smacof (version 2.1-7)

icExplore: Exploring Initial Configurations

Description

Allows to user to explore the effect of various random starting configurations when fitting an MDS model.

Usage

icExplore(delta, nrep = 100, returnfit = FALSE, ndim = 2, 
type = c("ratio", "interval", "ordinal","mspline"), weightmat = NULL, ties = "primary",	
verbose = FALSE, relax = FALSE, modulus = 1, itmax = 1000, eps = 1e-6, 
spline.degree = 2, spline.intKnots = 2)

Value

mdsfit

Fitted MDS objects (NULL if returnfit = FALSE)

conf

Configuration based on multiple random starts

stressvec

Vector with stress values

Arguments

delta

Either a symmetric dissimilarity matrix or an object of class "dist"

nrep

Number of initial random configurations

returnfit

If TRUE all fitted models are returned.

ndim

Number of dimensions

weightmat

Optional matrix with dissimilarity weights

type

MDS type: "interval", "ratio", "ordinal" (nonmetric MDS), or "mspline"

ties

Tie specification (ordinal MDS only): "primary", "secondary", or "tertiary"

verbose

If TRUE, replication number is printed

relax

If TRUE, block relaxation is used for majorization

modulus

Number of smacof iterations per monotone regression call

itmax

Maximum number of iterations

eps

Convergence criterion

spline.degree

Degree of the spline for "mspline" MDS type

spline.intKnots

Number of interior knots of the spline for "mspline" MDS type

Details

This function generates a large set of MDS solutions using random initial configurations, matches them all by Procrustean fittings, computes the inter-correlations of their point coordinates, and finally runs an interval MDS of these inter-correlations. It can be used to explore local minima.

In the plot function the number reflects the index of corresponding MDS fit, the size reflects the stress value: the larger the font, the larger the stress (i.e., the worse the solution). The size is associated with a corresponding color shading (the smaller the size the darker the color).

References

Borg, I. and Mair, P. (2017). The choice of initial configurations in multidimensional scaling: local minima, fit, and interpretability. Austrian Journal of Statistics, 46, 19-32. tools:::Rd_expr_doi("10.17713/ajs.v46i2.561")

See Also

mds

Examples

## simple example with 20 random starts
diss <- sim2diss(wish, method = 7)
set.seed(123)
res <- icExplore(diss, type = "ordinal", nrep = 20, returnfit = TRUE)
res
plot(res) 

res$mdsfit[[14]]  ## bad fitting solution
res$mdsfit[[3]]   ## better fitting solution