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Add more sophisticated goodness-of-fit measures for multidimensional scaling

For interpreting MDS solutions it is crucial to assess to what extent we are observing structure in the data instead of noise posing as structure. The use of Kruskal's "stress" has been criticized for this purpose, as this measure was conceived for ordinal MDS and is highly susceptible to the number of observations and variables. 

Please see an article by Patrick Mair and colleagues on this topic, here: https://www.researchgate.net/publication/309617943_Goodness-of-Fit_Assessment_in_Multidimensional_Scaling_and_Unfolding.

Current research proposes a range of better measures, including:

- Comparing the MDS solution with solutions obtained from a random solution or from a solution based on permutations

- Calculating stress-per-point measures, which determine how much individual variables contribute to the overall stress level. Stress-per-point can then be nicely plotted, to see which variables are the most/least certain.

- Mair et al. 2016 (link above) include some more advanced techniques which I will not list here

The SMACOF package in R is already able to conduct these calculations: https://cran.r-project.org/web/packages/smacof/vignettes/smacof.pdf

 

Perhaps it would be worthwile to consider similar measures in XLSTAT?

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  • Nov 26 2017
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