driftVectors function

Asymmetric MDS: Drift Vectors

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.

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.

Returns

• 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

References

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

Author(s)

Patrick Mair

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)