Modelling ordered data which violates proportional odds assumption I have a dependent variable which describes how many pounds an individual contributed to a cause. The amount is in whole pounds and out of a maximum of 5 (ie. 0,1,2,3,4,5). I have 2 independent variables as well as the interaction between them.
The majority of individuals pick 0 or 5 however I am also interested in the other amounts (1,2,3,4). I have tried to model this as a proportional odds model but the data violates the proportional odds assumption. 
Would it be acceptable to model this as 6 separate logistic models to see how the independent variables affected how often each possible amount was picked? 
The models would be as follows:
1) player contributed £0 versus any other amount 2) player contributed £1 versus any other amount 3) player contributed £2 versus any other amount  4) player contributed £3 versus any other amount 5) player contributed £4 versus any other amount 5) player contributed £5 versus any other amount.
If I did this should I make an p-value adjustment for multiple comparisons? 
 A: I am not 100% certain that you want to model as ordinal, but if you do, you can use a multinomial logit model, rather than run separate logit models. You interpret the coefficients similar to a logit model and similar to how you present it in your question (when you exponentiate the coefficients they are called relative risk ratios, rather than odds ratios). Using this model you don't need to adjust p-values because all levels are modeled at once. You can also test coefficients across models; you may find, for example, that there is a big difference between selecting 0, 1:4, and 5, in which case you could maybe collapse 1:4 pounds into one group.
There are other modeling approaches you could take. Without knowing more about the data, here are some to consider:
- Run a model with a beta distribution, rather than normal or logistic - others may have more experience with this, I haven't done it so can't give you any more to go on. R has a packages called betareg you could check out.
- You impy that donors are restricted to how much they can give; if that's the case you have a censored model - folks giving 5 pounds may want to give more, but because they can't, you see a spike at 5. If they could give an unlimited amount, you may actually see a long tail. R has a package called censReg that may be useful. Again I don't much experience with this, but it may give you a different path forward.
