SPSS command: SPSS PROXSCAL
Multidimensional scaling (MDS) in your browser
Multidimensional scaling finds a low-dimensional map in which the distances between objects reproduce their dissimilarities as closely as possible.
Free · No account · Files stay on your device · Updated 18 October 2026
What it tells you
Crosstabs runs the SPSS PROXSCAL procedure on your device with SMACOF majorization, from a proximity matrix in your data or from Euclidean distances it computes between variables or cases.
- How well a two- (or more) dimensional map fits the proximities: normalized raw Stress, Stress-I, Stress-II, S-Stress, dispersion accounted for and Tucker's congruence.
- The coordinates of every object, ready to plot as a perceptual map.
- Which objects are poorly represented, through each object's share of the stress.
- Whether only the rank order of the proximities matters (ordinal) or their ratios or intervals, via the Shepard diagram.
When to use it
Use it when
- You have judged similarities or confusions between products, brands or stimuli and want a map of how people perceive them.
- You want to see which survey items or variables behave alike, from distances between variables.
- Only the order of the dissimilarities is trustworthy — use the ordinal transformation (nonmetric MDS).
Use something else when
- Several proximity matrices, one per judge, that should share a common space with individual weights (INDSCAL): the panel fits one matrix with the identity model.
- You want ALSCAL's S-stress algorithm specifically: use the separate Multidimensional scaling (ALSCAL) procedure.
- Your data are a contingency table of counts: correspondence analysis is designed for that.
- You need groups rather than a continuous map: use hierarchical or k-means clustering on the same distances.
How to run it in Crosstabs
- 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.
- 02
Choose Multidimensional scaling
In the Dimension reduction group, pick Multidimensional scaling (PROXSCAL).
- 03
Say where the proximities come from
Under Proximities choose Create distances between variables, Create distances between cases (up to 200 complete cases, with Label cases by), or Square proximity matrix in the data, where you tick one column per object and set Proximity type to Dissimilarities or Similarities. For computed distances, Standardize with Z-scores or None.
- 04
Pick the transformation
Set Transformation to Ratio, Interval or Ordinal; for ordinal, choose how Tied proximities are handled (Keep tied or Untie).
- 05
Set dimensions and iterations
Choose Dimensions (1–6, default 2) and Maximum iterations (default 100), tick the variables or objects, then click Run multidimensional scaling.
- 06
Judge the fit
Read Stress-I against Kruskal's guideline, check the Shepard Diagram for systematic misfit, and raise Maximum iterations if a convergence warning appears. Weights are not used.
Worked example
Computed by the Crosstabs engine from the synthetic data below when this page was built — not typed in.
Data
Ten synthetic coffee brands rated on four attributes (price, premium image, roast level, bitterness). The ratings were simulated from two hidden dimensions — price tier and roast strength — plus noise with a fixed seed. In the panel this is “Create distances between cases” with z-scores, labelling cases by brand, so PROXSCAL scales the 10 × 10 Euclidean distance matrix.
| Measure | Value |
|---|---|
| Normalized Raw Stress | 0.00697 |
| Stress-I | 0.08349 |
| Stress-II | 0.23192 |
| S-Stress | 0.01198 |
| Dispersion Accounted For (D.A.F.) | 0.99303 |
| Tucker's Coefficient of Congruence | 0.99651 |
Ratio transformation, identity model, 2 dimensions; Torgerson start; 3 iterations.
| Object | Dimension 1 | Dimension 2 |
|---|---|---|
| Arbor | −0.292 | −0.628 |
| Bluebird | −0.798 | 0.048 |
| Cask | 0.813 | −0.236 |
| Dune | −0.367 | 0.297 |
| Ember | 0.371 | −0.099 |
| Fjord | 0.102 | 0.484 |
| Grove | 0.802 | 0.313 |
| Harbor | −0.351 | −0.517 |
| Isle | −0.344 | 0.763 |
| Juniper | 0.063 | −0.426 |
| Object | Stress |
|---|---|
| Arbor | 0.00064 |
| Bluebird | 0.00116 |
| Cask | 0.00053 |
| Dune | 0.00190 |
| Ember | 0.00009 |
| Fjord | 0.00073 |
| Grove | 0.00036 |
| Harbor | 0.00028 |
| Isle | 0.00045 |
| Juniper | 0.00084 |
| Total | 0.00697 |
How to read it
Stress-I is 0.083, which Kruskal's guideline (used in the panel's interpretation) rates as fair; the map accounts for 99.3% of the dispersion of the distances (Tucker's congruence 0.997). The remaining misfit comes from the rating noise around the two axes the data were generated from. Dune contributes most to the remaining stress (0.00190), so its position is the least certain. The classical (Torgerson) solution that seeds the iterations already captures 88.9% of the positive eigenvalue sum in its first two dimensions.
Output tables explained
- Stress and Fit Measures
- Normalized raw Stress, Stress-I, Stress-II, S-Stress, dispersion accounted for (D.A.F.) and Tucker's coefficient of congruence; Stress-I and Stress-II are reported as square roots.
- Common Space
- The map of objects on dimensions 1 and 2; the configuration is centered and rotated to principal axes.
- Shepard Diagram
- Map distances plotted against the proximities, with the fitted transformation as a line; vertical spread around the line is misfit.
- Final Coordinates
- Each object's coordinate on each dimension.
- Decomposition of Normalized Raw Stress
- Each object's share of the normalized raw Stress; the shares add to the total. Large values flag objects that do not fit the map.
- Classical (Torgerson) Scaling
- The classical metric solution that starts the iterations, with the eigenvalues of the double-centered squared proximities.
Assumptions and notes
- Dissimilarities are nonnegative; similarities are converted to dissimilarities (sign reversed, minimum shifted to 0) before scaling.
- For a matrix in the data, the first n rows of the n selected columns form the matrix; where both triangles are present their mean is used.
- A map is only as good as its stress: interpret positions only when Stress-I is acceptable for the number of objects and dimensions.
How the results are validated
Reference configurations come from an independent SMACOF implementation of the PROXSCAL rules, cross-checked against R smacof::smacofSym (Torgerson start, secondary ties), stats::cmdscale and, for the ratio case, scikit-learn's SMACOF. On two 12-object matrices (one with tied proximities), tests require Stress-I within 1e-7, normalized raw Stress and D.A.F. within 1e-8, Stress-II and S-Stress within 1e-6 and every inter-point distance within 1e-5, for ratio, interval and ordinal transformations; classical scaling matches cmdscale within 1e-9. Validation evidence
Questions
What is a good Stress-I value?
The panel uses Kruskal's rule of thumb: up to 0.025 excellent, 0.05 good, 0.10 fair, 0.20 poor. Stress rises with the number of objects and falls with more dimensions, so compare solutions rather than treating the cut-offs as tests.
Ratio, interval or ordinal — which transformation?
Ratio assumes distances are proportional to the proximities, interval allows an additive constant, and ordinal (nonmetric MDS) keeps only their rank order. Use ordinal for rating-based similarity judgments; it usually gives the lowest stress.
Should I keep tied proximities tied?
Keep tied (the secondary approach) forces equal proximities to equal transformed values. Untie (the primary approach) lets them differ, which lowers stress but can produce degenerate maps when there are many ties.
Can I scale survey variables instead of objects?
Yes. Choose Create distances between variables: the panel computes Euclidean distances between the selected variables, on z-scores by default, from complete cases, and maps the variables.
Why is the map rotated differently from another program's?
MDS solutions are unique only up to rotation, reflection and translation. PROXSCAL centers the configuration and rotates it to principal axes; distances between objects — and the stress — are what matter.
Related procedures
- Distances (Proximities)PROXIMITIES
- Hierarchical ClusterCLUSTER
- Correspondence AnalysisCORRESPONDENCE
- Factor AnalysisFACTOR
- Categorical Principal Components (CATPCA)CATPCA
- Free SPSS alternative: full coverage list
Run Multidimensional Scaling (PROXSCAL) on your own data
Open a .sav, CSV or Excel file. Everything runs in your browser; the file never leaves your device.
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