smacof (version 2.1-7)

smacofSym: Symmetric smacof

Description

Multidimensional scaling on a symmetric dissimilarity matrix using SMACOF.

Usage

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

Value

delta

Observed dissimilarities, not normalized

dhat

Disparities (transformed proximities, approximated distances, d-hats)

confdist

Configuration distances

conf

Matrix of fitted configurations

stress

Stress-1 value

spp

Stress per point (stress contribution of each point on a percentage scale)

resmat

Matrix with squared residuals

rss

Residual sum-of-squares

weightmat

Weight matrix

ndim

Number of dimensions

init

Starting configuration

model

Name of smacof model

niter

Number of iterations

nobj

Number of objects

type

Type of MDS model

Arguments

delta

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

ndim

Number of dimensions

weightmat

Optional matrix with dissimilarity weights

init

Either "torgerson" (classical scaling starting solution), "random" (random configuration), or a user-defined matrix

type

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

ties

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

principal

If TRUE, principal axis transformation is applied to the final configuration

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

Author

Jan de Leeuw, Patrick Mair, and Patrick Groenen

Details

The function mds() is a wrapper function and can be used instead of smacofSym(). It reports the Stress-1 value (normalized). The main output are the coordinates in the low-dimensional space (configuration; conf; see also plot.smacof).

Four types of MDS can be fitted: ratio MDS (no dissimilarity transformation), interval MDS (linear transformation), ordinal MDS (ordinal transformation with various options for handling ties), and spline MDS (monotone spline transformation). Shepard plots in plot.smacof give insight into this transformation.

Setting principal = TRUE is useful for interpretatbility of the dimensions, or to check hypotheses about the dimensions.

In case of missing input dissimilarities, the weightmat is computed internally so that missings are blanked out during optimization.

References

De Leeuw, J. & Mair, P. (2009). Multidimensional scaling using majorization: The R package smacof. Journal of Statistical Software, 31(3), 1-30, tools:::Rd_expr_doi("10.18637/jss.v031.i03")

Mair, P, Groenen, P. J. F., De Leeuw, J. (2022). More on multidimensional scaling in R: smacof version 2. Journal of Statistical Software, 102(10), 1-47. tools:::Rd_expr_doi("10.18637/jss.v102.i10")

Borg, I., & Groenen, P. J. F. (2005). Modern Multidimensional Scaling (2nd ed.). Springer.

Borg, I., Groenen, P. J. F., & Mair, P. (2018). Applied Multidimensional Scaling and Unfolding (2nd ed.). Springer.

See Also

smacofConstraint, smacofRect, smacofIndDiff, smacofSphere, plot.smacof

Examples

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

## ratio MDS, random starts
set.seed(123)
res <- mds(kinshipdelta, init = "random")
res

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

## spline MDS 
delta <- sim2diss(cor(PVQ40agg))
res <- mds(delta, type = "mspline", spline.degree = 3, spline.intKnots = 4)
res
plot(res, "Shepard")