TRANSFORMATION Subcommand (PREFSCAL command)

The TRANSFORMATION subcommand offers four different options for optimal transformation of the original proximities. The resulting values are called transformed proximities. The distances between the objects in the configuration should match these transformed proximities as closely as possible. The CONDITION subcommand specifies over which proximities the transformation is computed. The default transformation is ORDINAL with ties kept tied.

NONE. No scale transformation. The INTERCEPT keyword can be specified in parentheses following the NONE keyword. If INTERCEPT is specified, an intercept is estimated in the transformation.

LINEAR. Linear transformation. With this transformation, the transformed proximities are proportional to the original proximities (that is, the transformation function estimates a slope, and the intercept is fixed at 0). The INTERCEPT keyword can be specified in parentheses following the LINEAR keyword. If INTERCEPT is specified, an intercept is estimated in the transformation, resulting in an interval transformation. Without the keyword INTERCEPT, LINEAR only estimates a slope, which coincides with a ratio transformation.

ORDINAL. Ordinal transformation. The transformed proximities have the same order as the original proximities. ORDINAL can be followed by a keyword in parentheses to indicate how to handle tied proximities.

SMOOTH. Smooth ordinal transformation. The transformed proximities have the same order as the original proximities, including a smoothness restriction. This restriction takes the differences between subsequent values into account. Restricting subsequent differences allows for a smooth ordinal transformation. SMOOTH can be followed by a keyword in parentheses to indicate how to handle tied proximities.

SPLINE. Monotone spline transformation. The transformed proximities are a smooth nondecreasing piecewise polynomial transformation of the original proximities of the chosen degree. The pieces are specified by the number and placement of the interior knots, of which the number can be specified with INKNOT.

ORDINAL and SMOOTH Keywords

UNTIE. Untie ties. Allowing tied proximities to be untied during transformations (also known as the primary approach to ties).

KEEPTIES. Keep ties tied. Keeping tied proximities tied during transformations (also known as secondary approach to ties). This setting is the default.

SPLINE Keyword

INTERCEPT. Include intercept. If INTERCEPT is specified, an intercept is estimated in the transformation. Omitting this keyword sets the lower exterior knot equal to 0.

DEGREE. The degree of the polynomial. If DEGREE is not specified, the degree is assumed to be 2. The integer range of DEGREE is 1, 2, or 3.

INKNOT. The number of interior knots. If INKNOT is not specified, the number of interior knots is assumed to be 1. The integer range of INKNOT is between 0 and the number of different proximities minus 2.

Example

PREFSCAL var01 TO var15
  /TRANSFORMATION = ORDINAL(UNTIE).
  • In this example, the proximities are ordinally transformed, where tied proximities are allowed to be untied.
  • The CONDITION subcommand is omitted, and thus, the default conditionality ROW is in effect, which implies that the transformation is performed for each row separately.