Overview (PREFSCAL command)

PREFSCAL performs multidimensional unfolding of proximity data to find a least-squares representation of the row and column objects in a low-dimensional space. Individual differences models are allowed for multiple sources. A majorization algorithm minimizes penalized Stress and 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 rectangular matrices of proximities. Additionally, you can read weights, an initial configuration, and fixed coordinates.

Methodological Assumptions. On the CONDITION subcommand, you can specify transformations for all sources (unconditional), separate transformations for each source (matrix-conditional), or separate transformations for each row (row-conditional). Using the TRANSFORMATION subcommand, you can treat proximities as nonmetric (ordinal or smooth ordinal), as quasi-metric (splines), or as metric (linear with or without intercept). Ordinal and smooth ordinal transformations can keep tied observations tied (discrete) or untie them (continuous). You can use the PROXIMITIES subcommand to specify whether your proximities are similarities or dissimilarities.

Model Selection. You can specify multidimensional unfolding models by selecting a combination of PREFSCAL subcommands, keywords, and criteria. The subcommand MODEL offers the Identity model and two individual differences models. You can specify other selections on the CRITERIA subcommand.

Penalties. You can specify two penalty parameters in order to avoid degenerate solutions. On the PENALTY subcommand, LAMBDA is specified for the strength, and OMEGA is specified for the range. Penalized Stress penalizes solutions with insufficient variation in the transformed proximities.

Constraints. You can specify fixed coordinates on the RESTRICTIONS subcommand to restrict some or all common space coordinates of either row objects or column objects.

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 (biplots), individual space weights, transformations, fit, and residuals.

Basic Specification

The basic specification is PREFSCAL followed by a variable list. By default, PREFSCAL produces a two-dimensional metric Euclidean multidimensional unfolding solution (Identity model). Input is expected to contain one or more rectangular matrices with proximities that are dissimilarities. The transformation of the proximities is row-conditional. The analysis uses a classical scaling start as initial configuration. By default, output includes fit and Stress values, the coordinates of the common space, and a joint plot of the common space configuration.

Syntax Rules

  • If there is only one source, the model is always assumed to be Identity.
  • In the case of duplicate or contradicting subcommand specification, only the later subcommand applies.
  • There is no constraint with respect to the syntax order.

Limitations

  • PREFSCAL needs at least two objects in each set. At least two variables need to be specified in the variable list (two column objects), and the active data file needs to contain at least two cases (two row objects).
  • PREFSCAL does not honor SPLIT FILE.