R-structure in ZIP models
Hi Chris, The zero-inflation part of the model is like modelling a binary variable. Between observation heterogeneity in the probability of success cannot be observed (even if it exists) and so the residual variance is unestimable. For this reason I recommend fixing the residual variance of the zero-inflation process at something (usually one). By not fixing it, the posterior and prior for the residual variance will be identical. It turns out that the higher you fix the residual variance the better it mixes, but if it is too high you will get numerical problems trying to take the inverse logit of the latent variables. Different values of the residual variance will give different estimates or the fixed effects and other variance components. Diggle et al in their book on longitudinal analysis give a very accurate method for rescaling the effects back to what would be observed if the residual variance was zero (the assumption of most other programs). I'm not on my computer at the moment but the result can be found in the CourseNotes vignette. From memory, you divide the fixed effects by sqrt(1-c^2*R) where R is the estimated residual variance and c=(16*sqrt(3))/(15*pi). For the variance components divide by (1-c^2R). Cheers, Jarrod Quoting Christopher David Desjardins <desja004 at umn.edu>:
I recall that Jarrod recommended that I fix the variance in the R-structure when I set priors for ZIP models. However, I don't recall why. Was the reason that it expedites MCMC convergence? Thanks, Chris
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