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Here is the data I have:

  • Response variable : It contains proportions and it takes discrete values 0, 0.2, 0.4, 0.6, 0.8, 1. But there are 109 possible discrete values
  • Predictor variable.1: Discrete and ordinal. It contains these values 10, 20, 30, 40.
  • Predictor variable.2: Discrete and non-ordinal. It contains these values 'a', 'b', 'c'.

Neither normality (checked with Kolmogorov-Smirnov and by looking at a qqplot) nor homoscedasticity (checked with Fligner and by looking at a plot) are respected.

Which model should I use in order to infer whether any of the two predictor variable influence my response variable?

What about a logistic regression? Would it work?

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I'm curious as to why the proportion can only take discrete values, but, given that it does, and that they are ordinal, I'd suggest ordinal logistic regression.

If you have the raw data that made up the proportions, you could use (regular) logistic regression.

EDIT:

Given your revision, no, ordinal doesn't make sense anymore. An ordinal regression with 109 levels would be uninterpretable and almost surely over-fit. Now you could probably treat it as a continuous variable; some transformation may be necessary. Or, you could treat it as a bounded variable and use beta regression.

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  • $\begingroup$ My proportions take discrete values because it is a proportion of TRUE over a given number of TRUE/FALSE. For example if I have only 3 TRUE/FALSE possible statement, my proportions can only take the values 0,1/3,2/3,1. Does it make sense ? $\endgroup$ – Sulawesi Jul 24 '13 at 10:32
  • $\begingroup$ Indeed I kept only the proportions and not the raw data that made up the proportions. Thanks a lot for your help Peter Flom $\endgroup$ – Sulawesi Jul 24 '13 at 10:34
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    $\begingroup$ Yes, that makes sense. If the denominator is always the same, though, you could re-create the numerator from the proportion. Then you could do regular logistic. But ordinal may be just as good or better - depending on how you are thinking of the proportions. $\endgroup$ – Peter Flom - Reinstate Monica Jul 24 '13 at 10:37
  • $\begingroup$ Indeed the proportions carry more meaning that the raw data. I'll use the ordinal logistic regression. Thks $\endgroup$ – Sulawesi Jul 24 '13 at 11:11
  • $\begingroup$ Hi Peter Flom. I come back to the question of the other day because I'm affraid I have to much levels in my response variable. I have 109 levels. Does the ordinal logistic regression still makes sense ? $\endgroup$ – Sulawesi Jul 25 '13 at 7:53

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