smacofIndDiff function

SMACOF for Individual Differences

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.

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.

Returns

• 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

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")

Author(s)

Jan de Leeuw and Patrick Mair

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")