Software for Multidimensional Scaling

by Forrest W. Young


Thank you for your interest in the ALSCAL Multidimensional Scaling program developed here at the L. L. Thurstone Psychometric Laboratory by Prof. Forrest W. Young.

ALSCAL is available from us as a stand-alone program for machines with a FORTRAN compiler. ALSCAL is also distributed as part of the SPSS system. The SAS ALSCAL procedure has been superseded by the SAS MDS procedure available from SAS Institute, Inc. in the SAS-Stat addon to the basic SAS system.

On-Line material:
Prof. Young's on-line material about MDS includes

  1. Prof. Young's books on MDS
  2. Prof. Young's Monographs on MDS
  3. References to Prof. Young's Papers about MDS
  4. Class Notes for Prof. Young's Graduate Level course on MDS

Summary of ALSCAL's features:

ALSCAL performs metric or nonmetric Multidimensional Scaling and Unfolding with individual differences options. It can analyze one or more matrices of dissimilarity or similarity data. The analysis represents the rows and columns of the data matrix as points in a Euclidean space. If a row and column are similar, then their points are close together, while if the row and column are dissimilar, they are far apart.
  • ALSCAL performs metric and nonmetric analyses: The multidimensional scaling can be "metric" or "nonmetric". Metric scaling assumes that the dis/similarity data are quantitative -- that they are measured at the interval or ratio levels of measurement. Nonmetric scaling assumes that the data are qualitative -- that they are at the ordinal level of measurement.
  • ALSCAL analyzes one or more dissimilarity matrices: ALSCAL can analyze one or more matrices of dis/similarity data. The matrices may be rectangular or square, symmetric or asymmetric, conditional or unconditional, and may have missing elements. The program permits the analysis of any number of matrices, each having any number of rows or columns.
  • ALSCAL does Scaling and Unfolding: ALSCAL can analyze data whose rows and columns refer to the same set of objects or events (square data, which may be symmetric or asymmetric), or which refer to two different sets of objects or events (rectangular data). When the data are square the program performs multidimensional scaling, constructing a Euclidean space which has points in it for every object/event. When the data are rectangular the program performs multidimensional unfolding, constructing a Euclidean space which has points in it for every row and column object/event. In both cases, the distance between the points corresponding to the dis/similarity between the objects/events.
  • ALSCAL does Individual Differences Models: ALSCAL can analyze data that are contained in several matrices. With several matrices ALSCAL can perform replicated or individual differences multidimensional scaling or unfolding. For replicated scaling or unfolding the analysis constructs a Euclidean space just as when there is only one matrix of data. For individual differences (weighted) scaling or unfolding, the objects/events are represented by points in a Euclidean space (as above), while the matrices are represented by vectors of weights in an additional individual differences space. The replicated and weighted multidimensional scaling and unfolding analyses may be either metric or nonmetric.
  • Availability: ALSCAL is available as an IBM-PC (and compatible) executable. It requires a math-coprocessor. The FORTRAN source code, executable, test data and example output are distributed on IBM-PC diskettes, along with a user guide. The source code can be compiled on other machines. ALSCAL is available within SAS, SPSS and IMSL.

Downloading ALSCAL-PC

A zip file of ALSCAL can be obtained by clicking here. The zip file includes
  • ALSCAL.EXE, the version for IBM-compatible PCs under DOS.
  • ALSCAL84-1.0.sea, the Macintosh version.
  • FORTRAN source code of ALSCAL. If you have a FORTRAN compiler, this code can be compiled to run on other machines.
  • Test Data.


Usage: Enter 'ALSCAL' to start ALSCAL. The program then prompts you to enter the name of the input file and the output file. When the input filename is not specified, the program stops. When the output filename is not given, the program chooses the name 'ALSCAL.OUT'. An END-card causes the program to stop further reading of the input file. Thus remarks after the END-card will not cause an error message.

Getting the Documentation:
The ALSCAL User's Guide

Young, F.W. & Lewyckyj, R. - ALSCAL Users Guide.
This monograph presents a complete overview of how to use ALSCAL, including the SAS, stand-along mainframe and PC versions. Included is a detailed guide to the command language for each version, including a summary of 19 common types of analyses. The monograph also presents comments on unique aspects of ALSCAL's output, including descriptions of the individual differences indices and fit indices. In addition, extensive annotated examples of the input to and output from ALSCAL are presented, including figures published from the examples. These examples cover metric MDS, nonmetric MDS, unfolding, and individual difference scaling. Finally, a list of all diagnostics, including a full explanation of each, is presented.
Price: The ALSCAL Users Guide can be ordered for $5.00 plus the appropriate mailing charge:
  • Add $5.00 for mailing within USA & Canada
  • Add $10.00 for mailing to Mexico
  • Add $15.00 for mailing outside of North America.
Ordering: To order, please E-mail me your name, address and telephone number, telling me you are ordering ALSCAL documentation. In addition, mail the same information, plus your check or international postal order, to

Forrest W. Young
UNC Psychometric Laboratory
CB-3270 Davie Hall
Chapel Hill NC 27599-3270 USA.
The check or international postal order should be made payable to "UNC Psychometric Laboratory" (or "Forrest Young", if necessary). Please pay in US dollars only.