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

[Ben Bolker]

On Fri, Oct 5, 2018 at 4:07 PM Aaron Mackey <ajmackey using gmail.com> wrote:
>
> 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)?

  It generates the expected  *count* (not the log count) *of the
conditional part of the model only* (i.e. not including structural
zeros), based on the estimated parameters and a model matrix (either
the one from the model or a newly generated one, if newdata is
specified)

>
> -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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>>
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