Proportions and Beta-Binomial Models

[awaldman123]

I am working with data in which I have information on the proportional area taken by a tumor in different body sites (site 1, 2, and 3) stratified by different tumor phenotypes (type 1, 2, and 3). The data is clustered by individual animal (all sites and tumor phenotypes represented). The denominator used to derive the proportional area metric will be different for each of the different sites and the data includes 0 and 1. In looking at the following webpage: http://htmlpreview.github.io/?https://github.com/strengejacke/mixed-models-snippets/blob/master/overview_modelling_packages.html I was thinking of using a beta-binomial model to understand differences related to site and type. However, I am not sure if that is the right approach?

I tried it and in my formula I included the proportion information as the response:

glmmTMB::glmmTMB(TumorAreaRatio ~ Site*Phenotype + (1 | ID), family=betabinomial, data=data, REML=TRUE, control=glmmTMBControl(optimizer=optim, optArgs=list(method="BFGS")))

I then got the following warnings:

In eval(family$initialize) : non-integer #successes in a binomial glm!
In fitTMB(TMBStruc) : Model convergence problem; extreme or very small eigenvalues detected. See vignette('troubleshooting')

I looked in the troubleshooting vignette and this made we wonder if this would be the right model type to use since the proportions are not success/failure data per se but rather represent a normalized area?

In addition, my data seems to be skewed toward 0s and I thought zero-inflation may be appropriate. When trying varying zero-inflation formulas I consistently received the following error (the eigenvalue error went away):

In fitTMB(TMBStruc) :
Model convergence problem; non-positive-definite Hessian matrix. See vignette('troubleshooting')

I looked in the vignette and noticed that the zero-inflation parameter was very negative no matter what I included in the zero-inflation model formula. I don’t get the Hessian matrix error if the zero-inflation is removed. Therefore, would that indicate that it is appropriate to leave out the zero-inflation?