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so if i understand correctly, each individual (how many, by the way ?) is represented by his 13x12/2 = 78 similarity ratings (assuming the rating matrix is symetric ...) plus some other informations

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applying PCA (or rather Factorial Analysis) is always possible : you search for the best (linear) subspace of a given dimension to embed your data (best = maximizing the proportion of variance captured in the subspace)

if you are lucky, you might find that a low dimensional subspace (say d = 2 or 3) captures a significant proportion of the variance (say 75%) : in such case, staying with FA for a reduced dimension representation will be fine

if you are not lucky, then you'll find that you'll need 10, 15 or more dimensions to capture a significant proportion of the variance ; this is bad news since (my guessing ...) your dimension reduction objective is a really low dimensional space (3 maximum or so)

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in this case, you could go for MDS, to embed your 78-dimensional data into a low dimensional subspace (usually 2 or 3 dimensional)

MDS can be tricky as it comes in many different flavours (metric, non-metric, local, global ...) and its interpretation requires a good understanding of the loss function being optimized by the non-linear embedding ; that's why i would recommend to go for MDS only if FA fails

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this done, you end up with a description of each individual by a 2 or 3 dimensional vector ... connections with others variables will still require some more work !

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thank you very much for your answer! The sample will be about (hopefully!) 50-70 people... I just ask this question in advance, because I need an initial plan of how my analysis of the data will be, so I can write down the method part of my thesis (the theoretical background). Of course, it is highly likely that I will need to make some changes, especially in the case of missing data or outliers (this is always my greatest fear!). Thanks again!

I would say that 50-70 participants is insufficient for both apporaches. Sample size for factor analysis depends at least on the ratio of items per factor and the communalities. In the best case with e.g. 7 items per factor and communalities > .60 (more like .70 or .80) 60 peoply may suffice, but all other combinations lead to estimated sample sizes of 100-400. Especially low communalities have a negative impact on the quality of the factor solution and may require sample sizes of > 1000, if communalities are way smaller than .40

But please have a look at MacCallum, Widaman, Zhang & Hong (1999) Sample Size in Factor Analysis, Psychological Methods, 4(1), 84-99

thank you very much... I thought so too, however the sample may finally be 100, but not much more... I think I have to reconsider some parts of its design...

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given the small sample, i would give a try to "sparse factor analysis" with few factors

https://yunablum.files.wordpress.com/2014/06/user_2014_blum.pdf

not your vanilla FA indeed but not so wildly exotic ...

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thank you... I’ll check it...

Follow This link Please:

https://www.quora.com/Whats-the-difference-between-MDS-and-PCA