Creates a 3-dimensional chi2 distance array from the results of a sorting task.
Takes the results from a (plain) sorting task
where K assessors sort I observations into (mutually exclusive)
groups (i.e., one object is in one an only one group).
DistanceFromSort creates an
I*I*K array of distance in which
each of the k "slices" stores the (sorting) distance
matrix of the kth assessor.
In one of these distance matrices, the distance
between rows is the Chi2 distance between rows
when the results of the task are coded as 0/1 group coding
(i.e., the "complete disjunctive coding" as used iin multiple
correspondence analysis, see Abdi & Valentin, 2007, for more)
The ouput ot the function DistanceFromSort
is used as input for the function distatis.
Chi2DistanceFromSort(X)
X |
gives the results of a sorting task (see example below) as a objects (row) by assessors (columns) matrix. |
The input should have assessors as columns and observations as rows (see example below)
DistanceFromSort returns a
I*I*K
array of distances
Herve Abdi
See examples in
Abdi, H., Valentin, D., Chollet, S., & Chrea, C. (2007). Analyzing assessors and products in sorting tasks: DISTATIS, theory and applications. Food Quality and Preference, 18, 627–640.
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., & Valentin, D. (2007). Multiple correspondence analysis. In N.J. Salkind (Ed.): Encyclopedia of Measurement and Statistics. Thousand Oaks (CA): Sage. pp. 651-657.
These papers are available from www.utdallas.edu/~herve
# 1. Get the data from the 2007 sorting example
# this is the eay they look from Table 1 of
# Abdi et al. (2007).
# Assessors
# 1 2 3 4 5 6 7 8 9 10
# Beer Sex f m f f m m m m f m
# -----------------------------
#Affligen 1 4 3 4 1 1 2 2 1 3
#Budweiser 4 5 2 5 2 3 1 1 4 3
#Buckler_Blonde 3 1 2 3 2 4 3 1 1 2
#Killian 4 2 3 3 1 1 1 2 1 4
#St. Landelin 1 5 3 5 2 1 1 2 1 3
#Buckler_Highland 2 3 1 1 3 5 4 4 3 1
#Fruit Defendu 1 4 3 4 1 1 2 2 2 4
#EKU28 5 2 4 2 4 2 5 3 4 5
#
# 1.1. Create the
# Name of the Beers
BeerName <- c('Affligen', 'Budweiser','Buckler Blonde',
'Killian','St.Landelin','Buckler Highland',
'Fruit Defendu','EKU28')
# 1.2. Create the name of the Assessors
# (F are females, M are males)
Juges <- c('F1','M2', 'F3', 'F4', 'M5', 'M6', 'M7', 'M8', 'F9', 'M10')
# 1.3. Get the sorting data
SortData <- c(1, 4, 3, 4, 1, 1, 2, 2, 1, 3,
4, 5, 2, 5, 2, 3, 1, 1, 4, 3,
3, 1, 2, 3, 2, 4, 3, 1, 1, 2,
4, 2, 3, 3, 1, 1, 1, 2, 1, 4,
1, 5, 3, 5, 2, 1, 1, 2, 1, 3,
2, 3, 1, 1, 3, 5, 4, 4, 3, 1,
1, 4, 3, 4, 1, 1, 2, 2, 2, 4,
5, 2, 4, 2, 4, 2, 5, 3, 4, 5)
# 1.4 Create a data frame
Sort <- matrix(SortData,ncol = 10, byrow= TRUE, dimnames = list(BeerName, Juges))
#
#-----------------------------------------------------------------------------
# 2. Create the set of distance matrices (one distance matrix per assessor)
# (use the function DistanceFromSort)
DistanceCube <- Chi2DistanceFromSort(Sort)
#-----------------------------------------------------------------------------
# 3. Call the DISTATIS routine with the cube of distance
# obtained from DistanceFromSort as a parameter for the distatis function
testDistatis <- distatis(DistanceCube)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.