`bootvalid_variables.Rd`

Bootstrap validation of MCA, through the computation of the coordinates of active variables for bootstrap replications of the data.

`bootvalid_variables(resmca, axes = c(1,2), type = "partial", K = 30)`

- resmca
object of class

`speMCA`

.- axes
numeric vector of length 2, specifying the components (axes) to plot. Default is c(1,2).

- type
character string. Can be "partial", "total1", "total2" or "total3" (see details). Default is "partial".

- K
integer. Number of bootstrap replications (default is 30).

The bootstrap technique is used here as an internal and non-parametric validation procedure of the results of a multiple correspondence analysis. Following the work of Ludovic Lebart, several methods are proposed. The "total bootstrap" uses new MCAs computed from bootstrap replications of the initial data. In the type 1 total bootstrap (`type`

= "total1"), the sign of the coordinates is corrected if necessary (the direction of the axes of an ACM being arbitrary). In type 2 (`type`

= "total2"), the order of the axes and the sign of the coordinates are corrected if necessary. In type 3 (`type`

= "total3"), a procrustean rotation is used to find the best superposition between the initial axes and the replicated axes.
The "partial bootstrap"" (`type`

= "partial") does not compute new MCAs: it projects bootstrap replications of the initial data as supplementary elements of the MCA. It gives a more optimistic view of the stability of the results than the total bootstrap. It also runs faster. See references for more details, pros and cons of the various types, etc.

A data frame with the following elements :

- varcat
Names of the active categories

- K
Indexes of the bootstrap replications

- dim.x
Bootstrap coordinates on the first selected axis

- dim.y
Bootstrap coordinates on the second selected axis

Lebart L. (2006). "Validation Techniques in Multiple Correspondence Analysis". In M. Greenacre et J. Blasius (eds), *Multiple Correspondence Analysis and related techniques*, Chapman and Hall/CRC, p.179-196.

Lebart L. (2007). "Which bootstrap for principal axes methods?". In P. Brito et al. (eds), *Selected Contributions in Data Analysis and Classification*, Springer, p.581-588.

```
data(Taste)
junk <- c("FrenchPop.NA", "Rap.NA", "Rock.NA", "Jazz.NA", "Classical.NA",
"Comedy.NA", "Crime.NA", "Animation.NA", "SciFi.NA", "Love.NA",
"Musical.NA")
resmca <- speMCA(Taste[,1:11], excl = junk)
bv <- bootvalid_variables(resmca, type = "partial", K = 5)
str(bv)
#> 'data.frame': 110 obs. of 4 variables:
#> $ varcat: Factor w/ 22 levels "Animation.No",..: 1 1 1 1 1 2 2 2 2 2 ...
#> $ K : int 1 2 3 4 5 1 2 3 4 5 ...
#> $ dim.1 : num 0.02491 0.03145 0.00163 -0.00909 -0.00259 ...
#> $ dim.2 : num -0.0674 -0.0196 -0.0647 -0.0599 -0.0453 ...
```