# Non-metric Stress in 3 way Multidimensional Scaling (INDSCAL): individuals vs. group

My data consists of 19 participants giving dissimilarity ratings for every possible pairwise comparisons of a set of 12 epistemic adverbs (so each participant gives 66 ratings).

The goal is to explore how participants mentally organize the meaning of these adverbs, so I'm using multidimensional scaling as an analysis.

I am comparing two ways of doing it:

• 2 way non metric MDS on aggregated data across all participants (taking the mean dissimilarity for every pairwise comparison, thus yielding a 12 x 12 matrix)
• 3 way non metric MDS (INDSCAL) on individual data (i.e., a list of 19 12x12 matrices)

I ran these analyses using smacof in R (smacofSym for the 2 way MDS, and smacofIndDiff with "indscal" constraint for the 3 way MDS).

Based on scree plots and stress values, I chose a 3 dimensional solution.

For the the 2 way MDS (so the aggregated group analysis) I obtain Stress-1=.05 and an RSQ=.92, so I'm pretty happy with the fit.

For the 3 way MDS (individual differences analysis), I can look at Stress-1 values in two ways:

• An overall stress value for the group, here: group Stress-1=.75 (which seems horrendous).
• Stress values per participant: here, taking the mean of these 19 stress values yields: mean Stress-1=.16

Question: How to deal with stress for the 3 way MDS?

• Typically, which one (group vs. mean across participants stress) is the one one needs to report?

• What is the relation between these two stress values? The difference in magnitude is huge and I don't know what to make of it.

• What are guidelines and/or texts/articles/references that discuss stress values for an INDSCAL model? In all I could find, INDSCAL results are always discussed in terms of individual differences in weights given to the different dimensions, but never in terms of stress.

I've looked into 2 of Borg & Groenen's textbooks on MDS, several MDS chapters in general multivariate stats books, a number of articles using MDS, but I haven't really found answers to my questions.

Thanks a lot in advance for any help.