slidevector {asymmetry}

The slide-vector model

Description

The slide-vector model is a multidimensional scaling model for asymmetric proximity data. Here, an asymmetric distance model is fitted to the data, where the asymmetry in the data is represented by the projections of the coordinates of the objects onto the slide-vector. The slide-vector points in the direction of large asymmetries in the data. The interpretation of asymmetry in this model is aided by the use of projections of points onto the slide-vector. The distance from i to j is larger if the point $i$ has a higher projection onto the slide-vector than the distance from j to i. If the line connecting two points is perpendicular to the slide-vector the difference between the two projections is zero. In this case the distance between the two points is symmetric. The algorithm for fitting this model is derived from the majorization approach to multidimensional scaling.

d_{ij}(X)=\sqrt{\sum_{s=1}^p(x_{is}-x_{js}+z_{s})^2}.

Usage

slidevector(data, weight = NULL, ndim = 2, verbose = FALSE, itmax = 125, eps = 1e-12)

Arguments

data

Asymmetric dissimilarity matrix

weight

Optional non-negative matrix with weights, if no weights are given all weights are set equal to one

ndim

Number of dimensions

verbose

If TRUE, print the history of iterations

itmax

Maximum number of iterations

eps

Convergence criterion for the algorithm

Details

The slide-vector model is a special case of the unfolding model. Therefore, the algorithm for fitting this model is a constrained unfolding model. The coordinates of the objects are calculated by minimizing a least squares loss function. This loss function is called stress in the multidimensional scaling literature. The stress is minimized by a version of the SMACOF algorithm. The main output are the configuration of points and the slide-vector.

Value

ndim

Number of dimensions

stress

The raw stress for this model

confi

Returns the configuration matrix of this multidimensional scaling model

niter

The number of iterations for the algorithm to converge

nobj

The number of observations in this model

resid

A matrix with raw residuals

slvec

Coordinates of the slide-vector

model

Name of this asymmetric multidimensional scaling model

References

Zielman, B., and Heiser, W. J. (1993), The analysis of asymmetry by a slide-vector, Psychometrika, 58, 101-114.

See Also

plot.slidevector

Examples

## asymmetric distances between English towns
data(Englishtowns)
v <- slidevector(Englishtowns, ndim = 2, itmax = 250, eps = .001)
plot(v)