smacofIndDiff: SMACOF for Individual Differences

In smacof: Multidimensional Scaling

SMACOF for Individual Differences

Description

Performs smacof for individual differences also known as Three-Way smacof on a list of dissimilarity matrices. Various restrictions decompositions and restrictions on the weight matrix are provided. The most prominent models are INDSCAL and IDIOSCAL.

Usage

smacofIndDiff(delta, ndim = 2, type = c("ratio", "interval", "ordinal", "mspline"), 
              constraint = c("indscal", "idioscal", "identity"),
              weightmat = NULL, init = "torgerson", ties = "primary",  
              verbose = FALSE, modulus = 1, itmax = 1000, eps = 1e-6,
              spline.degree = 2, spline.intKnots = 2)
              
indscal(delta, ndim = 2, type = c("ratio", "interval", "ordinal", "mspline"), 
        weightmat = NULL, init = "torgerson", ties = "primary", 
        verbose = FALSE, modulus = 1, itmax = 1000, eps = 1e-6,
        spline.degree = 2, spline.intKnots = 2)

idioscal(delta, ndim = 2, type = c("ratio", "interval", "ordinal", "mspline"), 
         weightmat = NULL, init = "torgerson", ties = "primary", 
         verbose = FALSE, modulus = 1, itmax = 1000, eps = 1e-6,
         spline.degree = 2, spline.intKnots = 2)

Arguments

delta	A list of dissimilarity matrices or a list objects of class dist
ndim	Number of dimensions
type	MDS type: "interval", "ratio", "ordinal" (nonmetric MDS), or "mspline"
weightmat	Optional matrix with dissimilarity weights
init	Matrix with starting values for configurations (optional)
ties	Tie specification for non-metric MDS
constraint	Either "indscal", "idioscal", or "identity" (see details)
verbose	If TRUE, intermediate stress is printed out
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

If the constraint is "indscal", INDSCAL is performed with configuration weight matrices restricted to be diagonal. indscal() is a corresponding wrapper function that can be used instead of smacofIndDiff() with "indscal" constraints.

IDIOSCAL can be computed using the "idioscal" argument. The weight matrices are then unconstrained. idioscal() is a corresponding wrapper function that can be used instead of smacofIndDiff() with "idioscal" constraints.

Addtional weight restrictions can be imposed with "identity" which restricts the configurations across individuals/replications/ways to be equal.

Value

delta	Observed dissimilarities
obsdiss	List of observed dissimilarities, normalized
confdist	List of configuration dissimilarities
conf	List of matrices of final configurations
gspace	Joint configuration aka group stimulus space
cweights	Individual weights
stress	Stress-1 value
resmat	Matrix with squared residuals
rss	Residual sum-of-squares
spp	Stress per point (in percent)
spps	Stress per point per subject (in percent, conditional on subject)
sps	Stress per subject (in percent)
ndim	Number of dimensions
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, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v031.i03")}

See Also

smacofConstraint, smacofSym, smacofRect, smacofSphere

Examples

## Example 1: rectangle perception data
res.diag <- indscal(perception, type = "ordinal")        ## INDSCAL
res.diag$cweights
plot(res.diag)
plot(res.diag, type = "p", pch = 25, col = 4, label.conf = list(label = TRUE, pos = 3, col = 4))

res.idio <- idioscal(perception, type = "ordinal")  ## IDIOSCAL
Wk <- res.idio$cweights
G <- res.idio$gspace
G
G

## identity restricted weights
res.id <- smacofIndDiff(perception, type = "ordinal", constraint = "identity")     
summary(res.id)
res.id$cweights
plot(res.id)
plot(res.id, type = "p", pch = 25, col = 4, label.conf = list(label = TRUE, pos = 3, col = 4))


## Example 2: Helm's color data 
res.helm <- indscal(helm, type = "interval")
plot(res.helm, plot.type = "confplot")
barplot(sort(res.helm$sps, decreasing = TRUE), main = "Stress per Subject", cex.names = 0.8) 
plot(res.helm, plot.type = "bubbleplot")
plot(res.helm, plot.type = "stressplot")
plot(res.helm, plot.type = "Shepard")

## idioscal and indscal with random starting configuration:
set.seed(123)
startconf <- matrix(rnorm(20), 10, 2)
idioscal(helm, init = startconf, type = "interval")
indscal(helm, init = startconf, type = "interval")

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