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I am seeing a lot of different answers to percentage data, either beta or binomial with a logit link and not to use poison distribution because it isn't count data. My response variable is retention efficiency for different food types ((Incurrent food - excurrent food)/ incurrent food) *100. There are 5 different food types. I am looking to see if the sponges from different regions and genus differ in their consumption of the five food types. I am attaching a histogram of the data which has more values closer to 1 or 100% retention (none are actually 100%). I am wondering what distribution would be best at fitting my data which would be continuous proportion I think but the data is obviously not normal. I will probably be doing some sort of generalized linear mixed-effects model

enter image description here

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  • $\begingroup$ Do you have values that are 100% and 0%? Or are all observations between those two numbers? $\endgroup$ – Mark White Apr 6 '20 at 15:53
  • $\begingroup$ all are between 0 and 100, no 0% or 100% $\endgroup$ – Michael Apr 6 '20 at 16:32
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I would use beta regression with the logit link function. I would take your data, which is in percent, and then divide by 100 to get it to proportions and between the 0 and 1 range that standard beta regression expects.

From your histogram, it looks like you're using R. The {brms} package supports mixed models with beta regression, using the family = Beta() argument. The link function for the expected value is logit and for the dispersion parameter is log, by default.

The {gamlss} package also implements this, but they employ a less common reparameterization of the beta distribution.

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  • $\begingroup$ Thank you, I will try that package $\endgroup$ – Michael Apr 6 '20 at 19:51
  • $\begingroup$ Great! Glad to help. If that answers your question, feel free to mark it as answered to close the question out and help others. Thanks! $\endgroup$ – Mark White Apr 6 '20 at 19:54

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