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I am new to modelling percentage data, and I would be greatfull for some advice. I have proportion data (0,1] on a percentage of money sent by Player B to Player A. Participants received an amount of money, and could decide what percentage they will send back. I have two categorical predictors (1st with 3 factors, 2nd with 2); one continuous predictor; and one nesting factor (class). Since the data are bound between 0 and 1, I figured out that the best option would be Beta regression. I tried to use hglm package which fitted well, however, since the data are one-inflated (many people chose to send back the full amount), I am looking for other options.

As most appropriate seem to be gamlss package, which can use BEOI (Beta One Inflated) distribution. I used this code:

m1 <- gamlss(percent~cat1+cat2+continous, random(class), family=BEOI, data=dat, 
             mixture="gq", K=1)

From what I understand from package help files, this should be the simplest option. However, it produces very different results from the hglmcommand. Especially the standard errors are higher than beta coefficients, leading to non-significant results. I tried to specify other other functions in the model (e.g., K, sigma.formula, nu.formula, mixture etc.), but these are beyond my understanding, and I am not really sure what I did there.

I would very much appreciate any suggestions regarding either how to better specify the model, or simple explanations of gamlss function.

kjetil b halvorsen
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joe.s
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  • One possibility -- if you have access to zero-inflated beta regression, you could try to model how much they *don't* send back. – Glen_b Aug 24 '14 at 02:25
  • Thanks @Glen_b, I tried your suggestion with gamlss BEZI distribution but I got the same problem. In the end I ended up transforming the data with [this formula](http://stats.stackexchange.com/questions/31300/dealing-with-0-1-values-in-a-beta-regression) and using standard beta regression. This approach works fine; however, I still wonder what was wrong with the one-inflated model. – joe.s Sep 24 '14 at 17:47

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