I am new to the
gamlss package and would like to check that I am using the correct family for proportion data (tree species cover after treatment), which is bounded between zero and one. According to the documentation, the correct distribution family for data of this type is BEINF (Beta inflated), since it allows both 0 and 1 values. The data are highly zero-inflated, with 43/82 observations having a zero response, and 3/82 values at 1. I run the following model:
m1 <- gamlss(y ~ x1 + x2, sigma.formula=~1, nu.formula=~x1 + x3 + x4, tau.formula=~x5, family=BEINF, data=df)
The mean response values (and SEs) given by:
pred <- predict(m1, type='response', se.fit=T)
I am also interested in the probability of obtaining a zero response (i.e. the probability of having no individuals of the target species post-treatment). However, when i try to extract the fitted values of the nu parameter (which I believe to be the probability of obtaining a zero value), using:
prednu <- predict(m1, type="response", what="nu")
I am getting predicted values of the response in the range 0.01-44.6, which I find strange. I have tried this for both the model-fitting data and new data, with the same result. However, when I use
family=ZAGA (i.e. zero adjusted Gamma distribution which allows for a response with no upper bound), I get predictions between 0 and 1 for the response for the nu parameter, which seem more reasonable.
I therefore have 3 questions about my approach:
Is BEINF the correct choice of distribution family for zero-inflated proportion data bounded between zero and one, and including both zeros and one values?
predict(m1, type="response", what="nu")give the probability of obtaining a zero response?
predict(m1, type="response", what="nu")give values far outside the $[0,1]$ bounded range of the response variable?
We are happy to provide data if that would be helpful.
Any assistance you can provide regarding the correct use of these gamlss functionalities with my dataset would be greatly appreciated. Kind regards,
PS – This question has been sent to GAMLSS team a week ago but hasn’t been answered yet.