BootFromCompromise {DistatisR}

BootFromCompromise: Computes Bootstrap replicates of the (observation) factor scores by creating bootstrapped compromises.

Description

BootFromCompromise Computes observation Bootstrap replicates of the factor scores from bootstrapped compromises. BootFromCompromise is typically used to create confidence intervals and to compute Bootstrap ratios.

Usage

BootFromCompromise(
  LeCube2Distance,
  niter = 1000,
  Norm = "MFA",
  Distance = TRUE,
  RV = TRUE,
  nfact2keep = 3
)

Arguments

LeCube2Distance

The array of distance used to call distatis

niter

The number of bootstrap iterations (default = 1000)

Norm

should be the same as for the original call to distatis

Distance

should be the same as for the original call to distatis

RV

should be the same as for the original call to distatis

nfact2keep

number of factors to keep for the results

Value

the output is a 3-way array of dimensions "number of observations by number of factors by number of replicates."

Technicalities

The input of BootFromCompromise is the original cubeOfData used to compute the compromise by the function distatis. BootFromCompromise computes Bootstrap replicates of the observations by randomly selecting the observations with replacement. The output of BootFromCompromise is a 3-way array of dimensions "number of observations by number of factors by number of replicates." The output is typically used to plot confidence intervals (i.e., ellipsoids or convex hulls) or to compute t-like statistic called bootstrap ratios.

To compute a bootstrapped sample, a set of K distance matrices is selected with replacement from the original set of K distance matrices. A distatis compromise is then computed and projected on the factor space of the original solution to obtain the bootstrapped factor scores. This approach is also called total boostrap by Lebart (2007, see also Chateau and Lebart 1996, see also Abdi et al., 2009 for an example). Compared to the partial bootstrap (see help for BootFactorScores). This approach has the desadvantage of being slow especially for large data sets, but recent work (Cadoret & Husson, 2012) suggests that partial boostrap (i.e., computed from the partial factor scores) could lead to optimistic bootstrap estimates when the number of distance matrices is large and that it is preferable to use instead the total boostrap.

Author(s)

Herve Abdi

References

Abdi, H., & Valentin, D., (2007). Some new and easy ways to describe, compare, and evaluate products and assessors. In D., Valentin, D.Z. Nguyen, L. Pelletier (Eds) New trends in sensory evaluation of food and non-food products. Ho Chi Minh (Vietnam): Vietnam National University-Ho chi Minh City Publishing House. pp. 5-18.

Abdi, H., Dunlop, J.P., & Williams, L.J. (2009). How to compute reliability estimates and display confidence and tolerance intervals for pattern classiffers using the Bootstrap and 3-way multidimensional scaling (DISTATIS). NeuroImage, 45, 89–95.

Abdi, H., Williams, L.J., Valentin, D., & Bennani-Dosse, M. (2012). STATIS and DISTATIS: Optimum multi-table principal component analysis and three way metric multidimensional scaling. Wiley Interdisciplinary Reviews: Computational Statistics, 4, 124–167.

These papers are available from https://personal.utdallas.edu/~herve/

Additional references:

Cadoret, M., Husson, F. (2012) Construction and evaluation of confidence ellipses applied at sensory data. Food Quality and Preference, 28, 106–115.

Chateau, F., & Lebart, L. (1996). Assessing sample variability in the visualization techniques related to principal component analysis: Bootstrap and alternative simulation methods. In A. Prats (Ed.),Proceedings of COMPSTAT 2006. Heidelberg: Physica Verlag.

Lebart, L. (2007). Which bootstrap for principal axes methods? In Selected contributions in data analysis and classification, COMPSTAT 2006. Heidelberg: Springer Verlag.

See Also

BootFactorScores GraphDistatisBoot.

Examples

# 1. Load the Sort data set from the SortingBeer example
#    (available from the DistatisR package)
data(SortingBeer)
# Provide the "8 beers by 10 assessors" results of a sorting task
#-----------------------------------------------------------------------------
# 2. Create the set of distance matrices (one distance matrix per assessor)
#    (uses the function DistanceFromSort)
DistanceCube <- DistanceFromSort(Sort)

#-----------------------------------------------------------------------------
# 3. Call the distatis function with the cube of distance as parameter
testDistatis <- distatis(DistanceCube)
# The factor scores for the beers are in
# testDistatis$res4Splus$F
# the partial factor scores for the beers for the assessors are in
#  testDistatis$res4Splus$PartialF
#
# 4. Get the bootstraped factor scores (with default 1000 iterations)
#    Here we use the "total bootstrap"
 F_fullBoot <- BootFromCompromise(DistanceCube,niter=1000)