smacofSym: Symmetric smacof

In smacof: Multidimensional Scaling

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)

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

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.

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

Author(s)

Jan de Leeuw, Patrick Mair, and Patrick Groenen

References

De Leeuw, J. & Mair, P. (2009). Multidimensional scaling using majorization: The R package smacof. Journal of Statistical Software, 31(3), 1-30, \Sexpr[results=rd]{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. \Sexpr[results=rd]{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")

smacof documentation built on Oct. 10, 2024, 5:09 p.m.