MODEL Subcommand (PROXMAP command)

[/MODEL {IDENTITY**                 }]
        {DILATION                   }
        {WEIGHTED                   }
        {GENERALIZED [RANK = {n-1** }
                             {n     }

The MODEL subcommand specifies how proximities are mapped to distances, particularly when multiple sources are present in the data. It determines the ‘structure of individual differences’ across sources by selecting an appropriate space-weighting model. If only one data source is present, only the IDENTITY model is applicable.

The following subcommands are available.

IDENTITY

This is the default option when a single proximity matrix (source) is supplied (or derived). The following options apply only for multiple proximity matrices.

DILATION

Weighted identity model. Each source is assumed to perceive the same spatial configuration but scaled uniformly. This results in one dimension weight per source, allowing for ‘individual scaling’ of the common space across sources.

WEIGHTED EUCLIDEAN

Weighted Euclidean model (equivalent to the so-called ‘INDSCAL’ model). Each source derives its configuration by assigning a different weight to each dimension of the common space. This allows sources to emphasize different spatial features, resulting in multiple dimension weights per source.

GENERALIZED EUCLIDEAN

Generalized Euclidean model (equivalent to the IDIOSCAL model). The common space is rotated and re-weighted separately for each source. Space weights are the product of a rotation/projection matrix (or vector) and dimension weights. This model is the most flexible and can represent a wide range of individual differences.

For the reduced rank of the individual spaces in the GENERALIZED EUCLIDEAN model, the following keyword is used.

The RANK keyword controls whether the full or a reduced-rank model is estimated in the GENERALIZED EUCLIDEAN model. For the reduced-rank model, the dimensionality is set to n-1, where n is the dimensionality of the common space (Subcommand CRITERIA). This model allows the common space to be of higher dimensionality than the individual spaces.

• If a number other than n-1 or n is specified, it will be set to n-1.
• With the default of two dimensions for the common space, this results in a rank-1 model, meaning that each source is modeled in a 1-dimensional subspace of the common space.
• If the specified rank equals the number of dimensions, no rank reduction is applied, and the request is ignored silently.
• Without the RANK keyword, the default is full rank (equal to the number of dimensions).