Background
In a psychology experiment we had people interact with various 5-sided polygons drawn on the face of a clock (the specifics of the experiment are not pertinent to the question at hand).
For example, here is the polygon [0 1 3 6 9]:
Procedure
In the experiment, each of 66 possible polygons were scored according to some criterion (again, the specifics aren't relevant to the math).
Analysis
We hope to do an analysis that relates the count of different sized strings to the recorded performance for each polygon.
For that reason, we create string-length vectors representing the count of each string length found in each polygon. For instance, in the polygon presented in the example above we find 1 string of length 1 (green), 1 string of length 2 (teal), 4 strings of length 3 (blue), 1 string of length 4 (purple), 1 string of length 5 (red), and 2 strings of length 6 (orange). So the vector for this polygon is (1 1 4 1 1 2).
- We hope to be able to create an analysis that quantifies each string length's count individual contribution to the recorded performance.
Challenge
However, the string counts are not independent of one another, such that the presence of certain strings can necessitate or prevent the appearance of certain other strings (as every triangle formed between 3 strings must sum to 12).
We are struggling to come up with a way to disentangle the influence of the strings on one another in order to execute our analysis.
How can we disentangle the co-dependence of the strings such that we could isolate the contribution of the count of each string length in isolation?
Clarification
This is a more complex interaction than simply a correlation, because the interactions between the the counts of various string lengths appears to be non-trivial.
Any clever ideas on how we might solve our conundrum?
Thanks!