Procrustean Individual Differences Scaling (PINDIS)

Where equivalent MDS configurations have been produced for a number of different texts, it may be useful to continue the analysis to compare these results, to produce an ordering of the various text sources and to examine in detail their similarities and differences. The SELECT utility allows a number of configurations generated by MINISSA to be selected for analysis by Procrustean Individual Differences Scaling (PINDIS). As an alternative you can use Individual Differences Scaling to compare the matrices saved from analyses of jount frequencies of words or categories in the texts.

The results of a PINDIS analysis are temporarily displayed in graphical form.

By default, this shows first the centroid configuration, produced by subjecting the original 'subject' configurations - for the individual texts selected - to a series of transformations which preserve the orderings of the distances between the points corresponding to the words of the original configurations. This represents a kind of median of the individual configurations considered, and acts as a reference point for the examination of the similarities and differences between them.

Attention is drawn to the “Table of Subject Communalities for PINDIS Transformations“ at the end of the full PINDIS output listing. Where there is no improvement in fit for the successive models,  this immediately identifies cases in which distance-preserving transformations alone will account for the observed differences between the texts compared, so that the remaining PINDIS models become redundant.

The next plot is of the subject space, which shows the ordering of the original configurations which are being compared. An additional procedure, SUBJSTAT,  provides an appropriate arc-distance measure for the analysis of the significance of distances between items in the subject space coordinates produced by PINDIS  

It then remains to examine in turn the individual configurations, as transformed and re-scaled by PINDIS, to determine the extent and source(s) of specific departures from the centroid/initial configuration. The individual configurations have been submitted to a succession of decreasingly stringent distortions, the results of which serve to highlight the precise nature of these departures.

Using a hypothesis configuration as a starting point

 As a final stage, PINDIS also lends itself well to testing goodness of fit of observed configurations to a hypothetical or theoretically determined representation, which may be input to take the place of the centroid which is otherwise determined initially. Care is needed that any hypothetical configuration employed has the same format as the various 'subject' configurations which are to be compared to it, i.e. coordinates must be entered for the same number of vocabulary items ('stimuli') as was used in the original MINISSA configurations, and always for all three dimensions requested, even if the values for one or even two of these are all to be zero. In this way, the methods described here can be be employed strictly in the development of theoretical models of the structures of associations of ideas as they appear in texts of various kinds.

Langeheine(1980) (see references) describes tests of significance to permit the evaluation both of single transformations in PINDIS and of improvements in fit between the various transformations. His tables offer criterion values to test the hypothesis that the fit obtained could be generated by purely random configurations.

Advanced application of PINDIS

See also