Hurdle model: singular variance-covariance matrix

Yaiza,

The problem is that two coefficients are perfectly correlated with each other.  Since this happens in the models with interactions but not additive effects, my hunch is that the cross-product variable is very highly correlated with one of the original variables.  This can happen if one variable has a large mean and large variability and the second has a large mean and small variability.  If so, this is a numerical issue, not a conceptual, statistical or ecological issue.

I suggest you center all X variables to mean 0.  That often clears up numerical issues.  If it doesn't standardizing each to unit variance can also help.  Centering the X variables also has the statistical advantage that the intercept is directly interpretable.

Best wishes,
Philip Dixon