R: Symmetric smacof

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smacofSym {smacof}

R Documentation

Symmetric smacof

Description

Multidimensional scaling (stress minimization: SMACOF) on symmetric dissimilarity matrix.

Usage

smacofSym(delta, ndim = 2, type = c("ratio", "interval", "ordinal", "mspline"), 
          weightmat = NULL, init = NULL, ties = "primary", verbose = FALSE, 
          relax = FALSE, modulus = 1, itmax = 1000, eps = 1e-06, 
          spline.degree = 2, spline.intKnots = 2)

Arguments

`delta`	Either a symmetric dissimilarity matrix or an object of class `"dist"`
`ndim`	Number of dimensions
`weightmat`	Optional matrix with dissimilarity weights
`init`	Matrix with starting values for configurations (optional)
`type`	MDS type: `"interval"`, `"ratio"`, or `"ordinal"` (nonmetric MDS)
`ties`	Tie specification for ordinal MDS only: `"primary"`, `"secondary"`, or `"tertiary"`
`verbose`	If `TRUE`, intermediate stress is printed out
`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 is the simplest MDS-SMACOF version of the package. It solves the stress target function for symmetric dissimiliby means of the majorization approach (SMACOF) and reports the Stress-1 value (normalized). The main output are the coordinates in the low-dimensional space (configurations; conf). This function allows for fitting three basic types of MDS: ratio MDS (default), interval MDS (polynomial transformation), and ordinal MDS (aka nonmetric MDS). It also returns the point stress, i.e. the larger the contribution of a point to the total stress, the worse the fit (see also plot.smacof.

Value

`delta`	Observed dissimilarities, not normalized
`obsdiss`	Observed dissimilarities, normalized
`confdiss`	Configuration dissimilarities
`conf`	Matrix of fitted configurations
`stress`	Stress-1 value for metric MDS
`spp`	Stress per point
`ndim`	Number of dimensions
`model`	Name of smacof model
`niter`	Number of iterations
`nobj`	Number of objects
`type`	Type of MDS model

Author(s)

Jan de Leeuw and Patrick Mair

References

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.

Examples

## simple SMACOF solution for kinship data
data(kinshipdelta)
res <- smacofSym(kinshipdelta)
res
summary(res)
plot(res)
plot(res, type = "p", label.conf = list(TRUE, 3, "darkgray"), pch = 25, col = "red")

## interval MDS
res <- smacofSym(kinshipdelta, type = "interval")
res

## 3D nonmetric SMACOF solution for trading data (secondary approach to ties)
data(trading)
res <- smacofSym(trading, ndim = 3, type = "ordinal", ties = "secondary")
res

[Package smacof version 1.5-0 Index]