Zero-inflated Gaussian bi-variate models

Hello! My data concern a study in behavioural ecology, and are zero-inflated normally distributed. I have 2 continuous response variables, 2-4 fixed effects and 2-3 random effects. For my research question, I need to find the individual repeatability of the two response variables and the correlation between them. For this, I decided to make a bi-variate mixed effects model using brms.

However, I could not find a family called “Zero-inflated Gaussian”, and I got an error saying that the residual correlation cannot be obtained using any zero-inflated family. What should I do?

P.S: I am new to Bayesian statistics and to this forum. I apologise if I shouldn’t have asked this question here.

Welcome to the forums, @atharva_andhare. Sorry you haven’t gotten a response sooner.

I don’t know about brms, but you could build that model in Stan itself following the description in the User’s Guide section on inflation and hurdle models. If you can write the likelihood down, you can usually translate to Stan pretty easily.

I would make a concrete suggestion, but there are lots of decision points in such a model, such as whether the response is modeled as a bivariate normal or as conditionally independent univariate normals. If it’s bivariate normal, how does zero-inflation work? If one value is zero inflated, does the other one get a distribution conditioned on the first being zero? What’s the probability model for zero inflation patterns 00, 10, 01, and 11? Are the two dimensions independently zero inflated or does it have correlation? If the value for one is zero, does the other take the marginal multivariate normal distribution or the one conditioned on the zero?