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SPSS command: SPSS ALSCAL

ALSCAL multidimensional scaling in your browser

ALSCAL builds a map whose distances reproduce dissimilarities, fitting squared distances by alternating least squares.

Run Multidimensional Scaling (ALSCAL) in your browserAll SPSS procedures

Free · No account · Files stay on your device · Updated 18 October 2026

What it tells you

Crosstabs runs the SPSS ALSCAL algorithm on your device for one dissimilarity matrix under the Euclidean model, at the ordinal or ratio level.

  • Young's S-stress after each iteration and when the improvement fell below the criterion.
  • Kruskal's stress formula 1 and RSQ for the final configuration.
  • The stimulus coordinates, ready to plot as a perceptual map.

When to use it

Use it when

  • You want to reproduce or compare an ALSCAL analysis from older SPSS syntax.
  • Only the rank order of the dissimilarities is trustworthy (ordinal level).

Use something else when

  • You have several matrices with individual weights (INDSCAL): only one matrix with the simple Euclidean model is fitted.
  • You need the interval level: use PROXSCAL (Multidimensional scaling).

How to run it in Crosstabs

  1. 01

    Open your data

    Open a .sav, CSV or Excel file in the workspace and switch to Statistics mode. The file is read in your browser and never uploaded.

  2. 02

    Choose Multidimensional scaling (ALSCAL)

    In the Dimension reduction group, pick Multidimensional scaling (ALSCAL).

  3. 03

    Say where the dissimilarities come from

    Under Proximities choose distances between variables, distances between cases, or a Square dissimilarity matrix in the data, and tick the variables.

  4. 04

    Set the level and dimensions

    Choose the Level of measurement (Ordinal or Ratio), Tied proximities for ordinal data, Dimensions and Maximum iterations (default 30).

  5. 05

    Run

    Click Run ALSCAL and read the iteration history, fit measures and configuration.

Run Multidimensional Scaling (ALSCAL) in your browser

Output tables explained

Iteration History
S-stress and its improvement at every iteration; iterations stop when the improvement drops below 0.001.
Stress and Fit Measures
S-stress, Kruskal's stress formula 1 and RSQ between the disparities and the distances.
Stimulus Coordinates
Each object's coordinates, centred and scaled to a mean square of 1.

Assumptions and notes

  • Dissimilarities are symmetric; the lower triangle of a matrix is used.
  • The S-stress criterion weights large dissimilarities more than Kruskal's stress does, because it fits squared distances.

How the results are validated

An independent NumPy implementation of the ALSCAL chapter reproduces the additive constant, every S-stress in the iteration history, coordinates, disparities, Kruskal stress and RSQ within 1e-7 to 1e-9 for ordinal (ties kept or untied) and ratio levels; SciPy confirms the ratio solution is a stationary point of S-stress. Validation evidence

Questions

ALSCAL or PROXSCAL?

PROXSCAL minimizes Kruskal's raw stress and offers interval transformations; ALSCAL minimizes S-stress on squared distances. Use ALSCAL to match older analyses, PROXSCAL otherwise.

What is a good S-stress?

Lower is better; values below about 0.1 are usually considered acceptable, but compare solutions in different dimensions rather than relying on a fixed cut-off.

Why did it stop after a few iterations?

ALSCAL stops when S-stress improves by less than 0.001, as SPSS does by default.

Are weights used?

No. ALSCAL scales the dissimilarities as given.

Related procedures

Run Multidimensional Scaling (ALSCAL) on your own data

Open a .sav, CSV or Excel file. Everything runs in your browser; the file never leaves your device.

Open the workspace

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