<p>I guess it depends on your purpose. If you are doing the MDS for more heuristic purposes, then often two dimensions (or possibly three) will provide the greatest visual insight.</p>

<p>Also, my sense from looking at your dimension by stress plot is that the greatest gains are attained when going from one to two dimensions, that the gain from two to three dimensions is still substantial, but after that there are minimal gains.</p>

CC BY-SA 3.0
2014-09-09T16:44:08.587Z
thank you for your answer. I now have another question. I chose to display the ratings on two dimensions, the one being their distance in mean rating and the other I suspect the degree of inter-rater agreement. Is there a method for calculating inter-rater agreement for each and every item (in my case, every musical interval) in SPSS? Sadly, all the methods I know, provide a rather more general measure of reliability such as a mean correlation for all the intervals.
Lazaros Mitskopoulos
CC BY-SA 3.0
2014-09-10T01:45:04.927Z
@LarryM Welcome to the site. Feel free to ask another question. To do this, ask a separate question by clicking "Ask question". If it is related to this question, then add a link to this question from your new question.
Jeromy Anglim
CC BY-SA 3.0
2014-09-01T01:49:07.007Z
2014-09-01T01:49:07.007Z
Jeromy Anglim
<p>I have run an experiment on consonance-dissonance evaluation of musical intervals on 40 individuals using all the possible intervals from 3 registers (plus their inversions), and I want to apply a multidimensional scale analysis.</p>

<p>My problem is that the stress plot indicates the following:</p>

<blockquote>
  <p><img src="https://i.sstatic.net/h56di.jpg" alt="stress plot 8dim"></p>
</blockquote>

<p>I guess it would not be desirable to limit my analysis to 2 or 3 dimensions since the stress is high at these points, but I am not sure if adding dimensions helps either. Is there an optimal number of dimensions that I should consider, or should I follow the stress curve wherever it may take me?
Thanks.</p>

<experimental-psychology><statistics><psychophysics><psychoacoustics>
Optimal number of dimensions in multidimensional scaling
Lazaros Mitskopoulos
# Optimal number of dimensions in multidimensional scaling

(Asked by: username_0 on 2014-08-31)

I have run an experiment on consonance-dissonance evaluation of musical intervals on 40 individuals using all the possible intervals from 3 registers (plus their inversions), and I want to apply a multidimensional scale analysis.

My problem is that the stress plot indicates the following:

> ![stress plot 8dim](https://i.sstatic.net/h56di.jpg)

I guess it would not be desirable to limit my analysis to 2 or 3 dimensions since the stress is high at these points, but I am not sure if adding dimensions helps either. Is there an optimal number of dimensions that I should consider, or should I follow the stress curve wherever it may take me?
Thanks.

**Tags:** experimental-psychology, statistics, psychophysics, psychoacoustics


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## 1 answers

### Answer by username_1 on 2014-09-01. Score: 3 | Accepted answer

I guess it depends on your purpose. If you are doing the MDS for more heuristic purposes, then often two dimensions (or possibly three) will provide the greatest visual insight.

Also, my sense from looking at your dimension by stress plot is that the greatest gains are attained when going from one to two dimensions, that the gain from two to three dimensions is still substantial, but after that there are minimal gains.

> **Comments:**
> **username_0**: thank you for your answer. I now have another question. I chose to display the ratings on two dimensions, the one being their distance in mean rating and the other I suspect the degree of inter-rater agreement. Is there a method for calculating inter-rater agreement for each and every item (in my case, every musical interval) in SPSS? Sadly, all the methods I know, provide a rather more general measure of reliability such as a mean correlation for all the intervals.  
> **username_1**: @LarryM Welcome to the site. Feel free to ask another question. To do this, ask a separate question by clicking "Ask question". If it is related to this question, then add a link to this question from your new question.  

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