smacofSphere {smacof}

Spherical SMACOF

Description

Dual and primal approach for spherical SMACOF.

Usage

smacofSphere(delta, ndim = 2, type = c("ratio", "interval", "ordinal","mspline"), 
             algorithm = c("dual", "primal"), weightmat = NULL, 
             init = "torgerson", ties = "primary", verbose = FALSE, penalty = 100, 
             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

ndim

Number of dimensions

type

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

algorithm

Algorithm type (see details)

weightmat

Optional matrix with dissimilarity weights

init

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

ties

Tie specification for non-metric MDS only

verbose

If TRUE, intermediate stress is printed out

penalty

Penalty parameter for dual algorithm (larger 0), see details

relax

If TRUE, block relaxation is used for majorization (dual algorithm)

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

For large scale problems it is suggested to use the dual algorithm. Using the penalty parameter (dual algorithm), the user allow for slight point deviations from the circle (the higher the penalty, the stricter the algorithm is in terms of placing points in the sphere, see examples section below).

Value

delta

Observed dissimilarities

obsdiss

Observed dissimilarities, normalized

obsdiss1

Dual SMACOF: Observed dissimilarities

obsdiss2

Dual SMACOF: Restriction matrix

confdist

Configuration dissimilarities

conf

Matrix with fitted configurations

spp

Stress per point

resmat

Matrix with squared residuals

rss

Residual sum-of-squares

stress

Stress-1 value

init

Starting configurations

ndim

Number of dimensions

dummyvec

Dummy vector of restriction matrix

model

Type of smacof model

niter

Number of iterations

nobj

Number of objects

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, doi:10.18637/jss.v031.i03

See Also

smacofRect, smacofIndDiff, smacofSym,smacofConstraint

Examples

## spherical SMACOF solution for trading data
## dual algorithm
res <- smacofSphere(trading, type = "ordinal")  
res
plot(res)

## lower penalty
res <- smacofSphere(trading, penalty = 20, type = "ordinal")  
res
plot(res)

## primal algorithm, interval
res <- smacofSphere(trading, type = "interval", algorithm = "primal")  
res