| BootFactorScores {DistatisR} | R Documentation |
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
|
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)