> Wife        44.4620  10.312
#> Jointly      1.2004  69.118
#> Alternating  0.1037   2.783
#> 
#> Column relative contributions (%):
#>               Axis1   Axis2
#> Wife         80.188   15.24
#> Husband      77.203   20.75
#> Jointly       2.071   97.73
#> Alternating   0.478   10.51