[R-sig-ME] glmmTMB: how to calculate posterior prob. of structural zero?

[Aaron Mackey]

Thanks for this, it seems to provide sensible numbers; but just to confirm,
does predict(model, type="conditional") actually use the Y variable
observed count? Or does it generate the expected log count from the
provided X variables (as in the case when newdata is provided)?

-Aaron

On Wed, Oct 3, 2018 at 3:01 PM Ben Bolker <bbolker using gmail.com> wrote:

>
>   If you're fitting a zero-inflated Poisson model, it would be
> especially easy because the zero probability is simply exp(-lambda), so
> I believe the "posterior"(ish) probability that the zero is due to the
> structural rather than conditional part of the model would be
>
>  P(zero|structural)/P(zero) =
> P(zero|structural)/(P(zero_structural)+P(zero_conditional))
>
> or
>
> prob_struc <- function(model) {
>    strucprob <- predict(model, type="zprob")
>    condprob <- exp(-predict(model, type="conditional"))
>    return(strucprob/(strucprob+condprob))
> }
>
> For a negative binomial ("nbinom2", or quadratic parameterization) the
> zero probability is (k/(k+mu))^k (I think ... e.g.
> dnbinom(0,mu=0.5,size=0.5) is sqrt(0.5)).  sigma(model) returns the
> overdispersion parameter k, so a function as above but with
>
>   k <- sigma(model)
>   condprob <- (k/(k+predict(model,type="conditional")))^k
>
>  inserted should do the trick.  (Please test these yourself and make
> sure they are sensible before proceeding!)
>
> On 2018-10-03 02:18 PM, Aaron Mackey wrote:
> > I'm happily using glmmTMB to fit zero-inflated count models with my data,
> > but I'd like to also know which zeroes in my data are more likely (or
> not)
> > to be structural vs. expected from the conditional distribution. I know
> how
> > to use Bayes formula to calculate the posterior, and predict(zinb,
> > type="zprob") gives me the prior probabilites for each data point being
> > structural or not (respecting the zero inflation part of the model), and
> > the likelihoods for the structural components are 1 (if the data point
> is a
> > zero) or 0 (if the data point is not a zero) -- but is there a way to
> > extract the likelihood for each zero data point with respect to the
> > conditional part of the model?
> >
> > thanks,
> > -Aaron
> >
> >       [[alternative HTML version deleted]]
> >
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