distatis 3-Way MDS based on the STATIS optimization procedure

Description

Implements the DISTATIS method which a 3-way generalization of metric multidimensional scaling (a.k.a. classical MDS or principal coordinate analysis). distatis takes a set of K distance matrices describing a set of I observations and computes (1) a set of factor scores that describes the similarity structure of the 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) for the observations that best describes the similarity structure of the observations and (3) 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 matrix. distatis can also be applied to a set of covariance matrices.

Usage

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

Arguments

Details

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*I C matrix of scalar products (or Rv 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.CmatG The factor scores for the C matrix

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

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

• 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$PartialF an I*nf2keep*K array. Contains the partial factors for the distance matrices.

Author(s)

Herve Abdi

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 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.

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 www.utdallas.edu/~herve)

See Also

GraphDistatisAll GraphDistatisBoot GraphDistatisCompromise GraphDistatisPartial GraphDistatisRv DistanceFromSort BootFactorScores BootFromCompromise

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)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(DistatisR)
Loading required package: prettyGraphs
Loading required package: car
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/DistatisR/distatis.Rd_%03d_medium.png", width=480, height=480)
> ### Name: distatis
> ### Title: 'distatis' 3-Way MDS based on the STATIS optimization procedure
> ### Aliases: distatis DiSTATIS CovSTATIS covstatis
> ### Keywords: distatis mds
> 
> ### ** 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)
> 
> 
> 
> 
> dev.off()
null device 
          1 
>