Chi2DistanceFromSort function

Chi2DistanceFromSort: Creates a 3-dimensional $chi2$

distance array from the results of a sorting task.

Chi2DistanceFromSort: 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). Chi2DistanceFromSort creates an $I*I*K$ array of distance in which each of the $k$ "slices" stores the (sorting) distance matrix of the $k$th 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 in multiple correspondence analysis, see Abdi & Valentin, 2007, for more)

Chi2DistanceFromSort(X)

Arguments

• X: gives the results of a sorting task (see example below) as a objects (row) by assessors (columns) matrix.

Returns

Chi2DistanceFromSort returns an $I*I*K$

array of $K$ distances matrices (between the $I$ observations)

Details

The ouput ot the function Chi2DistanceFromSort

is used as input for the function distatis.

The input should have assessors as columns and observations as rows (see example below)

Examples

#  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)

References

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 https://personal.utdallas.edu/~herve/

See Also

distatis

Author(s)

Herve Abdi