TRANSFORMATION Subcommand (PROXMAP command)

[/TRANSFORMATIONS [SOURCES = srclist]
    FUNCTION = {NONE }]
               {INTERCEPT }
               {LINEAR [INTERCEPT = {NO    }] }
                                    {YES*}
               {POWER [INTERCEPT = {NO  }] }
                                   {YES*}
               {SPLINE [INTERCEPT = {NO    }] }
                                    {YES }] }
                       [DEGREE = {2}]
                                 {n}
                       [INKNOTS = {2}]
                                  {n}
                       [PLACEMENT = {INTERVALS*    }]
                                    {PERCENTILES}
               {ORDINAL** [APPROACH = {KEEPTIES} ]}
                                      {UNTIE*     }
[/TRANSFORMATIONS ...]

The TRANSFORMATIONS subcommand specifies how proximities are transformed prior to fitting the distances in the common configuration space. The objective is to match the inter-point distances in the derived spatial representation as closely as possible to the transformed proximities.

Different transformations for different sources can be specified by repeating the entire subcommand.

SOURCES

Specifies a list of source names.

FUNCTION

The following keywords are available for the TRANSFORMATION type.

Keyword	Description
NONE	No transformation is applied. The proximities are used directly.
INTERCEPT	Adds a constant offset to all proximities.
LINEAR	Applies a linear transformation to the proximities. For INTERCEPT = NO, a ratio transformation is performed, without adding a constant. For INTERCEPT = YES, an interval transformation is performed, allowing a constant shift.
POWER	Applies a power transformation to the proximities. For INTERCEPT = NO, a pure power function is applied, without a constant. For INTERCEPT = YES, a power function with a constant shift is applied.
SPLINE	Applies a monotonic spline transformation. This results in a smooth, non-decreasing transformation that adjusts proximities using piecewise polynomial segments. Spline transformations include the following options: INTERCEPT = NO or YES indicates whether to include a constant. DEGREE = n indicates the degree of the polynomial pieces. The default value is 2. INKNOTS = n indicates the number of interior knots. It must be an integer in the interval [0, n], where n is the number of distinct proximity values minus two. If INKNOTS is greater than this number, it is set to this maximum. Default value is 2. The maximum value for the sum of DEGREE and INKNOTS is the number of distinct proximity values minus 1. If this maximum is exceeded, the DEGREE specification is adapted. For PLACEMENT = INTERVALS, knots are placed at equal intervals across the range of proximities. For PLACEMENT = PERCENTILES, knots are placed at specific percentiles based on the distribution of proximities.

ORDINAL

Preserves only the rank order of the proximities. It does not assume a specific numeric relationship between values. Only their order matters.

Options for handling tied values:

APPROACH = UNTIE: Tied proximities may be slightly adjusted to enforce a strictly increasing transformation. This is the default.

APPROACH = KEEPTIES: Tied values in the proximities remain tied in the transformation.