driftVectors: Asymmetric MDS: Drift Vectors

In smacof: Multidimensional Scaling

Asymmetric MDS: Drift Vectors

Description

Takes an asymmetric dissimilarity matrix and decomposes it into a symmetric and a skew-symmetric part. Fits an MDS on the symmetric part and computes drift vectors for the skew-symmetric portion. This model makes it possible to see how these two components are related to each other. It is limited to two dimensions only.

Usage

driftVectors(data, type = c("ratio", "interval", "ordinal","mspline"), 
             weightmat = NULL, init = "torgerson", ties = "primary",  verbose = FALSE, 
             relax = FALSE, modulus = 1, itmax = 1000, eps = 1e-6, 
             spline.degree = 2, spline.intKnots = 2)
             
## S3 method for class 'driftvec'
plot(x, adjust = 1, main, xlim, ylim, 
                        xlab = "Dimension 1", ylab = "Dimension 2", pch = 20, asp = 1, 
                        col.conf = "black", col.drift = "lightgray", 
                        label.conf = list(label = TRUE, pos = 3, col = "black", 
                        cex = 0.8), ...) 

Arguments

data	Asymmetric dissimilarity matrix
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 for ordinal MDS only: "primary", "secondary", or "tertiary"
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
x	Object of class "driftvec"
adjust	Scaling factor for drift vectors (value larger than 1 increases the length)
main	Plot title
xlab	Label of x-axis
ylab	Label of y-axis
xlim	Scale x-axis
ylim	Scale y-axis
pch	Plot symbol
asp	Aspect ratio
col.conf	Point color (MDS configurations)
col.drift	Color for drift vectors (arrows)
label.conf	Settings for plotting labels
...	Additional plotting arguments

Details

The skew-symmetric values are embedded into the MDS representation of the symmetrized data by drawing errors (drift vectors) from each point i to each point j in the configuration so that these vectors correspond in length and direction to the values of row i of the skew-symmetric matrix.

Value

fitsym	MDS output for symmetric portion
sym	Symmetric matrix
skewsym	Skew-symmetric matrix
driftcoor	Drift vector coordinates
stress	Stress-1 value
niter	Number of iterations
nobj	Number of objects

Author(s)

Patrick Mair

References

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

See Also

smacofSym

Examples

## simple example
P <- matrix(c(0,  4,  6, 13, 
              5,  0, 37, 21, 
              4, 38,  0, 16, 
              8, 31, 18,  0), nrow = 4, ncol = 4, byrow = TRUE) 
D <- sim2diss(P, method = 40) 
res <- driftVectors(D, type = "interval")
plot(res)
plot(res, adjust = 0.1)    ## shorten drift vectors 

## Morse code data
fit.drift <- driftVectors(morse2, type = "ordinal")
fit.drift
plot(fit.drift)

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