distatis 3-Way MDS based on the STATIS optimization procedure
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.
distatis(LeCube2Distance, Norm = "MFA",
Distance = TRUE, RV = TRUE,
nfact2keep = 3,
compact = FALSE)LeCube2Distance |
an "observations * observations * distance matrices" array of dimensions I*I*K. Each of the K "slices" is a I*I square distance (or covariance) matrix describing the I observations. |
Norm |
Type of normalization used for each cross-product matrix derived from
the distance (or covariance) matrices.
Current options are |
Distance |
if TRUE ( |
RV |
TRUE ( |
nfact2keep |
Numner of factors to keep for the computation of the factor scores of the observations. |
compact |
if FALSE we provide detailled output, if TRUE
we send back only the alpha weights
(this option is used to make the bootstrap routine
|
DISTATIS is part of the STATIS family. It is often used to analyze the results of sorting tasks.
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 |
Results for the between distance matrices analysis. |
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 |
Results for the between observation analysis. |
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.
Herve Abdi
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)
# 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)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.