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As part of my research project, I'm studying the plumage of a species of bird called Brent Goose. The species can be divided into two subspecies, a dark-bellied form and a light-bellied form. The two subspecies are present side by side at a location in Northern England, whereas in Southern England, only dark-bellied is found. Ecological character displacement predicts that populations that winter side by side should be more different than populations that winter further from each other. 

Therefore, I want to make two comparisons:

  1. Northern England dark-bellied vs Northern England light-bellied

  2. Southern England dark-bellied vs Northern England light-bellied

If ecological character displacement theory holds, the difference between comparison 1 should be larger than comparison 2.  To test for this, I have scored 4 characters on a 3 point scale. As an example, I have scored the upper parts as follows: 1=blackish, 2=dark greyish-brown, 3=pale greyish-brown. 

I have two questions:

  1. Using my ordered character scores,  what would be an appropriate test to determine if the difference in comparison 1 is larger than comparison 2?

  2. Do I need to analyse each of the 4 characters separately or can they be combined into a single test?

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    $\begingroup$ Presumably we are to imagine observations on several birds and on each of four characters on each of these subspecies. As always, the idea that a test is the Holy Grail to seek in an analysis is not obvious: you are likely to get much more out of (say) a correspondence analysis. Whether your three grades are ordinal or nominal is not quite clear. Whether you can combine characters is not predictable by us in advance, but why go to the trouble of collecting detailed data only to want to mush it altogether? $\endgroup$
    – Nick Cox
    Jul 2, 2013 at 17:30
  • $\begingroup$ @Nick Cox: 'Presumably we are to imagine observations on several birds and on each of four characters on each of these subspecies' - yes this is correct. I would consider each variable to be ordinal. Could you provide more details of the correspondence analysis in form of an answer? $\endgroup$
    – luciano
    Jul 2, 2013 at 18:19
  • $\begingroup$ Correspondence analysis is so well documented in ecology that I don't feel inclined to add yet another summary. Sorry if it seems unhelpful, but we all ration our time somehow. $\endgroup$
    – Nick Cox
    Jul 2, 2013 at 18:27

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One approach to modeling a response that is ordered categorical is proportional odds logistic regression. But make sure that you understand what the assumptions are and what the model will tell you before fitting it. Make sure that it answers the real question of interest.

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  • $\begingroup$ would a separate logistic regression be required for each for the four measured characters? For how I've collected data, see first Nick Cox comment and my response. $\endgroup$
    – luciano
    Jul 2, 2013 at 19:50
  • $\begingroup$ @Luciano, are each of the questions of interest on their own? If so then I would analyze each with it's own separate model. $\endgroup$
    – Greg Snow
    Jul 2, 2013 at 21:18

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