MDS {MultBiplotR}

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)