BootFactorScores: Computes observation factor scores Bootstrap replicates from...

In DistatisR: DiSTATIS Three Way Metric Multidimensional Scaling

Computes observation factor scores Bootstrap replicates from partial factor scores.

Description

BootFactorScores: Computes Bootstrap replicates of the factor scores of the observations from the partial factor scores. BootFactorScores is typically used to create confidence intervals and to compute Bootstrap ratios.

Usage

BootFactorScores(PartialFS, niter = 1000)

Arguments

PartialFS	The partial factor scores (e.g., as obtained from distatis).
niter	number of boostrap iterations (default = 1000)

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 BootFactorScores is obtained from the distatis function, the output 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. The partial factors scores of the selected distance matrices are then averaged to produce the bootstrapped estimate of the factor scores of the observations. This approach is also called partial boostrap by Lebart (2007, see also Chateau & Lebart 1996). It has the advantage of being very fast even for very large data sets. Recent work (Cadoret & Husson, 2012), however, suggests that partial boostrap could lead to optimistic bootstrap estimates when the number of distance matrices is large and that it is preferable to use instead a total boostrap approach (i.e., creating new compromises by resampling and then projecting them on the common solution see function BootFromCompromise, and Cadoret & Husson, 2012 see also Abdi et al., 2009 for an example).

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

BootFromCompromise GraphDistatisBoot

Examples

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

#-----------------------------------------------------------------------------
# 3. Call the DISTATIS routine with the cube of distance as parameter
testDistatis <- distatis(DistanceCube)
# The factor scores for the beers are in
# testDistatis$res4Splus$F
# the partial factor score for the beers for the assessors are in
#  testDistatis$res4Splus$PartialF
#
# 4. Get the bootstraped factor scores (with default 1000 iterations)
BootF <- BootFactorScores(testDistatis$res4Splus$PartialF)

DistatisR documentation built on Dec. 5, 2022, 9:05 a.m.