icExplore function

Exploring Initial Configurations

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

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)

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).

Returns

• mdsfit: Fitted MDS objects (NULL if returnfit = FALSE)

• conf: Configuration based on multiple random starts

• stressvec: Vector with stress values

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