MultBiplotR (version 23.11.0)

SMACOF: SMACOF

Description

SMACOF algorithm for symmetric proximity matrices

Usage

SMACOF(P, X = NULL, W = NULL, 
Model = c("Identity", "Ratio", "Interval", "Ordinal"), 
dimsol = 2, maxiter = 100, maxerror = 1e-06, 
StandardizeDisparities = TRUE, ShowIter = FALSE)

Value

An object of class Principal.Coordinates and MDS. The function adds the information of the MDS to the object of class proximities. Together with the information about the proximities the object has:

Analysis

The type of analysis performed, "MDS" in this case

X

Coordinates for the objects

D

Distances

Dh

Disparities

stress

Raw Stress

stress1

stress formula 1

stress2

stress formula 2

sstress1

sstress formula 1

sstress2

sstress formula 2

rsq

Squared correlation between disparities and distances

rho

Spearman correlation between disparities and distances

tau

Kendall correlation between disparities and distances

Arguments

P

A matrix of proximities

X

Inial configuration

W

A matrix of weights~

Model

MDS model.

dimsol

Dimension of the solution

maxiter

Maximum number of iterations of the algorithm

maxerror

Tolerance for convergence of the algorithm

StandardizeDisparities

Should the disparities be standardized

ShowIter

Show the iteration proccess

Author

Jose Luis Vicente-Villardon

Details

SMACOF performs multidimensional scaling of proximity data to find a least- squares representation of the objects in a low-dimensional space. A majorization algorithm guarantees monotone convergence for optionally transformed, metric and nonmetric data under a variety of models.

References

Commandeur, J. J. F. and Heiser, W. J. (1993). Mathematical derivations in the proximity scaling (PROXSCAL) of symmetric data matrices (Tech. Rep. No. RR- 93-03). Leiden, The Netherlands: Department of Data Theory, Leiden University.

Kruskal, J. B. (1964). Nonmetric multidimensional scaling: A numerical method. Psychometrika, 29, 28-42.

De Leeuw, J. & Mair, P. (2009). Multidimensional scaling using majorization: The R package smacof. Journal of Statistical Software, 31(3), 1-30, http://www.jstatsoft.org/v31/i03/

Borg, I., & Groenen, P. J. F. (2005). Modern Multidimensional Scaling (2nd ed.). Springer.

Borg, I., Groenen, P. J. F., & Mair, P. (2013). Applied Multidimensional Scaling. Springer.

Groenen, P. J. F., Heiser, W. J. and Meulman, J. J. (1999). Global optimization in least squares multidimensional scaling by distance smoothing. Journal of Classification, 16, 225-254.

Groenen, P. J. F., van Os, B. and Meulman, J. J. (2000). Optimal scaling by alternating length-constained nonnegative least squares, with application to distance-based analysis. Psychometrika, 65, 511-524.

See Also

MDS, PrincipalCoordinates

Examples

data(spiders)
Dis=BinaryProximities(spiders)
MDSSol=SMACOF(Dis$Proximities)