DistanceFromSort function

Creates a 3-dimensional distance array from the results of a sorting task.

DistanceFromSort: 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 and 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 $k$th assessor. In one of these distance matrices, a value of 0 at the intersection of a row and a column means that the object represented by the row and the object represented by the column were sorted together (i.e., they are a distance of 0), and a value of 1 means these two objects were put into different groups.

The ouput ot the function DistanceFromSort

is used as input for the function distatis.

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

DistanceFromSort(X)

Arguments

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

Returns

DistanceFromSort

returns an $I * I * K$

array of distance.

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 <- DistanceFromSort(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.

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

See Also

distatis

Author(s)

Herve Abdi