# 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 Jul 10 '11 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 Jul 10 '11 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. – Gavin Simpson Jul 10 '11 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 Jul 11 '11 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 Jul 11 '11 at 14:21

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

Reference: 1) Greenacre, M. (2010). Biplots in Practice