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Proscal 5.1 is now available.

Changes from Proscal 5.0 include adaptations for SPlus 8.0 and an improved ability to handle coordinate constraints. 

Changes from Proscal 4.5 include the following:

  • an ability to evaluate liking ratings under the assumption of dependent sampling
  • an improved initial estimation procedure for liking ratings under independent sampling
  • a new optimization procedure which updates coordinates and measurement constant parameters at the same time instead of separately.
  • calculation of CAIC and BIC information criterion statistics

Dependent sampling has the provocative property of being able to uniquely estimate a multidimensional solution with just one ideal object using only liking rating data.  Dependent sampling must, of course, characterize the data as well as the model.  Tests of  whether data fit a dependent or independent sampling model may be made using the information criterion statistics provided by PROSCAL.  Another advantage of dependent sampling is that the variances on the real and ideal objects are uniquely estimated, even when the only data available are liking ratings. 

The ability to evaluate data with only one ideal object is valuable when testing whether a market is homogeneous or segmented.  It is also valuable when the traditional assumption that different segments perceive products in the same way is suspect.  This is a common occurrence.  Consumers who are diet conscious, for example, frequently perceive product properties differently from consumers who are not diet conscious.    

Data sets illustrating single ideal sampling as well as multiple ideal sampling and a variety of other probabilistic multidimensional scaling scenarios are available from the Downloads page.  The data sets are described in the manuals.  Manuals for both the SPlus and command line versions of Proscal have been updated.

A 2007 Journal of Mathematical Psychology paper which describes the theory behind the new dependent sampling models is available on the Publications page.


Feedback on Proscal 5.1 is desired.  Please send your comments to


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