Procrustean rotation : PROCRUSTES

is an abbreviated version of the full PINDIS procedure. As in the full version, it takes as its input data a number of configurations, which will normally be the result of some previous scaling analysis, although any technique giving dimensional output (such as factor or components analysis) is also suitable. The points in each of the configurations must be the same although the dimensionality of the spaces is allowed to differ between configurations.


The basic Procrustean model relies on the assumption that that MDS configurations are unique under translation, rotation, and reflection. The program takes each pair of configurations in turn and, by applying these transformations, brings them into maximum conformity with each other. This effectively eliminates any differences in the configurations due to the conventions of the program producing them and leaves the substantive differences - due to random error and differential cognition. A centroid configuration is formed simply by taking the average position of each point over all the configurations. The model implies that individual "subjects" (or data-sources)  make no systematic distortions of the group space (the centroid).

Instead of estimating the Centroid configuration, the user may input an external reference (or hypothetical) configuration of the same stimuli in the same number of dimensions (such as an original study of which the data are replications), or repeat the configuration for one of the subjects to which the others should be compared, introduced by READ HYPOTHESIS.

The higher order models in PINDIS allow that subjects may systematically distort this basic configuration.The first mode of distortion is analogous to that of the INDSCAL model in that subjects, in arriving at their perceptual spaces, are thought of as applying differential weights to the dimensions of the group space (the centroid).

The maximum number of dimensions in any one configuration is given in the DIMENSIONS statement, the number of configurations, by N OF SUBJECTS. The number of points in the configuration is given by N OF STIMULI and the data are read by the READ CONFIGS command. The INPUT FORMAT specification, if used, should read the longest row of the configurations. By default, free format input is assumed.

INPUT COMMANDS

Keyword                                            Function
N OF STIMULI    [number]         Number of stimuli in the analysis
N OF SUBJECTS [number]         Number of subject configurations to be
                                              compared in the analysis
DIMENSIONS     [number]         Maximum number of dimensions in
                                              any one configuration
LABELS  [followed by a series    Optionally identify the stimuli,
            of labels (<= 65 chars)  followed by the subjects, as 
            each on a separate       required. All labels should be
            line]                            entered, without omissions.
READ CONFIGS                        Input the subject configurations
                                               immediately following this command.
READ HYPOTHESIS                   (Optional) Input a configuration to
                                               use as a reference for comparisons;
                                               if not present, the centroid
                                               is used by default.

NOTES
1. The READ CONFIGS command is obligatory in PROCRUSTES.
2. READ MATRIX is not valid with PROCRUSTES.

PRINT   (to main output file)
Option                Form                   Description
CENTROID          p x r          The centroid configuration is printed
                                           at each phase, with the results of applying
                                           the basic similarity transformations
                                           P0 for each subject.

By default, CENTROID only is applied.

PLOT  (to main output file)
Option                      Description
CENTROID              The CENTROID (or HYPOTHESIS) configuration,
                              whichever is being used for reference,
                              is plotted at each phase.

By default, CENTROID only is applied.

PUNCH options (to secondary output file)
Option                     Description
CENTROID            The coordinates of the centroid
                            configuration are output.

PROGRAM LIMITS
Maximum no. of subjects = 100
Maximum no. of stimuli = 100
Maximum no. of dimensions = 4

See also

  • The NewMDSX commands in full