noisemds

How does MDS plot axes relate to S:N ratio?


Say I have a MDS plot as shown below:

enter image description here

Now, say everything in the MDS plot looks exactly the same (the position of the colored dots does not change). But only one thing changes: the x-axis ("first dimension"):

1) If the x-axis limits goes from -200 to 100 say (instead of -100 to 50 as it currently is), and the dots all appear the same distances from each other, can we say the S:N ratio is better (i.e. the groups are better separated) because the x-axis limit is larger?

2) If in one case the x-axis explains 25% of the variation, but in another case the x-axis explains 75% of the variation, if the dots all appear the same distances from each other in both cases, can we say the S:N ratio is better in the second case since those distances between the dots (samples) can be explained by even more variation?

Thank you for offering your ideas to these questions!


Solution

  • I don't think you can interpret the axes like that. MDS is just a method of contorting points separated in 3 dimensional space into 2 dimensions. You can't determine what proportion each of the axes explain in MDS unlike other constrained methods (PCA ect.) Instead, you are provided an R statistic, and when that R statistics exceeds 0.20, it means your MDS poorly represents the differences between the points.

    Sorry that I can't provide a more 'mathematical' answer.