I am working in R with a data set which includes a column of Shannon Indexes per location code. I would like to perform a GLMM using this column as the response variable. Treatment would be my fixed effect and then I have a couple of random effects as well. The issue is that the Shannon Indexes have an awkward distribution:
There is a zero inflation and ignoring that it presents a bimodal curve.
Below is the histogram of the non-zero subset of this data:
Would this be a zero-inflated gaussian distribution?
I tried fitting a Gaussian mixed model for the non-zero subset of this data:
> descdist(subset_Shan_lepi, discrete = FALSE, boot = 500)
summary statistics
------
min: 0.2337917 max: 1.819511
median: 0.7143846
mean: 0.8885969
estimated sd: 0.2991915
estimated skewness: 0.6367288
estimated kurtosis: 3.174011
> gaussian_mix_model <- normalmixEM(subset_Shan_lepi, k = 2)
number of iterations= 23
> hist(subset_Shan_lepi, probability = TRUE, col = "lightgray", main = "Histogram with Fitted Mixture Model")
> lines(density(gaussian_mix_model$mu), col = 2, lty = 2, lwd = 2)
It seems like a good fit but I gave no idea how to perform a GLMM on a data with this mixed distribution let alone including the zeroinflated data.
Any help welcome, thanks for reading!