Ellipses of bootstrap validation (active variables)

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

ggbootvalid_variables(resmca, axes = c(1,2), type = "partial", K = 30,
                      ellipse = "norm", level = 0.95,
                      col = NULL, legend = "right")

Arguments

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).
ellipse: character string. The type of ellipse. The default "norm" assumes a multivariate normal distribution, "t" assumes a multivariate t-distribution, and "euclid" draws a circle with the radius equal to level, representing the euclidean distance from the center.
level: numerical value. The level at which to draw an ellipse, or, if ellipse="euclid", the radius of the circle to be drawn.
col: Character string. Color name for the ellipses and labels of the categories. If NULL (default), the default ggplot2 palette is used, with one color per variable.
legend: the position of legends ("none", "left", "right", "bottom", "top", or two-element numeric vector). Default is right.

Details

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 Lebart, several methods are proposed. The total bootstrap uses new MCAs computed from bootstrap replications of the initial data. In the type 1 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 is also faster. See references for more details, pros and cons of the various types, etc.

The default parameters for ellipses assume a multivariate normal distribution drawn at level 0.95.

Value

a ggplot2 object

Note

If col argument is NULL, ellipses and labels are colored according to the variables, using the default ggplot2 palette. The palette can be customized using any scale_color_* function, such as scale_color_brewer(), scale_color_grey() or scale_color_manual().

References

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.

Author

Nicolas Robette

Examples

# specific MCA of Taste example data set
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")
mca <- speMCA(Taste[,1:11], excl = junk)
# bootstrap validation ellipses for active variables
ggbootvalid_variables(mca, type = "partial", K = 5)