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 theGENERALIZED 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).
Examples
-
GET FILE ’States.sav’. PROXMAP /SOURCEID DATA = income illit life homic school fail NAME = $SRC1 /SOURCEID DATA = popul freeze NAME = $SRC2 /DATA = MULTIVARIATE /MODEL = WEIGHTED.
In this example, two sources are analyzed. The Weighted Euclidean model is applied.
-
GET FILE ’States.sav’. PROXMAP /SOURCEID DATA = income life NAME = $SRC1 /SOURCEID DATA = school fail NAME = $SRC2 /SOURCEID DATA = popul freeze NAME = $SRC3 /DATA = MULTIVARIATE /MODEL = GENERALIZED RANK = 1 /CRITERIA DIMENSIONS = 2.
In this example, three sources are analyzed. The Generalized Euclidean model is fitted, with two dimensions in the common space. Each individual space obtains a reduced rank 1. With this model, each source is represented as a one-dimensional subspace of the common space.
-
GET FILE ’States.sav’. PROXMAP /SOURCEID NAME = $SRC1 LABEL = ‘income’ DATA = income /SOURCEID NAME = $SRC2 LABEL = ‘illit’ DATA = illit /SOURCEID NAME = $SRC3 LABEL = ‘life’ DATA = life /SOURCEID NAME = $SRC4 LABEL = ‘homic’ DATA homic /SOURCEID NAME = $SRC5 LABEL = ‘school’ DATA school /SOURCEID NAME = $SRC6 LABEL = ‘fail’ DATA fail /SOURCEID NAME = $SRC7 LABEL = ‘popul’ DATA popul /SOURCEID NAME = $SRC8 LABEL = ‘freeze’ DATA freeze /DATA = MULTIVARIATE /MODEL GENERALIZED RANK = 1 /CRITERIA DIMENSIONS =2.
In this example, each variable defines a source. The Generalized Euclidean model is fitted, with two dimensions in the common space. Each individual space has rank 1, because each source contains only one variable. With this model, each source (variable) is represented as a subspace of the common space.