Capabilities

The MDS Procedure

fits two-way and three-way, metric and nonmetric multidimensional scaling models
estimates the following parameters by nonlinear least squares:
- configuration — the coordinates of each object in a Euclidean or weighted Euclidean space of one or more dimensions
- dimension coefficients — for each data matrix, the coefficients that multiply each coordinate of the common or group weighted Euclidean space to yield the individual unweighted Euclidean space
- transformation parameters — intercept, slope, or exponent in a linear, affine, or power transformation relating the distances to the data
fits either a regression model of the form

fit(datum) = fit(trans(distance)) + error
or a measurement model of the form

fit(trans(datum)) = fit(distance) + error
where
- fit is a predetermined power or logarithmic transformation
- trans is an estimated (“optimal”) linear, affine, power, or monotone transformation
- datum is a measure of the similarity or dissimilarity of two objects or stimuli
- distance is a distance computed from the estimated coordinates of the two objects and estimated dimension coefficients in a space of one or more dimensions
- error is an error term assumed to have an approximately normal distribution and to be independently and identically distributed for all data

For further details see the SAS/STAT User's Guide: The MDS Procedure
( PDF | HTML )

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