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I am learning individual differences scaling (AKA three-way multidimensional scaling) and I want to know what different ways there are to state that my results are reliable.

I had to perform individual differences scaling in 2 dimensions on the data, and give the group object space. I work in R, with the smacof package (this is obligatory). So far I am ok. But this is an additional question:

It is recommended to supplement the analysis with additional investigations before placing too much belief in its results. List 3 investigations that you would undertake and explain the reasons for performing these analyses.

The answer I can think of:

1) Check the overall stress of the model against a similar model with random data. If the stress levels are not significantly lower, you probably got a configuration that is based on coincidence.

2) Try the model with more and less dimensionalities, and look at the scree plot of the stress levels. This can tell you if choosing a 2-dimensional solution was the best decision.

3) Check the individual configurations, to see whether some persons used different criteria than others. Then it would be better to look at the individual pictures, instead of the group object space.

Could anyone give any feedback on this answer? I can't seem to find much info anywhere else.

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    $\begingroup$ I found that I cannot do it for one dimension: > regular_indscal1<-smacofIndDiff(regular_list, ndim=1, metric=FALSE, constraint="indscal",itmax=10000) Error in wr[[j]] %*% yr[[j]] %*% bconf[[j]] : non-conformable arguments Maybe that compromises my second proposal? $\endgroup$
    – Marloes
    Jan 13, 2013 at 1:14
  • $\begingroup$ I'm curious what is the name and level of the course. $\endgroup$
    – rolando2
    Jan 13, 2013 at 13:26
  • $\begingroup$ Uni-and multidimensional scaling / Masters level / Leuven University $\endgroup$
    – Marloes
    Jan 13, 2013 at 13:44

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There are some good ideas in Chen and Chen's article on diagnostic plots for multidimensional scaling at - http://www3.stat.sinica.edu.tw/statistica/oldpdf/A10n31.pdf - that might be adaptable. They review usual methods and add some of their own.

I wonder if you could also adapt a jacknife approach - take out one individual at a time and all the differences that relate to them from your original distances data, refit the model each time, and compare the distribution of those models with your actual model. I've never tried this but it might be worth a go (in fact, I now see that there is an article Weinberg, S. L., Carroll, J. D. and Cohen, H. S. (1984). "Confidence regions for INDSCAL using the jackknife and bootstrap techniques." Psychometrika 49, 475-491. which looks relevant).

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