Multidimensional scaling models and methods for the visualization and analysis of asymmetric proximity data. An asymmetric data matrix has the same number of rows and columns, and these rows and columns refer to the same set of objects. At least some elements in the upper-triangle are different from the corresponding elements in the lower triangle. An example of an asymmetric matrix is a student migration table, where the rows correspond to the countries of origin of the students and the columns to the destination countries. This package provides algorithms for three multidimensional scaling models, the slide-vector model, a scaling model with unique dimensions and the asymscal model. Furthermore, some other procedures, such as a heat map for skew-symmetric data, and the decomposition of asymmetry are also provided for the exploratory analysis of asymmetric tables.
This R package provides a comprehensive suite of tools for the analysis and visualization of asymmetric data using Multidimensional Scaling (MDS) and related decomposition techniques. Asymmetry is a common challenge in social sciences, marketing, and sensory research, where the relationship from object $i$ to $j$ does not necessarily equal the relationship from $j$ to $i$. The package implements several specialized models to capture these directional differences:
ASYMSCAL: A weighted MDS model that accounts for asymmetry through differential weighting of dimensions, estimated via the SMACOF (Scaling by Majorizing a Complicated Function) framework.
MDS with Unique Dimensions: An extension that identifies specific dimensions or "uniqueness" values unique to individual rows or columns within a distance matrix.
Slide-vector Model: A method that models asymmetry by adding a directional "slide" vector to a symmetric configuration, representing a shared bias or trend in the data.
Skew-symmetric Decomposition: Tools to decompose a square matrix into its symmetric and skew-symmetric components ($S$ and $A$), including singular value decomposition (SVD) of the skew-symmetric part for low-dimensional representation. Beyond model fitting, the package includes robust diagnostic and visualization functions. It offers heatmap visualizations for dominance relations, as well as specialized plot methods for configurations, slide-vectors, and skew-symmetric planes.