SAS/STAT Software

MDS Procedure

The MDS procedure fits two- and three-way, metric and nonmetric multidimensional scaling models. Multidimensional scaling refers to a class of methods. These methods estimate coordinates for a set of objects in a space of specified dimensionality. The input data are measurements of distances between pairs of objects. A variety of models can be used that include different ways of computing distances and various functions relating the distances to the actual data. The following are highlights of the MDS procedure's features:

  • 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
    • 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
  • performs BY group processing, whcih enables you to obtain separate analyses on grouped observations
  • performs weighted analysis
  • creates a SAS data set that corresponds to any output table
  • automatically creates graphs by using ODS Graphics

For further details see the MDS Procedure