Overview (PROXSCAL command)

PROXSCAL performs multidimensional scaling of proximity data to find a least-squares representation of the objects in a low-dimensional space. Individual differences models are allowed for multiple sources. A majorization algorithm guarantees monotone convergence for optionally transformed metric and nonmetric data under a variety of models and constraints.

Options

Data Input. You can read one or more square matrices of proximities that can either be symmetrical or asymmetrical. Alternatively, you can provide specifications with the TABLE subcommand for matrices with proximities in a stacked format. You can read proximity matrices created by PROXIMITIES and CLUSTER with the MATRIX subcommand. Additionally, you can read weights, initial configurations, fixed coordinates, and independent variables.

Methodological Assumptions. You can specify transformations considering all sources (unconditional) or separate transformations for each source (matrix-conditional) on the CONDITION subcommand. You can treat proximities as nonmetric (ordinal) or as metric (numerical or splines) using the TRANSFORMATION subcommand. Ordinal transformations can treat tied observations as tied (discrete) and untied (continuous). You can specify whether your proximities are similarities or dissimilarities on the PROXIMITIES subcommand.

Model Selection. You can specify multidimensional scaling models by selecting a combination of PROXSCAL subcommands, keywords, and criteria. The subcommand MODEL offers, besides the identity model, three individual differences models. You can specify other selections on the CRITERIA subcommand.

Constraints. You can specify fixed coordinates or independent variables to restrict the configuration(s) on the RESTRICTIONS subcommand. You can specify transformations (numerical, nominal, ordinal, and splines) for the independent variables on the same subcommand.

Output. You can produce output that includes the original and transformed proximities, history of iterations, common and individual configurations, individual space weights, distances, and decomposition of the stress. Plots can be produced of common and individual configurations, individual space weights, transformations, and residuals.

Basic Specification

The basic specification is PROXSCAL followed by a variable list. By default, PROXSCAL produces a two-dimensional metric Euclidean multidimensional scaling solution (identity model). Input is expected to contain one or more square matrices with proximities that are dissimilarities. The ratio transformation of the proximities is matrix-conditional. The analysis uses a simplex start as an initial configuration. By default, output includes fit and stress values, the coordinates of the common space, and a chart of the common space configuration.

Syntax Rules

  • The number of dimensions (both minimum and maximum) may not exceed the number of proximities minus one.
  • Dimensionality reduction is omitted if combined with multiple random starts.
  • If there is only one source, then the model is always assumed to be identity.

Limitations

  • PROXSCAL needs at least three objects, which means that at least three variables must be specified in the variable list. In the case of the TABLE subcommand, the minimum value for rowid and columnid must be at least three.
  • PROXSCAL recognizes data weights created by the WEIGHT command but only in combination with the TABLE subcommand.
  • Split-file has no implications for PROXSCAL.