TRANSFORMATION Subcommand (PROXSCAL command)

TRANSFORMATION 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.

RATIO. No transformation. Omitting the entire subcommand is equivalent to using this keyword. In both cases, the transformed proximities are proportional to the original proximities. This “transformation” is only allowed for positive dissimilarities. In all other cases, a warning is issued and the transformation is set to INTERVAL.

INTERVAL. Numerical transformation. In this case, the transformed proximities are proportional to the original proximities, including free estimation of the intercept. The inclusion of the intercept assures that all transformed proximities are positive.

ORDINAL. Ordinal transformation. The transformed proximities have the same order as the original proximities. In parentheses, the approach to tied proximities can be specified. Keeping tied proximities tied, also known as secondary approach to ties, is default. Specification may be implicit, ORDINAL, or explicit, ORDINAL(KEEPTIES). Allowing tied proximities to be untied, also known as the primary approach to ties, is specified as ORDINAL (UNTIE).

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.