Multidimensional scaling (MDS) is a technique used to analyze proximities or distances between pairs of objects. The goal of MDS is to place objects in a dimensional space such that the distances between objects in that space correspond as closely as possible to the proximities in the original data. There are metric and nonmetric approaches to MDS depending on the level of measurement of the proximities. MDS can be used to visualize perceptions of similarity between objects and allows for further analysis of the dimensional configuration.

1. Multidimensional ScalingAdvance StatisticsCPS510DDr. Carlo MagnoCounseling and Educational Psychology DepartmentDe La Salle University-Manila

2. Multidimensional Scaling (MDS)Measures of proximity between pairs of objects.

3. Proximity measure – index over pairs of objects that quantifies the degree to which the two object are alike.

4. Measure of similarity – correspond to stimulus pairs that are alike or close in proximity.

5. Measure of dissimilarity – correspond to stimulus pairs that are least alike or far in proximity.MDSUse:

6. When our information is an assessment of the relative proximity or similarity between pairs of objects in the data set.

7. Goal:

8. Use information about relative proximity to create a map of appropriate dimensionality such that the distances in the map closely correspond to the proximities used to create it.

9. Consideration:

10. The coordinate locations of the objects are interval scaled variables that can be used in subsequent analysis.Approaches of MDSProximities between pairs of objects from the same set.Metric MDSNonmetric MDSIndividual differences scaling Proximities between objects from disjoint setsUnfolding model

11. Metric MDSProximity between pairs of objects reflect the actual physical distances.Judgment of the respondents’ proximity using well calibrated instruments.Level of measurement: ratioEx. Actual distances of one city to another.

12. Example of Proximities

13. Configuration of distances

14. Nonmetric MDSPerceived similarity of different stimuli judged on a scale that is assumed ordinal in nature.Level of measurement: interval, ratioSteps:1. Choose the number of dimensions2. Plot the configurations3. Calculate the distances4. Achieve monotonic correspondence between actual distance and dissimilarities.5. Reduce stress

15. People’s Judgment on the similarity of negative emotions15 negative emotions were judged in the study

16. Configuration of the negative emotionsStep 2

17. Calculated distances of negative emotionsStep 3Estimates are calculated Eucledian distances

18. Step 4Achieving monotonic correspondence

19. Stress EstimatesSTRESS

20. Goodness of fit of the configuration

21. The larger the difference between the actual distance (d)and the transformed distance ( ) in the monotone curve, the greater the stress, the poorer the fit.

22. Raw stress = 13.94786;

23. Alienation = .2470421

24. D-hat: ( ) Raw stress = 8.131408;

25. Stress = .1901042Step 4