[R-sig-ME] R-structure in ZIP models

[Jarrod Hadfield]

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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