# Interpretation of MDS factor plot

Suppose I run Multidimensional Scaling and I got the resulting plot. Can anybody suggest me how to interpret the plot. Please find one of my result below. Here I've 5 concepts which I run the MDS based on 10 variables. I'll be grateful if somebody can help me out.

Regards, Ari

• Can you provide more information on your design: what are 'concepts', how many subjects, context, etc. Also, shall we assume that this is standard 'metric'-scaling (equivalent to PCA for the first two PCs), or did you rely on non-metric multidimensional scaling?
– chl
Commented Jul 10, 2011 at 20:25
• Hi Chl: I did metric scaling to get the plot. The data set has 100 respondent who are shown different ads capturing certain concepts. These concepts are reflected in the variables mentioned. Then they were asked to rank the variables from 1(dissatisfactory) to 4 (satisfactory).We need to create the "perceptual map" from it.
– Beta
Commented Jul 10, 2011 at 20:34
• What dissimilarity is used in the analysis? Also, are you the same person I helped on SO recently: stackoverflow.com/q/6613046/429846 ?? If so, it is important to let people know what software you used to do the analysis. Commented Jul 10, 2011 at 22:06
• Hi @Gavin, I'm the same guy you helped. I've gone through the entire doc of vegan package as well as relevant literatures. But unfortunately didn't get any material on how to interpret the result. We can do it just by reading the data points. But is there any more methodical way to do it?
– Beta
Commented Jul 11, 2011 at 10:34
• In MDS, can I rotate the principal components for loading across the variables & then try to interpret it? Just like we do in Principle Component Analysis. Can anybody help me to give the code. The "vegan" tutorial doesn't have that.
– Beta
Commented Jul 11, 2011 at 14:21

## 1 Answer

I'm answering my own question for 2 reason:1) I want to be clear what I've understood is correct or not. 2) If somebody is looking for the same reason he/she should find it here.I hardly found book that gives a clear explanation of interpretation of MDS biplots. I'll also give few references where people can read more about interpretation of MDS ploting to better understand it.

This answer is divided in few parts: Part 1: The axis of the biplot are the principal components. x-axis has the PC 1, which reflect the max variance in the dataset. y-axis has the PC 2, whichreflect 2nd most variance. E.g. in my example x-axis represent 72% of the variance, while y-axis represent 16% of the variance in the data.

 PC1      PC2      PC3      PC4
0.727891 0.166721 0.070320 0.003048


Part 2: The arrows reflect how the variables are loaded in each PCs. E.g. in my example "uncluttered" & "visualization" is highly negatively loaded to PC 2, hence y-axis. Similarly, "no water","fast relief" & "convinient" is highly plositively loaded to PC 2, hence x-axis.This gives us a visualization about how variables are loaded in different PCs.

                    NMDS1     NMDS2
Safe                      0.616967 -0.786989
Highly.efficacious       -0.135565  0.990768
Same.side.effect.profile  0.822707 -0.568466
Fast.Relief               0.988621 -0.150428
No.Water                  0.990893  0.134648
Convenient                0.989206  0.146534
Convincing                0.763225 -0.646133
Visually.appealing        0.154414 -0.988006
Very.novel                0.900984  0.433853
Noticeable                0.691596  0.722284
Likely.to.be.read         0.887028 -0.461715
Uncluttered               0.031498 -0.999504
Interesting               0.872584 -0.488465
Credible                  0.620556 -0.784162
Prescribe.Recommend       0.809955 -0.586492


part 3: Concept points tells us how dissimilar they are from the each other. So, in my example Concept 1 & Concept 2 are very different from rest of them. Concept 2 is both bad in terms of visual appeal as well as convenience. Whereas concept 3 & 4 are more alike. They are also good in terms of visualization as well as convenience.

Reference: 1) Greenacre, M. (2010). Biplots in Practice
2) Everitt & Hothorn: An Introduction to Multivariate Analysis with R(Chapter 4).
3) Hair: Multivariate Data Analysis

• Thank you for this useful post. Hi what do you mean by highly plositively loaded to PC 2 hence x axis? Highly negatively loaded to PC-2 hence Y axis? Can you please elaborate on this? Commented Mar 25, 2013 at 1:28