projectVoc function

Compute barycentric projections for count-like description of the items of a distatis-type of analysis.

projectVoc

Compute barycentric projection for count-like description of the items of a distatis-type of analysis. The data need to be non-negative and typically represent the vocabulary (i.e., words) used to describe the items in a sorting/ranking/projective-mapping task.

Source

Abdi, H, & Valentin, D. (2007). Papers available from https://personal.utdallas.edu/~herve/

projectVoc(CT.voc, Fi, namesOfFactors = NULL)

Arguments

• CT.voc: a matrix or data.frame storing a $I$ items by $J$ descriptors contingency table where the $i,j$-th cell gives the number of times the $j$-th descriptor (in the column) was used to describe the $i$-th item (in the row). CT.voc

  needs to contain only non-negative numbers.

• Fi: a matrix or data.frame storing the $I$ items by $L$ factor scores obtained from the compromise of a distatis

  analysis or equivalent.

• namesOfFactors: (Default: NULL), if NULL, projectVoc uses the names of the columns of Fi for the names of the projected factors; if namesOfFactors is one word then this word is used to name the factors of the projections; if namesOfFactors

  is a character vector, it is used to name the factors of the projection.

Returns

a list with 1) Fvoca.bary: the barycentric projections of the words, and 2) Fvoca.normed: the CA normalized (i.e., variance of projections equals eigenvalue) barycentric projections of the words.

Details

two types of projection are computed: 1) a plain barycentric (words are positioned at the barycenter--a.k.a. center of mass--of the items it describes) and 2) a correspondence analysis barycentric where the variance of the projected words is equal to the variance of the items (as for correspondence analysis when using the "symmetric" representation).

Examples

# use the data from the BeersProjectiveMapping dataset
data("BeersProjectiveMapping")
# Create the I*J*K brick of data
zeBrickOfData <- projMap2Cube(
                  BeersProjectiveMapping$ProjectiveMapping, 
                  shape = 'flat',  nVars = 2)
# create the cube of covariance matrices between beers
cubeOfCov <- createCubeOfCovDis(zeBrickOfData$cubeOfData)
# Call distatis
testDistatis <- distatis(cubeOfCov$cubeOfCovariance, Distance = FALSE)
# Project the vocabulary onto the factor space
F4Voc <- projectVoc(BeersProjectiveMapping$CT.vocabulary, 
                    testDistatis$res4Splus$F)

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.

and

Lahne, J., Abdi, H., & Heymann, H. (2018). Rapid sensory profiles with DISTATIS and barycentric text projection: An example with amari, bitter herbal liqueurs. Food Quality and Preference, 66, 36-43.

Author(s)

Herve Abdi