implements three way metric multidimensional scaling: DISTATIS and COVSTATIS.

Description

DistatisR: package implements three way metric multidimensional scaling: DISTATIS and COVSTATIS.

Details

Analyzes sets of distance (or covariance) matrices collected on the same set of observations and find common and specific metric spaces.

The example shown here comes from Abdi et al. (2007), distatis paper on the sorting task.

Author(s)

Derek Beaton [aut, com, ctb], & Herve Abdi [aut, cre]

Maintainer: Herve Abdi <herve@utdallas.edu>

References

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

Abdi, H., Valentin, D., O'Toole, A.J., & Edelman, B. (2005). DISTATIS: The analysis of multiple distance matrices. Proceedings of the IEEE Computer Society: International Conference on Computer Vision and Pattern Recognition. (San Diego, CA, USA). pp. 42-47.

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., 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.

Chollet, S., Valentin, D., & Abdi, H. (2014). The free sorting task. In. P.V. Tomasco & G. Ares (Eds), Novel Techniques in Sensory Characterization and Consumer Profiling. Boca Raton: Taylor and Francis.

Valentin, D., Chollet, S., Nestrud, M., & Abdi, H. (2018). Sorting and similarity methodologies. In. S. Kemp, S., J. Hort, & T. Hollowood (Eds.), Descriptive Analysis in Sensory Evaluation. London: Wiley-Blackwell.

See Also

distatis BootFactorScores BootFromCompromise DistanceFromSort distatis GraphDistatisAll GraphDistatisBoot GraphDistatisCompromise GraphDistatisPartial GraphDistatisRv mmds prettyGraphs

Examples

# Here we use the sorting task from Abdi et al.' (2007) paper.
# where 10 Assessors sorted 8 beers.

#-----------------------------------------------------------------------------
#  1. Get the data from the 2007 sorting example
#      this is the way 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))
#     (alternatively we could have read a csv file)
# 1.5 Example of how to read a csv filw
# Sort <- read.table("BeeerSortingTask.csv", header=TRUE,
#   sep=",", na.strings="NA", dec=".", row.names=1, strip.white=TRUE)

#------------------------------------------------------------------
# 2. Create the set of distance matrices 
#  (one distance matrix per assessor)
#    (uses 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 factor scores for the assessors are in (RV matrice)
#  testDistatis$res4Cmat$G

#------------------------------------------------------------------
# 4. Inferences on the beers obtained via bootstrap
#    here we use two different bootstraps:
#    1. Bootstrap on factors (very fast but could be too liberal
#         when the number of assessors is very large)
#    2. Complete bootstrap obtained by computing sets of compromises
#       and projecting them (could be significantly longer because a lot
#       of computations is required)
#
# 4.1 Get the bootstrap factor scores (with default 1000 iterations)
BootF <- BootFactorScores(testDistatis$res4Splus$PartialF)
#
# 4.2 Get the boostrap from full bootstrap (default niter = 1000)
 F_fullBoot <- BootFromCompromise(DistanceCube,niter=1000)


#------------------------------------------------------------------
# 5. Create the Graphics
# 5.1 an Rv map
 rv.graph.out <- GraphDistatisRv(testDistatis$res4Cmat$G)
# 5.2 a compromise plot
 compromise.graph.out <- GraphDistatisCompromise(testDistatis$res4Splus$F)
# 5.3 a partial factor score plot
 partial.scores.graph.out <-
 	GraphDistatisPartial(testDistatis$res4Splus$F,testDistatis$res4Splus$PartialF)
# 5.4 a bootstrap confidence interval plot
 #5.4.1 with ellipses
 boot.graph.out.ell <- GraphDistatisBoot(testDistatis$res4Splus$F,BootF)
 #or
 # boot.graph.out <- GraphDistatisBoot(testDistatis$res4Splus$F,F_fullBoot)
 #5.4.2 with hulls
 boot.graph.out.hull <- GraphDistatisBoot(testDistatis$res4Splus$F,BootF,ellipses=FALSE)
 #or
 # boot.graph.out <- GraphDistatisBoot(testDistatis$res4Splus$F,F_fullBoot,ellipses=FALSE)
#5.5 all the plots at once
all.plots.out <-
	GraphDistatisAll(testDistatis$res4Splus$F,testDistatis$res4Splus$PartialF,
		BootF,testDistatis$res4Cmat$G)

An example of an excel file storing the Flash Profile of 6 (fictitious) assessors evaluating 7 (imaginary) beers. This excel file can be read by read.df.excel.

Description

BeersFlashProfile: An example of an excel file storing the Flash Profile of 6 (fictitious) assessors evaluating 7 (imaginary) beers. This excel file can be read by read.df.excel.

Details

In this example of Flash Profiling 6 (fictitious) assessors evaluated 7 (imaginery) beers. First, Each assessor chose a set of descriptors suited to describe these beers and then ranked (or rated in variations of the technique) the beers for each dimension. Note that the descriptors as well as the number of descriptors vary with the judges.

Note: The names of the variables starts with the Judges ID (J1- to J6-).

Note: the data are stored in the Excel Sheet called Rankings of the excel file BeersFlashProfile.xlsx.

FileName

BeersFlashProfile.xlsx

Author(s)

Hervé Abdi

Source

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

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.

See Also

BeersProjectiveMapping BeersProjectiveMapping_xlsx

Examples

# get the path and file name
path2file <- system.file("extdata",
                  "BeersFlashProfile.xlsx", package = 'DistatisR')
# read the data in excel file with read.df.excel
beerDataFlash  <- read.df.excel(path = path2file,
                           sheet = 'Rankings')$df.data
 # the Flash Profiling data are now in the data.frame beerDataFlash                        

7 (fictitious) assessors sort and verbally describe 7 Beers using Projective Mapping.

Description

BeersProjectiveMapping: 7 (fictitious) assessors evaluated 7 Beers using Projective Mapping (with verbal description).

Usage

data("BeersProjectiveMapping")

Format

a list with 3 elements: 1) ProjectiveMapping: a matrix of dimensions 7 beers by 7*2 assessors-dimensions of the coordinates of the beers on the sheet of paper; 2) Vocabulary: a Beers (rows) by Assessors (columns) data.frame where each element of Vocabulary stores the words used by one assessor to describe a beer (words are separated with spaces); and 3) CT.vocabulary a matrix storing the I Products by N words (from the Vocabulary) contingency table, in CT.vocabulary the number at the intersection of a row (beer) and a column (word) is the number of assessors who used this word to describe that beer.

Details

First, Each assessor positioned the 7 beers on a sheet of paper according to the perceived similarity between the beers. For each assessor, the position of the beers was recorded from the X and Y coordinates. Second, the assessors were asked if they could describe each beer with some freely chosen descriptors. These descriptors are stored in a dataframe with 7 elements (one per assessor) where each element of the dataframe is a 7 component vector (one per beer) where each element stores the words used to describe a beer (words are separated with spaces).

Author(s)

Hervé Abdi

Source

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

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.

An example of an excel file with Projective Mapping data and vocabulary. This excel file can be read by read.df.excel.

Description

BeersProjectiveMapping_xlsx: an example of an excel file with Projective Mapping and vocabulary. This excel file can be read by read.df.excel. In this example 7 (fictitious) assessors evaluated 7 Beers.

Details

In this example of projective mapping with vocabulary, 7 (fictitious) assessors evaluated 7 Beers First, each assessor positionned the 7 beers on a sheet of paper according to the perceived similarity between the beers. For each assessor, the position of the beers is recorded from the X and Y coordinates. Second, the assessors are asked if they can describe the beers with some freely chosen descriptors. These descriptors are stored in a list with 7 elements (one per assessor) where each element of the list is a 7 component vector (one per beer) where each element stores the words used to describe a beer (words are separated with spaces). The coordinates of the beers on the sheet of paper are stored in the sheet Maps, the Vocabulary generated by the assessors is stored in the sheet Vocabulary

FileName

BeersProjectiveMapping_xlsx.xlsx

Author(s)

Hervé Abdi

Source

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

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.

See Also

BeersProjectiveMapping

Examples

# get the path and file name
path2file <- system.file("extdata",
       "BeersProjectiveMapping_xlsx.xlsx", package = 'DistatisR')
# read the data in excel file with read.df.excel
beerDataPM  <- read.df.excel(path = path2file,
                           sheet = 'Maps',
                       voc.sheet = 'Vocabulary')

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

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)

BootFromCompromise: Computes Bootstrap replicates of the (observation) factor scores by creating bootstrapped compromises.

Description

BootFromCompromise Computes observation Bootstrap replicates of the factor scores from bootstrapped compromises. BootFromCompromise is typically used to create confidence intervals and to compute Bootstrap ratios.

Usage

BootFromCompromise(
  LeCube2Distance,
  niter = 1000,
  Norm = "MFA",
  Distance = TRUE,
  RV = TRUE,
  nfact2keep = 3
)

Arguments

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 BootFromCompromise is the original cubeOfData used to compute the compromise by the function distatis. BootFromCompromise computes Bootstrap replicates of the observations by randomly selecting the observations with replacement. The output of BootFromCompromise 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. A distatis compromise is then computed and projected on the factor space of the original solution to obtain the bootstrapped factor scores. This approach is also called total boostrap by Lebart (2007, see also Chateau and Lebart 1996, see also Abdi et al., 2009 for an example). Compared to the partial bootstrap (see help for BootFactorScores). This approach has the desadvantage of being slow especially for large data sets, but recent work (Cadoret & Husson, 2012) suggests that partial boostrap (i.e., computed from the partial factor scores) could lead to optimistic bootstrap estimates when the number of distance matrices is large and that it is preferable to use instead the total boostrap.

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

BootFactorScores GraphDistatisBoot.

Examples

# 1. Load the Sort data set from the SortingBeer example
#    (available from the DistatisR package)
data(SortingBeer)
# Provide the "8 beers by 10 assessors" results of a sorting task
#-----------------------------------------------------------------------------
# 2. Create the set of distance matrices (one distance matrix per assessor)
#    (uses the function DistanceFromSort)
DistanceCube <- DistanceFromSort(Sort)

#-----------------------------------------------------------------------------
# 3. Call the distatis function with the cube of distance as parameter
testDistatis <- distatis(DistanceCube)
# The factor scores for the beers are in
# testDistatis$res4Splus$F
# the partial factor scores for the beers for the assessors are in
#  testDistatis$res4Splus$PartialF
#
# 4. Get the bootstraped factor scores (with default 1000 iterations)
#    Here we use the "total bootstrap"
 F_fullBoot <- BootFromCompromise(DistanceCube,niter=1000)

CP2MFAnormedCP

Description

MFA normalizes a cube of cross-product matrices

Usage

CP2MFAnormedCP(CP3)

Arguments

Value

The 3D array of the normalized cross-product matrices.

Examples

D3 <- array(c(0, 1, 2, 1, 0, 1, 2, 1, 0,
              0, 3, 3, 3, 0, 3, 3, 3, 0), 
           dim = c(3, 3, 2))
CP2MFAnormedCP(D3)         

CP2NuclearNormedCP

Description

Nuclear Norm normalizes a cube of cross-product matrices

Usage

CP2NuclearNormedCP(CP3)

Arguments

Value

The 3D array of the normalized cross-product matrices.

Examples

D3 <- array(c(0, 1, 2, 1, 0, 1, 2, 1, 0,
              0, 3, 3, 3, 0, 3, 3, 3, 0), 
           dim = c(3, 3, 2))
CP2NuclearNormedCP(D3)         

CP2SUMPCAnormedCP

Description

SUMPCA normalizes a cube of cross-product matrices.

Usage

CP2SUMPCAnormedCP(CP3)

Arguments

Value

The 3D array of the normalized cross-product matrices.

Examples

D3 <- array(c(0, 1, 2, 1, 0, 1, 2, 1, 0,
              0, 3, 3, 3, 0, 3, 3, 3, 0), 
           dim = c(3, 3, 2))
CP2SUMPCAnormedCP(D3)         

Computes the \chi^2 distance between the rows of a rectangular matrix (with positive elements).

Description

Chi2Dist: Computes the I\times I matrix D which is the \chi^2 distance matrix between the rows of an I\times J rectangular matrix X (with non-negative elements), and provides the I\times 1 m vector of mass (where the mass of a row is the sum of the entries of this row divided by the grand total of the matrix). When the distance matrix and the associated vector of masses are used as input to the function mmds the results will give the factor scores of the correspondence analysis of the matrix X. The function is used by the function Chi2DistanceFromSort that computes the \chi^2 distance for the results of a sorting task.

Usage

Chi2Dist(X)

Arguments

Value

Sends back a list:

Author(s)

Herve Abdi

References

The procedure and references are detailled in (Paper available from https://personal.utdallas.edu/~herve/): Abdi, H. (2007). Distance. In N.J. Salkind (Ed.): Encyclopedia of Measurement and Statistics. Thousand Oaks (CA): Sage. pp. 304–308.

And in:
Abdi, H., & Valentin, D. (2006). Mathematiques pour les Sciences Cognitives (Mathematics for Cognitive Sciences). Grenoble: PUG.

See also (for the example):

Abdi, H., & Williams, L.J. (2010). Principal component analysis. Wiley Interdisciplinary Reviews: Computational Statistics, 2, 433–459.

See Also

Chi2DistanceFromSort distatis mmds

Examples

# Here is a data matrix from Abdi & Williams (2012)
# page 449, Table 15. Punctuation of 6 French authors
Punctuation = matrix(c(
  7836,   13112,   6026,
 53655,   102383, 42413, 
115615,   184541, 59226, 
161926,   340479, 62754, 
 38177,   105101, 12670, 
 46371,    58367, 14299),
     ncol =3,byrow = TRUE)
colnames(Punctuation) <-c('Period','Comma','Other')
rownames(Punctuation) <-c('Rousseau','Chateaubriand',
                   'Hugo','Zola','Proust','Giroudoux') 
# 1. Get the Chi2 distance matrix
#     between the rows of Punctuation 
Dres <- Chi2Dist(Punctuation)
# check that the mds of the Chi2 distance matrix
# with CA-masses gives the CA factor scores for I 
# 2. Use function mmds from DistatisR 
#
testmds <- mmds(Dres$Distance,masses=Dres$masses)
# Print the MDS factor scores from mmds
print('Factor Scores from mds')
print(testmds$FactorScores)
print('It matches CA on X (see Abdi & Williams, 2010. Table 16, p. 449)')
# Et voila!

Chi2DistanceFromSort: Creates a 3-dimensional \chi^2 distance array from the results of a sorting task.

Description

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 \times I \times 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 \chi^2 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)

Usage

Chi2DistanceFromSort(X)

Arguments

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)

Value

Chi2DistanceFromSort returns an I\times I \times K array of K distances matrices (between the I observations)

Author(s)

Herve Abdi

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

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)

ComputeSplus

Description

Compute the compromise matrix for STATIS/DISTATIS

Usage

ComputeSplus(CubeCP, alpha)

Arguments

Value

The compromise matrix computed as the alpha-weighted sum of the cross-product matrices.

Examples

D3 <- array(c(0, 1, 2, 1, 0, 1, 2, 1, 0, 
              0, 3, 3, 3, 0, 3, 3, 3, 0), 
            dim = c(3, 3, 2))
ComputeSplus(D3, alpha = c(1, 0.5))

Double Center a distance matrix

Description

Double Center a distance matrix

Usage

DblCenterDist(Y)

Arguments

Value

a cross-product matrix (if the distance is Euclidean)

Examples

Y <- toeplitz(c(0, 3, 3))
DblCenterDist(Y)

Dist2CP

Description

Transforms a cube of distance matrices into a cube of cross-product matrices.

Usage

Dist2CP(D3)

Arguments

Value

the cube of cross-product matrices.

Examples

D3 <- array(c(0, 1, 2, 1, 0, 1, 2, 1, 0, 
              0, 3, 3, 3, 0, 3, 3, 3, 0), 
            dim = c(3, 3, 2))
Dist2CP(D3)

Four computer algorithms evaluate the similarity of six faces for distatis analysis

Description

Provide the data.frame DistAlgo Data set to be used to illustrated the use of the package DistatisR. Four algorithms evaluate the similarity (i.e., distance) between six faces (3 females and 3 males). Each algorithm provides a 6\times 6 distance matrix evaluating the distance between each pair of faces.

Format

an 6\times6\times4 array. Each 6\times 6 matrix is a distance matrix

Author(s)

Herve Abdi

Source

Abdi et al. (2005). https://personal.utdallas.edu/~herve/

References

Abdi, H., Valentin, D., O'Toole, A.J., & Edelman, B. (2005). DISTATIS: The analysis of multiple distance matrices. Proceedings of the IEEE Computer Society: International Conference on Computer Vision and Pattern Recognition. (San Diego, CA, USA). pp. 42–47.

DistanceFromRank: Creates a 3-dimensional distance array from the results of a ranking task.

Description

DistanceFromRank: Takes the results from a (plain) ranking task where K assessors rank (with possible ties) I observations on one dimension and transform it into a brick of data to be used by distatis.

Usage

DistanceFromRank(X)

Arguments

Details

DistanceFromRank creates an I \times I \times K array of distance in which each of the K "slices" stores the (squared Euclidean ranking) distance matrix of the kth assessor. In one of these distance matrices, the distance between two objects is computed from he Pythagorean theorem. The ouput ot the function DistanceFromRank is used as input for the function distatis.

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

Value

DistanceFromRank returns an I\times I \times K array of distance.

Author(s)

Herve Abdi

See Also

distatis DistanceFromSort

Examples

# Use the data set WinesRankingRawData stored in an excel file.
path2file <- system.file("extdata",
           "WinesRankingRawData.xlsx", package = 'DistatisR')
ranking6Wines <- read.df.excel(path = path2file, sheet = 'Ranking')
aCubeOfDistance <- DistanceFromRank(ranking6Wines$df.data)

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

Description

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 \times I \times 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, 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)

Usage

DistanceFromSort(X)

Arguments

Value

DistanceFromSort returns an I\times I \times K array of distance.

Author(s)

Herve Abdi

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

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)

GetCmat

Description

Computes the RV coefficient matrix

Usage

GetCmat(CubeCP, RV = TRUE)

Arguments

Value

A matrix of either RV coefficients or scalar products.

Examples

D3 <- array(c(0, 1, 2, 1, 0, 1, 2, 1, 0, 
              0, 3, 3, 3, 0, 3, 3, 3, 0), 
            dim = c(3, 3, 2))
GetCmat(D3)             

GetRectCmat

Description

Computes the rectangular RV coefficient matrix between two arrays of conformable matrices

Usage

GetRectCmat(CubeCP1, CubeCP2, RV = TRUE)

Arguments

Value

A rectangular matrix of either RV coefficients or scalar products.

Examples

D3.1 <- array(c(0, 1, 2, 1, 0, 1, 2, 1, 0, 
              0, 3, 3, 3, 0, 3, 3, 3, 0), 
            dim = c(3, 3, 2))
D3.2 <- array(c(1, 0, 0, 0, 1, 0, 0, 0, 1, 
                 1, 1, 1, 1, 1, 1, 1, 1, 1, 
                 0, 0, 0, 0, 0, 0, 0, 0, 0), 
            dim = c(3, 3, 3))
GetRectCmat(D3.1, D3.2)             

This function combines the functionality of GraphDistatisCompromise, GraphDistatisPartial, GraphDistatisBoot, and GraphDistatisRv.

Description

This function produces 4 plots: (1) a compromise plot, (2) a partial factor scores plot, (3) a bootstrap confidence intervals plot, and (4) an Rv map.

Usage

GraphDistatisAll(
  FS,
  PartialFS,
  FBoot,
  RvFS,
  axis1 = 1,
  axis2 = 2,
  constraints = NULL,
  item.colors = NULL,
  participant.colors = NULL,
  ZeTitleBase = NULL,
  nude = FALSE,
  Ctr = NULL,
  RvCtr = NULL,
  color.by.observations = TRUE,
  lines = TRUE,
  lwd = 3.5,
  ellipses = TRUE,
  fill = TRUE,
  fill.alpha = 0.27,
  percentage = 0.95
)

Arguments

Value

Author(s)

Derek Beaton and Herve Abdi

See Also

GraphDistatisAll GraphDistatisCompromise GraphDistatisPartial GraphDistatisBoot GraphDistatisRv distatis

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 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)
#-----------------------------------------------------------------------------
# 5. Create the Graphics with GraphDistatisAll
#
GraphDistatisAll(testDistatis$res4Splus$F,testDistatis$res4Splus$PartialF,
	BootF,testDistatis$res4Cmat$G)

GraphDistatisBoot Plot maps of the factor scores of the observations and their bootstrapped confidence intervals (as confidence ellipsoids or peeled hulls) for a DISTATIS analysis.

Description

GraphDistatisBoot plots maps of the factor scores of the observations from a distatis analysis. GraphDistatisBoot gives a map of the factors scores of the observations plus the boostrapped confidence intervals drawn as "Confidence Ellipsoids" at the percentage level (see parameter percentage).

Usage

GraphDistatisBoot(
  FS,
  FBoot,
  axis1 = 1,
  axis2 = 2,
  item.colors = NULL,
  ZeTitle = "Distatis-Bootstrap",
  constraints = NULL,
  nude = FALSE,
  Ctr = NULL,
  lwd = 3.5,
  ellipses = TRUE,
  fill = TRUE,
  fill.alpha = 0.27,
  percentage = 0.95
)

Arguments

Details

The ellipses are plotted using the function dataEllipse() from the package car. The peeled hulls are plotted using the function peeledHulls() from the package prettyGraphs.

Note that, in the current version, the graphs are plotted as R-plots and are not passed back by the function. So the graphs need to be saved "by hand" from the R graphic windows. We plan to improve this in a future version. See also package PTCA4CATA for ggplot2 based graphs.

Value

Author(s)

Derek Beaton and Herve Abdi

References

The plots are similar to the graphs described in:

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.

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., & 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

GraphDistatisAll GraphDistatisCompromise GraphDistatisPartial GraphDistatisBoot GraphDistatisRv distatis

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 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)
#-----------------------------------------------------------------------------
# 5. Create the Graphics with GraphDistatisBoot
#
GraphDistatisBoot(testDistatis$res4Splus$F,BootF)

Plot maps of the factor scores of the observations for a DISTATIS analysis

Description

Plot maps of the factor scores of the observations for a distatis analysis. GraphDistatis gives a map of the factor scores for the observations. The labels of the observations are plotted by defaults but can be omitted (see the nude=TRUE option).

Usage

GraphDistatisCompromise(
  FS,
  axis1 = 1,
  axis2 = 2,
  constraints = NULL,
  item.colors = NULL,
  ZeTitle = "Distatis-Compromise",
  nude = FALSE,
  Ctr = NULL
)

Arguments

Details

Note that, in the current version, the graphs are plotted as R-plots and are not passed back by the routine. So the graphs need to be saved "by hand" from the R graphic windows. We plan to improve this in a future version.

Value

Author(s)

Derek Beaton and Herve Abdi

References

The plots are similar to the graphs from

Abdi, H., Valentin, D., O'Toole, A.J., & Edelman, B. (2005). DISTATIS: The analysis of multiple distance matrices. Proceedings of the IEEE Computer Society: International Conference on Computer Vision and Pattern Recognition. (San Diego, CA, USA). pp. 42-47.

Paper available from: https://personal.utdallas.edu/~herve/

See Also

GraphDistatisAll GraphDistatisCompromise GraphDistatisPartial GraphDistatisBoot GraphDistatisRv distatis

Examples

# 1. Load the DistAlgo data set (available from the DistatisR package)
data(DistAlgo)
# DistAlgo is a 6*6*4 Array (face*face*Algorithm)
#-----------------------------------------------------------------------------
# 2. Call the DISTATIS routine with the array of distance (DistAlgo) as parameter
DistatisAlgo <- distatis(DistAlgo)
# 3. Plot the compromise map with the labels for the first 2 dimensions
# DistatisAlgo$res4Splus$F are the factors scores for the 6 observations (i.e., faces)
# DistatisAlgo$res4Splus$PartialF are the partial factors scores
	##(i.e., one set of factor scores per algorithm)
 GraphDistatisCompromise(DistatisAlgo$res4Splus$F)

Plot maps of the factor scores and partial factor scores of the observations for a DISTATIS analysis.

Description

GraphDistatisPartial plots maps of the factor scores of the observations from a distatis analysis. GraphDistatisPartial gives a map of the factors scores of the observations plus partial factor scores, as "seen" by each of the matrices.

Usage

GraphDistatisPartial(
  FS,
  PartialFS,
  axis1 = 1,
  axis2 = 2,
  constraints = NULL,
  item.colors = NULL,
  participant.colors = NULL,
  ZeTitle = "Distatis-Partial",
  Ctr = NULL,
  color.by.observations = TRUE,
  nude = FALSE,
  lines = TRUE
)

Arguments

Details

Note that, in the current version, the graphs are plotted as R-plots and are not passed back by the routine. So the graphs need to be saved "by hand" from the R graphic windows. We plan to improve this in a future version.

Value

Author(s)

Derek Beaton and Herve Abdi

References

The plots are similar to the graphs from

Abdi, H., Valentin, D., O'Toole, A.J., & Edelman, B. (2005). DISTATIS: The analysis of multiple distance matrices. Proceedings of the IEEE Computer Society: International Conference on Computer Vision and Pattern Recognition. (San Diego, CA, USA). pp. 42-47.

Paper available from https://personal.utdallas.edu/~herve/

See Also

GraphDistatisAll GraphDistatisCompromise GraphDistatisPartial GraphDistatisBoot GraphDistatisRv distatis

Examples

# 1. Load the DistAlgo data set (available from the DistatisR package)
data(DistAlgo)
# DistAlgo is a 6*6*4 Array (face*face*Algorithm)
#-----------------------------------------------------------------------------
# 2. Call the DISTATIS routine with the array of distance (DistAlgo) as parameter
DistatisAlgo <- distatis(DistAlgo)
# 3. Plot the compromise map with the labels for the first 2 dimensions
# DistatisAlgo$res4Splus$F are the factors scores for the 6 observations (i.e., faces)
# DistatisAlgo$res4Splus$PartialF are the partial factors scores
	##(i.e., one set of factor scores per algorithm)
 GraphDistatisPartial(DistatisAlgo$res4Splus$F,DistatisAlgo$res4Splus$PartialF)

Plot maps of the factor scores (from the Rv matrix) of the distance matrices for a DISTATIS analysis

Description

Plot maps of the factor scores of the observations for a distatis analysis. The factor scores are obtained from the eigen-decomposition of the between distance matrices cosine matrix (often a matrix of Rv coefficients). Note that the factor scores for the first dimension are always positive. There are used to derive the \alpha weights for DISTATIS.

Usage

GraphDistatisRv(
  RvFS,
  axis1 = 1,
  axis2 = 2,
  ZeTitle = "Distatis-Rv Map",
  participant.colors = NULL,
  nude = FALSE,
  RvCtr = NULL
)

Arguments

Details

Note that, in the current version, the graphs are plotted as R-plots and are not passed back by the routine. So the graphs need to be saved "by hand" from the R graphic windows. We plan to improve this in a future version.

Value

Author(s)

Derek Beaton and Herve Abdi

References

The plots are similar to the graphs described in:

Abdi, H., Valentin, D., O'Toole, A.J., & Edelman, B. (2005). DISTATIS: The analysis of multiple distance matrices. Proceedings of the IEEE Computer Society: International Conference on Computer Vision and Pattern Recognition. (San Diego, CA, USA). pp. 42-47.

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.

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., & 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.

The R_V coefficient is described in

Abdi, H. (2007). RV coefficient and congruence coefficient. In N.J. Salkind (Ed.): Encyclopedia of Measurement and Statistics. Thousand Oaks (CA): Sage. pp. 849–853.

Abdi, H. (2010). Congruence: Congruence coefficient, RV coefficient, and Mantel Coefficient. In N.J. Salkind, D.M., Dougherty, & B. Frey (Eds.): Encyclopedia of Research Design. Thousand Oaks (CA): Sage. pp. 222–229.

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

See Also

GraphDistatisAll GraphDistatisCompromise GraphDistatisPartial GraphDistatisBoot GraphDistatisRv distatis

Examples

# 1. Load the DistAlgo data set (available from the DistatisR package)
data(DistAlgo)
# DistAlgo is a 6*6*4 Array (faces*faces*Algorithms)
#-----------------------------------------------------------------------------
# 2. Call the DISTATIS routine with the array of distance (DistAlgo) as parameter
DistatisAlgo <- distatis(DistAlgo)
# 3. Plot the compromise map with the labels for the first 2 dimensions
# DistatisAlgo$res4Cmat$G are the factors scores
#  for the 4 distance matrices (i.e., algorithms)
 GraphDistatisRv(DistatisAlgo$res4Cmat$G,ZeTitle='Rv Mat')
# Et voila!

MFAnormCP

Description

Normalizeq a positive semi-definite matrix matrix product such that its first eigenvalue is equal to one

Usage

MFAnormCP(Y)

Arguments

Value

The normalized matrix

Examples

A <- toeplitz(c(1, 0.6))
MFAnormCP(A)

NuclearNormedCP

Description

Normalizes a positive semi-definite matrix by diving it by its nuclear norm (i.e., the sum of the square root of its eigen-values).

Usage

NuclearNormedCP(Y)

Arguments

Value

The normalized matrix

Examples

A <- toeplitz(c(1, 0.6))
NuclearNormedCP(A)

OrangeJuiceSortingRawData: an example of an excel file with Sorting data and vocabulary. This excel file can be read by read.df.excel.

Description

OrangeJuiceSorting: an example of an excel file with sorting data (10 Orange Juices sorted by 44 Assessors) and an an associated vocabulary contingency table (10 Orange Juices by 23 descriptors). Can be read by read.df.excel.

Details

In this example of a "sorting task" with vocabulary, 44 assessors sorted 10 orange juices and freely described each group of juices with a few words. The data from the sorting task are in the sheet "Sorting" and the contingency table (10 Orange Juices by 23 descriptors) is in the sheet "Vocabulary". To fetch this dataset use system.file() (see example below).

FileName

OrangeJuiceSortingRawData.xlsx

Author(s)

Herve Abdi

Examples

path2file <- system.file("extdata",
           "OrangeJuiceSortingRawData.xlsx", package = 'DistatisR')
OrangeDataSort <- read.df.excel(path = path2file,
                           sheet = 'Sorting',
                       voc.sheet = 'Vocabulary')

SUMPCAnormCP

Description

Normalizes a positive semi-definite matrix (i.e., total intertia=1)

Usage

SUMPCAnormCP(Y)

Arguments

Value

Normalized matrix

Examples

A <- toeplitz(c(1, 0.6))
SUMPCAnormCP(A)

Ten Assessors sorted eight beers for distatis analysis

Description

Provide the data.frame Sort: Data set to be used to illustrated the use of the package DistatisR. Ten assessors sorted eight beers. These data come from the Abdi et al.' (2007) paper in Food Quality and Preference. Each column represents the results of the sorting task for one assessor. Beers with the same number were sorted together.

Format

a data frame file containing 10 columns, 8 rows plus the names of the rows and the columns.

Source

Abdi et al. (2007), see https://personal.utdallas.edu/~herve/.

References

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.

21 French assessors sorted 16 blends of Spice for distatis analysis

Description

Provide the data.frame SortSpice: Data set to illustrate the use of the package DistatisR. Assessors are sorting spices. Each column represents the results of the sorting task for one assessor. Spices with the same number were sorted together.

Format

a data frame file containing 21 columns, 16 rows plus the names of the rows and the columns.

Source

Chollet et al. (2014). Paper available from https://personal.utdallas.edu/~herve/

References

Chollet, S., Valentin, D., & Abdi, H. (2014). The free sorting task. In. P.V. Tomasco & G. Ares (Eds), Novel Techniques in Sensory Characterization and Consumer Profiling. Boca Raton: Taylor and Francis.

WinesRankingRawData: an example of an excel file with (simulated) ranking data. Can be read with the function read.df.excel().

Description

WinesRankingRawData: an example of an excel file with (simulated) ranking data (6 wines ranked by 80 Assessors). Can be read by read.df.excel.

Details

In this example of a "ranking task," 80 (simulated or fictitious) assessors ranked 6 red wines from Burgundy (France). The assessor first chooses the most relevant dimension for these wines and then positions the wines on a scale from 1 to 9 for this dimension. The names of the assessors is composed of 4 characters of the general composition w/ma/f01 : 80. The assessors were 40 men and 40 women (first character w/n) and 40 American or 40 French (second character a/f). The red wines that were tasted are Irancy, Saint-Brie, Beaune, Nuits (Cote de Nuits), Beaujolais, and Beaujolais-Nouveau. Irancy & Saint-Brie are near the cities of Auxerre and Chablis, Beaune & Cote de Nuits are from central Burgundy, and Beaujolais and Beaujolais Nouveau are from the south of Burgundy; Beaujolais Nouveau is a young wine (a primeur) released in November of its year, after only a few weeks of fermentation.

Availability

To fetch this dataset use system.file() (see example below).

FileName

WinesRankingRawData.xlsx

Author(s)

Herve Abdi

Examples

path2file <- system.file("extdata",
           "WinesRankingRawData.xlsx", package = 'DistatisR')
ranking6Wines <- read.df.excel(path = path2file, sheet = 'Ranking')

25 assessors twice sort and describe 12 amaris (i.e., bitter)

Description

sortingAmari: 25 assessors twice sort and describe 12 amaris (i.e., bitter). The data consist in a list containing 3 objects: 1) Sorting a data frame with the 12 by 25*2 sorting data, 2) cubeOfVocabulary: an array of dimensions a 12 products * 41 words (vocabulary) * 50 assessors-repetition (i.e., 25 assessors *2 repetitions), and 3) a data frame: information4Amaris storing the description of the amaris.

Usage

data("amariSorting")

Format

a list containing 3 objects: 1) Sorting a data frame with the 12 by 25*2 sorting data, 2) cubeOfVocabulary: and array of dimensions a 12 products * 41 words (vocabulary) * 50 assessors-repetition (i.e., 25 assessors *2 repetitions), and 3) a data frame: information4Amaris storing the description of the amaris.

Details

The assessors are described by their 5 character names with the following code: the first letter m/f give the gender of the assessors (male versus female), the second and third characters go from 01 to 25 and uniquely identify the assessor, the fourth and fifth characters identify the repetition (r1 vs. r2).

Some words of the vocabulary have been shortened for convenience; here is the list of the short and long versions of the descriptors that have shortened: 'coffee_chocolate' <- 'coffee', fortified wine' <- 'wine', 'red fruit' <- 'red', 'soy sauce' <- 'soy', spirit (green)' <- 'spirit', 'vegetal_green' <- 'vegetal', and 'warm spice' <- 'spice'.

In the data sets, the amaris are identified with shortened names, the whole names can be found in the data frame information4Amaris.

Author(s)

Jacob Lahne, Hervé Abdi, & Hildegarde Heymann

Source

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. (available from https://personal.utdallas.edu/~herve/).

References

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.

Novices and Experts sorted 3 types of beers from 3 different brewers without and without seeing the beers.

Description

beersBlindSorting: several different groups of Novices and Beer-Experts sorted 9 beers with (Vision) or without (Blind) visual information. The 9 beers were 3 types of beers (blond, amber, and dark) obtained from 3 different brewers (Pelforth, Chti, & Leffe).

Usage

beersBlindSorting

Format

A list with 11 lists each storing a 9*9*N_k cubeOfDistance and one 9*9 distance table. Specifically:

$EV

9*9* 17 Experts, Vision

$EBr1

9*9* 13 Experts, Blind, rep 1

$EBr2

9*9* 13 Experts, Blind, rep 2

$EBr3

9*9* 13 Experts, Blind, rep 3

$EBr4

9*9* 13 Experts, Blind, rep 4

$NV

9*9* 21 Novices, Vision

$NBr1

9*9* 18 Novices, Blind, rep 1

$NBr2

9*9* 18 Novices, Blind, rep 2

$NBr3

9*9* 18 Novices, Blind, rep 3

$NBr4

9*9* 18 Novices, Blind, rep 4

$N2B

9*9* 37 Novices, Blind. (Group 2)

Details

Nine different commercial beers (denoted PelfBL, PelfA, PelfBR, ChtiBL, ChtiA, ChtiBR, LeffBL, LeffA, and LeffBR) were evaluated. These beers came from three different breweries: Pelforth (noted Pelf), Chti, (Chti), and Leffe (Leff), and each brewery provided three types of beer: blond (BL), amber (A), and dark (BR).

For each sorting task the data file gives the sorting distance matrix: A 9-beers by 9-beers distance matrix in which at the intersection of a row (representing one beer) and a column (representing another beer) a value of 0 indicates that these two beers were sorted in the same group and a value of 1 indicates that these two beers were sorted in different groups.

Multiple groups of novices and experts participated to the experiments. In the blind condition, the group of experts and one group of novices repeated four times the sorting taks (replication 1 to 4).

Author(s)

Maud Lelièvre, Sylvie Chollet , Hervé Abdi, and Dominique Valentin.

Source

A longer description of the data, story, first analysis, etc. can be found in: Lelièvre M., Chollet, S., Abdi, H., & Valentin, B. (2009). Beer trained and untrained assessors rely more on vision than on taste when they categorize beers. Chemosensory Perception, 2, 143-153. available from https://personal.utdallas.edu/~herve/abdi-lcav09-inpress.pdf

Computes group alphas and group factor scores for K groups of observations in distatis.

Description

computePartial4Groups: Computes group alphas and group factor scores for K groups of observations used to compute the compromise (i.e., matrix **S**) in a distatis analysis.

Usage

computePartial4Groups(resDistatis, DESIGN)

Arguments

Details

In DISTATIS, the compromise is computed as a weighted (with the alpha-coefficients) sum of the K pseudo-covariance matrices **S**k, computePartial4Groups sums all the alpha coefficients of a group to compute each group partial factor scores.

Value

A list with

• "GroupFS: " The K weighted mean coordinates

• "groupAlpha: " The K alpha weights

Author(s)

Hervé Abdi

See Also

distatis

compute a cube of covariance and a cube of distance between the items (rows) of a brick of measurements (when all blocks have the same number of variables).

Description

createCubeOfCovDis compute a cube of covariance and a cube of (squared) Euclidean distance between the items (rows) of a brick of measurements. The variables describing the items can scaled to norm 1 and centered. The whole matrix can be scaled by its first eigenvalue (a la DISTATIS). All "slices" of the brick should have the same number of variables. For different number of variables per block, see list2CubeOfCov.

Usage

createCubeOfCovDis(brickOfData, scale = TRUE, center = TRUE, ev.scale = TRUE)

Arguments

Details

The input of createCubeOfCovDis is a I items by J quantitative variables by K assessors (as obtained, e.g., from a projective mapping task).

By default createCubeOfCovDis centers and normalizes each column for each slice of the brick and then normalize each covariance matrix such that the first eigenvalue of each covariance matrix is equal to 1.

A distatis analysis of the Distance matrices with the option Distance = TRUE will give the same results as the distatis analysis of the Covariance matrices with the option Distance = FALSE.

Value

a list with 1) cubeOfCovariance a cube of K I by I covariance matrices; and 2) codecubeOfDistance a cube of K I by I (squared) Euclidean distance matrices.

Author(s)

Herve Abdi

See Also

list2CubeOfCov

Examples

# use the data from the BeersProjectiveMapping dataset
data("BeersProjectiveMapping") 
# Create the I*J_k*K brick of data
zeBrickOfData <- projMap2Cube(
                     BeersProjectiveMapping$ProjectiveMapping, 
                     shape = 'flat',  nVars = 2)
# Create the cubes of Covariance and Distance                     
cubes <- createCubeOfCovDis(zeBrickOfData$cubeOfData)

3-Way MDS based on the "STATIS" optimization procedure.

Description

distatis: Implements the DISTATIS method which is a 3-way generalization of metric multidimensional scaling (a.k.a. classical MDS or principal coordinate analysis).

Usage

distatis(
  LeCube2Distance,
  Norm = "MFA",
  Distance = TRUE,
  double_centering = TRUE,
  RV = TRUE,
  nfact2keep = 3,
  compact = FALSE
)

Arguments

Details

distatis takes as input a set of K distance matrices (or positive semi-definite matrices such as scalar products, covariance, or correlation matrices) describing a set of I observations. From this set of matrices distatis computes: (1) a set of factor scores that describes the similarity structure of the K distance matrices (e.g., what distance matrices describe the observations in the same way, what distance matrices differ from each other) (2) a set of factor scores (called the compromise factor scores) that best describes the similarity structure of the I observations and (3) I sets of partial factor scores that show how each individual distance matrix "sees" the compromise space.

distatis computes the compromise as an optimum linear combination of the cross-product matrices associated to each distance (or positive positive semi-definite) matrix.

distatis can also be applied to a set of scalar products, covariance, or correlation matrices.

DISTATIS is part of the STATIS family. It is often used to analyze the results of sorting tasks.

Value

distatis sends back the results via two lists: res.Cmat and res.Splus. Note that items with a * are the only ones sent back when using the compact = TRUE option.

• res.Cmat$C The I\times I C matrix of scalar products (or R_V between distance matrices).

• res.Cmat$vectors The eigenvectors of the C matrix

• res.Cmat$alpha * The \alpha weights

• res.Cmat$value The eigenvalues of the C matrix

• res.Cmat$G The factor scores for the C matrix

• res.Cmat$ctr The contributions for res.Cmat$G,

• res.Cmat$cos2 The squared cosines for res.Cmat$G

• res.Cmat$d2 The squared Euclidean distance for res.Cmat$G.

• res.Splus$SCP an I\times I\times K array. Contains the (normalized if needed) cross product matrices corresponding to the distance matrices.

• res.Splus$Splus * The compromise (optimal linear combination of the SCP's').

• res.Splus$eigValues * The eigenvalues of the compromise).

• res.Splus$eigVectors * The eigenvectors of the compromise).

• res.Splus$tau * The percentage of explained inertia of the eigenValues).

• res.Splus$ProjectionMatrix The projection matrix used to compute factor scores and partial factor scores.

• res.Splus$F The factor scores for the observations.

• res.Splus$ctr The contributions for res.Cmat$F.

• res.Splus$cos2 The squared cosines for res.Cmat$F.

• res.Splust$d2 The squared Euclidean distance for res.Cmat$F.

• res.Splus$PartialF an I \times \code{nf2keep} \times K array. Contains the partial factors for the distance matrices.

Author(s)

Hervé Abdi #@seealso GraphDistatisAll GraphDistatisBoot #GraphDistatisCompromise # GraphDistatisPartial #GraphDistatisRv DistanceFromSort #BootFactorScores BootFromCompromise #as help,

References

Abdi, H., Valentin, D., O'Toole, A.J., & Edelman, B. (2005). DISTATIS: The analysis of multiple distance matrices. Proceedings of the IEEE Computer Society: International Conference on Computer Vision and Pattern Recognition. (San Diego, CA, USA). pp. 42–47.

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., Dunlop, J.P., & Williams, L.J. (2009). How to compute reliability estimates and display confidence and tolerance intervals for pattern classifiers 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.

The R_V coefficient is described in

Abdi, H. (2007). RV coefficient and congruence coefficient. In N.J. Salkind (Ed.): Encyclopedia of Measurement and Statistics. Thousand Oaks (CA): Sage. pp. 849–853.

Abdi, H. (2010). Congruence: Congruence coefficient, RV coefficient, and Mantel Coefficient. In N.J. Salkind, D.M., Dougherty, & B. Frey (Eds.): Encyclopedia of Research Design. Thousand Oaks (CA): Sage. pp. 222–229.

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

Examples

# 1. Load the DistAlgo data set 
# (available from the DistatisR package).
data(DistAlgo)
# DistAlgo is a 6*6*4 Array (face*face*Algorithm)
#------------------------------------------------------------------
# 2. Call the DISTATIS routine with the array 
#  of distance (DistAlgo) as parameter
DistatisAlgo <- distatis(DistAlgo)

Left (i.e., pre) Multiply a matrix by a diagonal matrix

Description

ldiag: Left (i.e., pre) Multiply a matrix by a diagonal matrix (with only the diagonal elements being given).

Usage

ldiag(y, X)

Arguments

Value

an I by J matrix equal to diag(y)

Author(s)

Hervé Abdi

See Also

rdiag

compute a cube of covariance and a cube of distance between the items (rows) of a matrix of measurements comprising K different blocks of possibly different number of variables.

Description

list2CubeOfCovDis compute a cube of covariance and a cube of (squared) Euclidean distance between the items (rows) a matrix of measurements comprising K different blocks of possibly different number of variables. The variables describing the items can scaled to norm 1 and centered. The whole matrix for a block can be scaled by its first eigenvalue (a la DISTATIS). Blocks can have different number of variables and when all blocks have same number of variables list2CubeOfCovDis is a more efficient alternative

Usage

list2CubeOfCovDis(Data, Judges, scale = TRUE, center = TRUE, ev.scale = TRUE)

Arguments

Details

The input of list2CubeOfCovDis is a I items by J quantitative variables that are organized in K blocks (i.e., submatrices) each comprising J_k variables (with sum J_k = J).

By default list2CubeOfCovDis centers and normalizes each column for each block and then normalize each covariance matrix such that the first eigenvalue of each covariance matrix (for a given block) is equal to 1.

A distatis analysis of the Distance matrices with the option Distance = TRUE will give the same results as the distatis analysis of the Covariance matrices with the option Distance = FALSE.

Value

a list with 1) cubeOfCovariance a cube of K I by I covariance matrices; and 2) codecubeOfDistance a cube of K I by I (squared) Euclidean distance matrices.

Author(s)

Herve Abdi

See Also

list2CubeOfCov

Examples

path2file <- system.file("extdata",
                        "BeersFlashProfile.xlsx", 
                        package = 'DistatisR')
# read the data in the excel file with read.df.excel
beerDataFlash  <- read.df.excel(path = path2file,
                               sheet = 'Rankings')$df.data
# Extract the namers of the judges (first 2 characters)
JudgesVars <- colnames(beerDataFlash)
zeJudges <- substr(JudgesVars,1,2)
 # call list2CubeOfCovDis
test.list2 <- list2CubeOfCovDis(Data = beerDataFlash ,
                               Judges =  zeJudges)

Metric (classical) Multidimensional Scaling (a.k.a Principal Coordinate Analysis) of a (squared Euclidean) Distance Matrix.

Description

mmds: Perform a Metric Multidimensional Scaling (MMDS) of an (squared Euclidean) distance matrix measured between a set of objects (with or without masses).

Usage

mmds(DistanceMatrix, masses = NULL)

Arguments

Details

mmds gives factor scores that make it possible to draw a map of the objects such that the distances between objects on the map best approximate the original distances between objects.

Value

Sends back a list

Method

MMDS transform the squared Euclidean distance matrix into a (double centered) covariance-like matrix which is then analyzed via its eigen-decomposition. The factor scores of each dimension are scaled such that their variance (i.e., the sum of their weighted squared factor scores) is equal to the eigen-value of the corresponding dimension. Note that if the masses vector is absent, equal masses (i.e., 1 divided by number of objects) are used.

Technicalities

the distance matrix to be analyzed is supposed to be a squared Euclidean distance matrix. Note also that a non Euclidean distance matrix will have negative eigenvalues that will be ignored by mmds which, therefore, gives the best Euclidean approximation to this non-Euclidean distance matrix (note that, non-metric MDS maybe a better method in these cases).

Author(s)

Herve Abdi

References

The procedure and references are detailed in: Abdi, H. (2007). Metric multidimensional scaling. In N.J. Salkind (Ed.): Encyclopedia of Measurement and Statistics. Thousand Oaks (CA): Sage. pp. 598–605.

(Paper available from https://personal.utdallas.edu/~herve/).

See Also

GraphDistatisCompromise distatis

Examples

# An example of MDS from Abdi (2007)
# Discriminability of Brain States
# Table 1.
# 1. Get the distance matrix
D <- matrix(c(
0.00, 3.47, 1.79, 3.00, 2.67, 2.58, 2.22, 3.08,
3.47, 0.00, 3.39, 2.18, 2.86, 2.69, 2.89, 2.62,
1.79, 3.39, 0.00, 2.18, 2.34, 2.09, 2.31, 2.88,
3.00, 2.18, 2.18, 0.00, 1.73, 1.55, 1.23, 2.07,
2.67, 2.86, 2.34, 1.73, 0.00, 1.44, 1.29, 2.38,
2.58, 2.69, 2.09, 1.55, 1.44, 0.00, 1.19, 2.15,
2.22, 2.89, 2.31, 1.23, 1.29, 1.19, 0.00, 2.07,
3.08, 2.62, 2.88, 2.07, 2.38, 2.15, 2.07, 0.00),
ncol = 8, byrow=TRUE)
rownames(D) <- c('Face','House','Cat','Chair','Shoe','Scissors','Bottle','Scramble')
colnames(D) <- rownames(D)
# 2. Call mmds
BrainRes <- mmds(D)
# Note that compared to Abdi (2007)
# the factor scores of mmds are equal to F / sqrt(nrow(D))
# the eigenvalues of mmds are equal to \Lambda *{1/nrow(D)}
# (ie., the normalization differs but the results are proportional)
# 3. Now a pretty plot with the prettyPlot function from prettyGraphs
prettyGraphs::prettyPlot(BrainRes$FactorScore,
           display_names = TRUE,
           display_points = TRUE,
           contributionCircles = TRUE,
           contributions = BrainRes$Contributions)
# 4. et Voila!

62 assessors from 5 countries sort 16 spice samples

Description

multiculturalSortingSpices: 62 participants from 5 different countries (USA, France, India, Spain, and Vietnam) for 16 different spices (including 6 mixtures of spices).

The data consist in a list containing 7 objects (for all sorting data the number at the intersection of a row and a colum indicates the number of the pile in which the spice was sorted);): : A data frame containing the 1) sortAll: A data frame containing the results of the sorting task for all 62 participants, 2) sortAmerican: A data frame containing the results of the sorting task for the 9 American participants, 3) sortFrench: A data frame containing the results of the sorting task for the 21 French participants, 4) sortIndian: A data frame containing the results of the sorting task for the 15 Indian participants, 5) sortSpanish: A data frame containing the results of the sorting task for the 11 Spanish participants, 6) sortVietnamese: A data frame containing the results of the sorting task for the 6 Vietnamese participants, and 7) spicesDescription A data frame containing the description of the Spices.

Usage

data("multiculturalSortingSpices")

Format

A list containing 7 objects (for all sorting data, the number at the intersection of a row and a colum indicates the number of the pile in which the spice was sorted): : A data frame containing the 1) sortAll: A data frame containing the results of the sorting task for all 62 participants, 2) sortAmerican: A data frame containing the results of the sorting task for the 9 American participants, 3) sortFrench: A data frame containing the results of the sorting task for the 21 French participants, 4) sortIndian: A data frame containing the results of the sorting task for the 15 Indian participants, 5) sortSpanish: A data frame containing the results of the sorting task for the 11 Spanish participants, 6) sortVietnamese: A data frame containing the results of the sorting task for the 6 Vietnamese participants, and 7) spicesDescription A data frame containing the description of the Spices.

Details

In the data frames, the spice blends are identifed wiht acronyms that are expended in the data frame spicesDescription.

Author(s)

Chollet, S., Valentin, D., & Abdi, H.

References

Part of these data (i.e., the French sample) is described and analyzed in Chollet, S., Valentin, D., & Abdi, H. (2014). Free sorting task. In P.V. Tomasco & G. Ares (Eds), Novel Techniques in Sensory Characterization and Consumer Profiling. Boca Raton: Taylor and Francis. pp 207-227.

Print C matrix results

Description

Print C matrix results.

Usage

## S3 method for class 'Cmat'
print(x, ...)

Arguments

Value

an array with results from the analysis. prints to screen

Author(s)

Derek Beaton

Print DistatisR results

Description

Print DistatisR results.

Usage

## S3 method for class 'DistatisR'
print(x, ...)

Arguments

Value

an array with results from the analysis. prints to screen

Author(s)

Derek Beaton

Change the print function for objects of the class 'F4voc' (e.g., output from function projectVoc).

Description

Change the print function for objects of the class 'F4voc' (e.g., ooutput from function projectVoc).

Usage

## S3 method for class 'F4voc'
print(x, ...)

Arguments

Value

invisible; contents are printed to screen

Author(s)

Hervé Abdi

Print F_alpha_k results

Description

Print F_alpha_k results

Usage

## S3 method for class 'F_alpha_k'
print(x, ...)

Arguments

Value

invisible; contents are printed to screen

Author(s)

Hervé Abdi

Print S+ matrix results

Description

Print S+ matrix results.

Usage

## S3 method for class 'Splus'
print(x, ...)

Arguments

Value

an array with results from the analysis. prints to screen

Author(s)

Derek Beaton

Change the print function for class 'beersBlind'

Description

Change the print function for class 'beersBlind'

Usage

## S3 method for class 'beersBlind'
print(x, ...)

Arguments

Value

invisible; contents are printed to screen

Author(s)

Hervé Abdi

Change the print function for the class cubeOfCovDis

Description

Change the print function for the class cubeOfCovDis: (output of createCubeOfCovDis.

Usage

## S3 method for class 'cubeOfCovDis'
print(x, ...)

Arguments

Value

invisible; contents are printed to screen

Author(s)

Hervé Abdi

Change the print function for cubeSort

Description

Change the print function for cubeSort

Usage

## S3 method for class 'cubeSort'
print(x, ...)

Arguments

Value

invisible; contents are printed to screen

Author(s)

Herve Abdi

Change the print function for the data set: dataAmari

Description

Change the print function for the data set: dataAmari

Usage

## S3 method for class 'dataAmari'
print(x, ...)

Arguments

Value

invisible; contents are printed to screen

Author(s)

Hervé Abdi

Change the print function for the data set: multiculturalSortingSpices

Description

Change the print function for the data set: multiculturalSortingSpices (class dataSortingSpices)

Usage

## S3 method for class 'dataSortingSpices'
print(x, ...)

Arguments

Value

invisible; contents are printed to screen

Author(s)

Hervé Abdi

Change the print function for the data set: dataSortingWines

Description

Change the print function for the data set: dataSortingWines

Usage

## S3 method for class 'dataSortingWines'
print(x, ...)

Arguments

Value

invisible; contents are printed to screen

Author(s)

Hervé Abdi

Change the print function for objects of class distatis.data output ofread.df.excel

Description

Change the print function for bootRatios

Usage

## S3 method for class 'distatis.data'
print(x, ...)

Arguments

Value

invisible; contents are printed to screen

Author(s)

Hervé Abdi

Change the print function for the data set: str_BeersProjectiveMapping

Description

Change the print function for the data set: str_BeersProjectiveMapping

Usage

## S3 method for class 'str_BeersProjectiveMapping'
print(x, ...)

Arguments

Value

invisible; contents are printed to screen

Author(s)

Hervé Abdi

Change the print function for voc4distatis

Description

Change the print function for voc4distatis class objects (e.g.,output of Rv).

Usage

## S3 method for class 'voc4distatis'
print(x, ...)

Arguments

Value

invisible; contents are printed to screen

Author(s)

Hervé Abdi

\ reshape a data matrix from projective mapping into a brick of data for a distatis analysis.

Description

projMap2Cube reshapes a data matrix from projective mapping into a brick of data for a distatis analysis. With I products, J variables, and K blocks (assessors), the original data can be 1) "flat" (e.g., I rows as products, columns as K blocks of J Variables) or 2) "long" "flat" (e.g., K blocks of I rows as products by assessors, columns as J Variables).

Usage

projMap2Cube(Data, shape = "flat", nVars = 2, nBlocks = NULL)

Arguments

Details

the output projMap2Cube (i.e., the brick of data) is used as input to the function cubeOfCov that will create the cubeOfDistance (or covariance) that will be used as input of distatis. projMap2Cube guesses the names of the products and variables from the rownames and columns of the data, but this guess needs to be verified.

Value

An I by J by K array (i.e., a brick) to be used to create a cube of distance or covariance.

Author(s)

Herve Abdi

Examples

# Use the data from the BeersProjectiveMapping dataset
data("BeersProjectiveMapping")
# Create the I*J_k*K brick of data
dataBrick <- projMap2Cube(BeersProjectiveMapping$ProjectiveMapping, 
                        shape = 'flat',  nVars = 2)

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

Description

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.

Usage

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

Arguments

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).

Value

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.

Author(s)

Herve Abdi

Source

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

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.

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)

right (i.e., post) Multiply a matrix by a diagonal matrix

Description

rdiag: right (i.e., post) Multiply a matrix by a diagonal matrix (with only the diagonal elements being given).

Usage

rdiag(X, y)

Arguments

Value

an I by J matrix equal to X

Author(s)

Hervé Abdi

See Also

ldiag

read.df.excel reads distatis formated ranking or sorting data from an excel file.

Description

read.df.excel reads distatis formated ranking or sorting data from an excel file.

Usage

read.df.excel(path, sheet, col_names = TRUE, voc.sheet = NULL)

Arguments

Details

@details The data are read from an excel file in which the rows are the Products to evaluate and the columns are the Assessors (e.g., Judges, Participants, Subjects, Evaluators). Depending upon the type of data, the numbers represent a partition, a rank, or a score. These data are used as input of DistanceFromSort or DistanceFromRank. A contingency table for the vocabulary can also be read in a different sheet. read.df.excel is a (small) shell on top of readxl::read_excel, note however that whereas readxl::read_excel returns a tibble, read.df.excel returns a list with one or two (depending upon the options) dataframe(s).

Author(s)

Herve Abdi

Function to compute the RV coefficient between to conformable matrices

Description

Function to compute the RV coefficient between to conformable matrices

Usage

rv(A, B)

Arguments

Value

the RV coefficient between A and B.

Examples

A <- toeplitz(2:1)
B <- diag(2)
rv(A, B)

A variation over the base R scale function that avoids the "divide by 0 = NA" problem.

Description

scale1: A variation over the base R scale function. The function scale1: centers (if needed) and scales a vector to norm 1; if the vector contains values all equal to a constant, scale1 sets all values to 0 (in lieu of NA as scale does). Usefull when pre-processing tables for PCA-like type of analyses.

Usage

scale1(x, scale = TRUE, center = TRUE)

Arguments

Value

a centered (if required) and norm-1 (if required) normalized vector.

Author(s)

Hervé Abdi

Examples

 toto   <- runif(10)     # 10 random numbers between 0 and 1
 tutu   <- scale1(toto)  # toto centered and normalized
 toto0  <- rep(1,10)     # 10 numbers all equal to 1
 tutu0  <- scale1(toto0) # scaled to 0 # Compare with
 tutuNA <- scale(toto0)  # all numbers set to NA

Novices and wines experts sort red, rosé, and white wines

Description

sortingWines: 26 novices participants and 19 wine experts sort (by smell alone, without visual information) 18 wines (6 red, 6 rosé, and 6 whites) into three categories. The experts also performed a free sorting task on the wines (i.e. with as many groups as the wished).

The data consist in a list containing 4 objects: 1) freeSortExperts: a data frame with the 18 wines by 19 experts free sorting data (the number at the intersection of a row and a colum indicates the number of the pile in which the wine was sorted); 2) ternarySortExperts: a data frame with the 18 wines by 19 experts ternary (i.e., in three piles) sorting data (the number at the intersection of a row and a colum indicates the number of the pile in which the wine was sorted); 3) $ternarySortNovices: a data frame with the 18 wines by 19 novices ternary (i.e., in three piles) sorting data (the number at the intersection of a row and a colum indicates the number of the pile in which the wine was sorted); and 4) vinesDescription a data frame storing the description of the 18 wines.

Usage

data("sortingWines")

Format

a list containing 4 objects: 1) freeSortExperts: a data frame with the 18 wines by 19 experts free sorting data (the number at the intersection of a row and a colum indicates the number of the pile in which the wine was sorted); 2) ternarySortExperts: a data frame with the 18 wines by 19 experts ternary (i.e., in three piles) sorting data (the number at the intersection of a row and a colum indicates the number of the pile in which the wine was sorted); 3) $ternarySortNovices: a data frame with the 18 wines by 19 nivices ternary (i.e., in three piles) sorting data (the number at the intersection of a row and a colum indicates the number of the pile in which the wine was sorted); and 4) vinesDescription a data frame storing the description of the 18 wines.

Details

The wines were served in dark glasses and the sorting task was performed with red light (this way all wines look black). In the experiment, the wines were labeled with three-digit codes, for more details see Ballester et al. (2009). Only the experts performed the free sorting task.

In the data sets, the wines are identified with shortened names, the whole names can be found in the data frame. All the wines were from the 2005 vintage (see Ballester et al., 2009 for details)

Compared to the original data, some missing data were added to the set after imputation of the missing data (a total of 4 entries). The current data include only 19 experts out the original 27 experts. vinesDescription.

Author(s)

Ballester, J., Abdi, H., Langlois, J., Peyron, D., & Valentin, D.

References

For more details see:

Ballester, J., Abdi, H., Langlois, J., Peyron, D., & Valentin, D. (2009). The odor of colors: Can wine experts and novices distinguish the odors of white, red, and rosé wines? Chemosensory Perception, 2, 203-213.

Supplementary element(s) projection in DISTATIS

Description

supplementalProjection4distatis: Computes for distatis the projection as supplementary element(s) (a.k.a. "out of sample") of a set of squared matrices. The matrices to be projected need to be of the same type (e.g., distance, correlation) as the matrices used inn the original call to distatis.

Usage

supplementalProjection4distatis(res.distatis, elsupp)

Arguments

Value

the coordinates of the supplementary and active elements in the RV space. *** HA comment: Maybe we also want to send the square cosines to give the quality of representation.

Author(s)

Vincent Guillemot

Transforms a data.frame of products by vocabulary of assessors into a products by words (from vocabulary) contingency table.

Description

vocabulary2CT Transforms a data.frame of products by vocabulary of assessors into 1) a cube of 0/1 contingency tables (one per assessor); and 2) a products by words (from vocabulary) contingency table. In this contingency table, the number at the intersection of a row (product) and a column (word) is the number of assessors who used this word to describe that product.

@details the cube of 0/1 contingency tables (i.e., cubeOfVocabulary can also be analyzed with the package PTCA4CATA as a pseudo Check All That Apply (CATA) data set.

Usage

vocabulary2CT(df.voc)

Arguments

Value

a list with 1) cubeOfVocabulary: a 0/1 array of dimension products by words (from the vocabulary) by assessors where each "products by vocabulary" slice gives the vocabulary chosen by the assessor to describe the products; and 2) CT.vocabulary a matrix storing the products by words contingency table.

Author(s)

Herve Abdi

See Also

unnest_tokens count BeersProjectiveMapping

Examples

# Get the BeersProjectiveMapping example
data("BeersProjectiveMapping")
aContingenyTable <- vocabulary2CT(BeersProjectiveMapping$Vocabulary)