MDS: Multidimensional Scaling

In MultBiplotR: Multivariate Analysis Using Biplots in R

Multidimensional Scaling

Description

Multidimensional Scaling using SMACOF algorithm and Bootstraping the coordinates.

Usage

MDS(Proximities, W = NULL, Model = c("Identity", "Ratio", "Interval", "Ordinal"), 
dimsol = 2, maxiter = 100, maxerror = 1e-06, Bootstrap = FALSE, nB = 200, 
ProcrustesRot = TRUE, BootstrapMethod = c("Sampling", "Permutation"), 
StandardizeDisparities = FALSE, ShowIter = FALSE)

Arguments

Proximities	An object of class proximities
W	A matrix of weigths
Model	MDS model. "Identity", "Ratio", "Interval" or "Ordinal".
dimsol	Dimension of the solution
maxiter	Maximum number of iterations of the algorithm
maxerror	Tolerance for convergence of the algorithm
Bootstrap	Should Bootstraping be performed?
nB	Number of Bootstrap samples.
ProcrustesRot	Should the bootstrap replicates be rotated to match the initial configuration using Procrustes?
BootstrapMethod	The bootstrap is performed by samplig or permutaing the residuals?
StandardizeDisparities	Should the disparities be standardized
ShowIter	Show the iteration proccess

Details

Multidimensional Scaling using SMACOF algorithm and Bootstraping the coordinates. MDS 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.

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
Model	MDS model used
RowCoordinates	Coordinates for the objects in the MDS procedure
RawStress	Raw Stress values
stress1	stress formula 1
stress2	stress formula 2
sstress1	sstress formula 1
sstress2	sstress formula 2
rsq	Squared correlation between disparities and distances
Spearman	Spearman correlation between disparities and distances
Kendall	Kendall correlation between disparities and distances
BootstrapInfo	The result of the bootstrap calculations

Author(s)

Jose Luis Vicente Villardon

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

BootstrapSmacof

Examples

data(spiders)
Dis=BinaryProximities(spiders)
MDSSol=MDS(Dis, Bootstrap=FALSE)
plot(MDSSol)

MultBiplotR documentation built on Nov. 21, 2023, 5:08 p.m.