ALSCAL
Multidimensional Scaling Program

ALSCAL is a FORTRAN77 program which carries out multidimensional scaling (MDS).

It uses the alternating least squares approach to scaling. It is capable of a wide range of analyses, and is suitable for any type of two or three way data, measured at the nominal, ordinal, interval or ratio level.

Related Data and Programs:

ALSCAL is available in a FORTRAN77 version and a FORTRAN90 version.

ALSCAL_DATA_CONVERT is a FORTRAN90 program which reads a data file containing object names and distances between objects and reformats the data for input to ALSCAL.

Reference:

1. Forrest Young, Rostyslaw Lewyckyj,
   ALSCAL User's Guide,
   L L Thurstone Psychometric Laboratory,
   University of North Carolina,
   Chapel Hill, North Carolina, 27599
2. the ALSCAL web page.

Source Code:

• alscal.f, the source code;
• alscal.csh, commands to compile and load the source code;

Examples and Tests:

• car.txt, a dataset;
• car_output.txt, analysis of the car dataset;
• city.txt, a dataset;
• city2.txt, a dataset;
• cityfam.txt, a dataset;
• inddiff.txt, a dataset;
• jakobo.txt, a dataset;
• jones.txt, a dataset;
• trade.txt, a dataset;

List of Routines:

• MAIN is the main program.
• ARNGE rearranges the weight and stimulus matrices.
• BLOC2 finds blocks of ties.
• CATSES computes a discrete nominal transformation.
• CJEIG computes the eigenvalues and eigenvectors of a real symmetric matrix.
• CLEAR clears the screen.
• COEF obtains least stress coordinates.
• DISTP computes distances and disparities for coordinates and weights.
• DRIVER controls the flow of the program.
• EIGK implements Kaiser's JK method for eigenanalysis of a real symmetric matrix.
• HITR requests that the user hit RETURN, and waits for input.
• INIT computes the initial configuration estimation in INDSCAL.
• INNER computes stimulus coordinates.
• INSWM computes the initial configuration for the stimulus weighted model.
• LENGTH normalizes the length of disparities.
• LINT performs constrained least squares linear regression.
• MINV computes the inverse of a symmetric matrix.
• MSTRS calculates the stress of two vectors and estimates missing data.
• NORMW normalizes weight matrices for output.
• NORMX normalizes the configuration for printing at end of job.
• OUTA prints out asymmetric and rectangular matrices.
• OUTS prints out symmetric matrices.
• PAGE writes a form feed.
• PDDISP prepares disparities for PDSCAL.
• PDDIST calculates principal direction distances.
• PDINWT obtains an initial estimate of the principal direction weights.
• PDMAIN is the main subroutine for principal direction scaling.
• PDOUTT prints Tucker's oblique decomposition of a subject's matrix of principal weights.
• PDOUTY prints out CK, WK and XK.
• PDPLOT plots each pair of directions of xk
• PDSCAL computes principal direction weights.
• PDSTRS calculates unnormalized stress.
• PDTUCK obtains Tucker's oblique decomposition of WK.
• PDWGHT calculates a(p,q), the weight of variable p on principal direction q.
• PDYUNG obtains Young's principal directions solution.
• PLOTR is a plot routine for ALSCAL.
• POLYF does polynomial fitting.
• PPLOT is a plot routine for ALSCAL.
• PRS prepares ties for continuous ordinal transformation.
• SCUBE solves a cubic equation.
• SES prepares ties for discrete ordinal transformation.
• SHEL9 sorts data using Shell's sort.
• STEP0 reads and checks the problem parameters.
• STEP1 is the data input routine.
• STEP2 obtains starting configurations and scalings.
• STEP3 is the major computational routine.
• STEP3A prints stress and correlations in distances.
• STEP4 outputs the results.
• TRS computes Kruskal's least squares monotonic transformation.
• WPLOT writes file "cplot.dat" for rotation of configuration by use of CPLOT.

You can go up one level to the FORTRAN77 source codes.