[R-sig-ME] Question about zero-inflated Poisson glmer

Philipp Singer killver at gmail.com
Mon Jun 27 15:18:45 CEST 2016 

The variance is:

Conditional model:
 Groups            Name        Variance  Std.Dev.
 obs               (Intercept) 8.991e+01 9.4823139



2016-06-27 15:06 GMT+02:00 Thierry Onkelinx <thierry.onkelinx at inbo.be>:

> Dear Philipp,
>
> How strong is the variance of the observation level random effect? I would
> trust a model with large OLRE variance.
>
> Best regards,
>
> Thierry
>
> ir. Thierry Onkelinx
> Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
> Forest
> team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
> Kliniekstraat 25
> 1070 Anderlecht
> Belgium
>
> To call in the statistician after the experiment is done may be no more
> than asking him to perform a post-mortem examination: he may be able to say
> what the experiment died of. ~ Sir Ronald Aylmer Fisher
> The plural of anecdote is not data. ~ Roger Brinner
> The combination of some data and an aching desire for an answer does not
> ensure that a reasonable answer can be extracted from a given body of data.
> ~ John Tukey
>
> 2016-06-27 14:59 GMT+02:00 Philipp Singer <killver at gmail.com>:
>
>> I have now played around more with the data an the models both using lme4
>> and glmmTMB.
>>
>> I can report the following:
>>
>> Modeling the data with a zero-inflated Poisson improves the model
>> significantly. However, when calling predict and simulating rpoissons, I
>> end up with nearly no values that are zero (in the original data there are
>> 96% zero).
>>
>> When I model the data with overdisperion by including an observation-level
>> random effect, I can also improve the model (not surprisingly due to the
>> random effect). When I predict outcomes by ignoring the observation-level
>> random effect (in lme4), I receive bad prediction if I compare it to the
>> original data. While many zeros can be captured (of course), the positive
>> outcomes can not be captured well.
>>
>> Combining zero inflation and overdispersion further improves the model,
>> but
>> I can only do that with glmmTMB and then have troubles doing predictions
>> ignoring the observation-level random effect.
>>
>> Another side question:
>>
>> In lme4, when I do:
>>
>> m = glm(x~1,family="poisson")
>> rpois(n=len(data),lambda=predict(m, type='response',re.form=NA)
>>
>> vs.
>>
>> simulate(1,m,re.form=NA)
>>
>> I receive different outcomes? Do I understand these function wrongly?
>>
>> Would appreciate some more help/pointers!
>>
>> Thanks,
>> Philipp
>>
>> 2016-06-24 15:52 GMT+02:00 Philipp Singer <killver at gmail.com>:
>>
>> > Thanks - I started an issue there to answer some of my questions.
>> >
>> > Regarding the installation: I was trying to somehow do it in anaconda
>> with
>> > a specific R kernel and had some issues. I am trying to resort that with
>> > the anaconda guys though, if I have a tutorial on how to properly setup
>> > glmmTMB in anaconda, I will let you know. The install worked fine in my
>> > standard R environment.
>> >
>> >
>> > On 24.06.2016 15:40, Ben Bolker wrote:
>> >
>> >>   Probably for now the glmmTMB issues page is best.
>> >>
>> >>   When you go there:
>> >>
>> >>    - details on installation problems/hiccups would be useful
>> >>    - a reproducible example for the problem listed below would be
>> useful
>> >>    - dispformula is for allowing dispersion/residual variance to vary
>> >> with covariates (i.e., modeling heteroscedasticity)
>> >>
>> >>    cheers
>> >>      Ben Bolker
>> >>
>> >>
>> >> On 16-06-24 09:13 AM, Philipp Singer wrote:
>> >>
>> >>> Update, I tried it like that, but receive an error message.
>> >>>
>> >>> Warning message:
>> >>> In nlminb(start = par, objective = fn, gradient = gr): NA/NaN function
>> >>> evaluation
>> >>>
>> >>> Error in solve.default(hessian.fixed): Lapack routine dgesv: system is
>> >>> exactly singular: U[3,3] = 0
>> >>> Traceback:
>> >>>
>> >>> 1. glmmTMB(y ~ 1 + x + (1 | b),
>> >>>    .     data = data, family = "poisson", dispformula = ~1 + x)
>> >>> 2. sdreport(obj)
>> >>> 3. solve(hessian.fixed)
>> >>> 4. solve(hessian.fixed)
>> >>> 5. solve.default(hessian.fixed)
>> >>>
>> >>> Any ideas on that?
>> >>>
>> >>> BTW: Is it fine to post glmmTMB questions here, or should I rather use
>> >>> the github issue page, or is there maybe a dedicated mailing list?
>> >>>
>> >>> Thanks,
>> >>> Philipp
>> >>>
>> >>> On 24.06.2016 14:35, Philipp Singer wrote:
>> >>>
>> >>>> It indeed seems to run quite fast; had some trouble installing, but
>> >>>> works now on my 3.3 R setup.
>> >>>>
>> >>>> One question I have is regarding the specification of dispersion as I
>> >>>> need to specify the dispformula. What is the difference here between
>> >>>> just specifying fixed effects vs. also the random effects?
>> >>>>
>> >>>> On 23.06.2016 23:07, Mollie Brooks wrote:
>> >>>>
>> >>>>> glmmTMB does crossed RE. Ben did some timings in vignette("glmmTMB")
>> >>>>> and it was 2.3 times faster than glmer for one simple GLMM.
>> >>>>>
>> >>>>>
>> >>>>> On 23Jun 2016, at 10:44, Philipp Singer <killver at gmail.com> wrote:
>> >>>>>>
>> >>>>>> Did try glmmADMB but unfortunately it is way too slow for my data.
>> >>>>>>
>> >>>>>> Did not know about glmmTMB, will try it out. Does it work with
>> >>>>>> crossed random effects and how does it scale with more data? I will
>> >>>>>> check the docu and try it though. Thanks for the info.
>> >>>>>>
>> >>>>>> On 23.06.2016 19:14, Ben Bolker wrote:
>> >>>>>>
>> >>>>>>>    I would also comment that glmmTMB is likely to be much faster
>> >>>>>>> than the
>> >>>>>>> lme4-based EM approach ...
>> >>>>>>>
>> >>>>>>>    cheers
>> >>>>>>>      Ben B.
>> >>>>>>>
>> >>>>>>> On 16-06-23 12:47 PM, Mollie Brooks wrote:
>> >>>>>>>
>> >>>>>>>> Hi Philipp,
>> >>>>>>>>
>> >>>>>>>> You could also try fitting the model with and without ZI using
>> >>>>>>>> either
>> >>>>>>>> glmmADMB or glmmTMB. Then compare the AICs. I believe model
>> >>>>>>>> selection
>> >>>>>>>> is useful for this, but I could be missing something since the
>> >>>>>>>> simulation procedure that Thierry described seems to recommended
>> >>>>>>>> more
>> >>>>>>>> often.
>> >>>>>>>>
>> >>>>>>>> https://github.com/glmmTMB/glmmTMB
>> >>>>>>>> http://glmmadmb.r-forge.r-project.org
>> >>>>>>>>
>> >>>>>>>> glmmTMB is still in the development phase, but we’ve done a lot
>> of
>> >>>>>>>> testing.
>> >>>>>>>>
>> >>>>>>>> cheers, Mollie
>> >>>>>>>>
>> >>>>>>>> ------------------------ Mollie Brooks, PhD Postdoctoral
>> Researcher,
>> >>>>>>>> Population Ecology Research Group Department of Evolutionary
>> Biology
>> >>>>>>>> & Environmental Studies, University of Zürich
>> >>>>>>>> http://www.popecol.org/team/mollie-brooks/
>> >>>>>>>>
>> >>>>>>>>
>> >>>>>>>> On 23Jun 2016, at 8:22, Philipp Singer <killver at gmail.com>
>> wrote:
>> >>>>>>>>>
>> >>>>>>>>> Thanks, great information, that is really helpful.
>> >>>>>>>>>
>> >>>>>>>>> I agree that those are different things, however when using a
>> >>>>>>>>> random effect for overdispersion, I can simulate the same
>> number of
>> >>>>>>>>> zero outcomes (~95%).
>> >>>>>>>>>
>> >>>>>>>>> On 23.06.2016 15:50, Thierry Onkelinx wrote:
>> >>>>>>>>>
>> >>>>>>>>>> Be careful when using overdispersion to model zero-inflation.
>> >>>>>>>>>> Those are two different things.
>> >>>>>>>>>>
>> >>>>>>>>>> I've put some information together in
>> >>>>>>>>>> http://rpubs.com/INBOstats/zeroinflation
>> >>>>>>>>>>
>> >>>>>>>>>> ir. Thierry Onkelinx Instituut voor natuur- en bosonderzoek /
>> >>>>>>>>>> Research Institute for Nature and Forest team Biometrie &
>> >>>>>>>>>> Kwaliteitszorg / team Biometrics & Quality Assurance
>> >>>>>>>>>> Kliniekstraat 25 1070 Anderlecht Belgium
>> >>>>>>>>>>
>> >>>>>>>>>> To call in the statistician after the experiment is done may be
>> >>>>>>>>>> no more than asking him to perform a post-mortem examination:
>> he
>> >>>>>>>>>> may be able to say what the experiment died of. ~ Sir Ronald
>> >>>>>>>>>> Aylmer Fisher The plural of anecdote is not data. ~ Roger
>> >>>>>>>>>> Brinner The combination of some data and an aching desire for
>> an
>> >>>>>>>>>> answer does not ensure that a reasonable answer can be
>> extracted
>> >>>>>>>>>> from a given body of data. ~ John Tukey
>> >>>>>>>>>>
>> >>>>>>>>>> 2016-06-23 12:42 GMT+02:00 Philipp Singer <killver at gmail.com
>> >>>>>>>>>> <mailto:killver at gmail.com <mailto:killver at gmail.com>>>:
>> >>>>>>>>>>
>> >>>>>>>>>> Thanks! Actually, accounting for overdispersion is super
>> >>>>>>>>>> important as it seems, then the zeros can be captured well.
>> >>>>>>>>>>
>> >>>>>>>>>>
>> >>>>>>>>>> On 23.06.2016 11:50, Thierry Onkelinx wrote:
>> >>>>>>>>>>
>> >>>>>>>>>>> Dear Philipp,
>> >>>>>>>>>>>
>> >>>>>>>>>>> 1. Fit a Poisson model to the data. 2. Simulate a new response
>> >>>>>>>>>>> vector for the dataset according to the model. 3. Count the
>> >>>>>>>>>>> number of zero's in the simulated response vector. 4. Repeat
>> >>>>>>>>>>> step 2 and 3 a decent number of time and plot a histogram of
>> >>>>>>>>>>> the number of zero's in the simulation. If the number of
>> zero's
>> >>>>>>>>>>> in the original dataset is larger than those in the
>> >>>>>>>>>>> simulations, then the model can't capture all zero's. In such
>> >>>>>>>>>>> case, first try to update the model and repeat the procedure.
>> >>>>>>>>>>> If that fails, look for zero-inflated models.
>> >>>>>>>>>>>
>> >>>>>>>>>>> Best regards,
>> >>>>>>>>>>>
>> >>>>>>>>>>> ir. Thierry Onkelinx Instituut voor natuur- en bosonderzoek /
>> >>>>>>>>>>> Research Institute for Nature and Forest team Biometrie &
>> >>>>>>>>>>> Kwaliteitszorg / team Biometrics & Quality Assurance
>> >>>>>>>>>>> Kliniekstraat 25 1070 Anderlecht Belgium
>> >>>>>>>>>>>
>> >>>>>>>>>>> To call in the statistician after the experiment is done may
>> >>>>>>>>>>> be no more than asking him to perform a post-mortem
>> >>>>>>>>>>> examination: he may be able to say what the experiment died
>> of.
>> >>>>>>>>>>> ~ Sir Ronald Aylmer Fisher The plural of anecdote is not data.
>> >>>>>>>>>>> ~ Roger Brinner The combination of some data and an aching
>> >>>>>>>>>>> desire for an answer does not ensure that a reasonable answer
>> >>>>>>>>>>> can be extracted from a given body of data. ~ John Tukey
>> >>>>>>>>>>>
>> >>>>>>>>>>> 2016-06-23 11:27 GMT+02:00 Philipp Singer <killver at gmail.com
>> >>>>>>>>>>> <mailto:killver at gmail.com <mailto:killver at gmail.com>>>:
>> >>>>>>>>>>>
>> >>>>>>>>>>> Thanks Thierry - That totally makes sense. Is there some way
>> of
>> >>>>>>>>>>> formally checking that, except thinking about the setting and
>> >>>>>>>>>>> underlying processes?
>> >>>>>>>>>>>
>> >>>>>>>>>>> On 23.06.2016 11:04, Thierry Onkelinx wrote:
>> >>>>>>>>>>>
>> >>>>>>>>>>>> Dear Philipp,
>> >>>>>>>>>>>>
>> >>>>>>>>>>>> Do you have just lots of zero's, or more zero's than the
>> >>>>>>>>>>>>
>> >>>>>>>>>>> Poisson
>> >>>>>>>>>>>
>> >>>>>>>>>>>> distribution can explain? Those are two different things.
>> >>>>>>>>>>>>
>> >>>>>>>>>>> The example
>> >>>>>>>>>>>
>> >>>>>>>>>>>> below generates data from a Poisson distribution and has
>> >>>>>>>>>>>>
>> >>>>>>>>>>> 99% zero's
>> >>>>>>>>>>>
>> >>>>>>>>>>>> but no zero-inflation. The second example has only 1%
>> >>>>>>>>>>>>
>> >>>>>>>>>>> zero's but is
>> >>>>>>>>>>>
>> >>>>>>>>>>>> clearly zero-inflated.
>> >>>>>>>>>>>>
>> >>>>>>>>>>>> set.seed(1) n <- 1e8 sim <- rpois(n, lambda = 0.01) mean(sim
>> >>>>>>>>>>>> == 0) hist(sim)
>> >>>>>>>>>>>>
>> >>>>>>>>>>>> sim.infl <- rbinom(n, size = 1, prob = 0.99) * rpois(n,
>> >>>>>>>>>>>>
>> >>>>>>>>>>> lambda = 1000)
>> >>>>>>>>>>>
>> >>>>>>>>>>>> mean(sim.infl == 0) hist(sim.infl)
>> >>>>>>>>>>>>
>> >>>>>>>>>>>> So before looking for zero-inflated models, try to model
>> >>>>>>>>>>>>
>> >>>>>>>>>>> the zero's.
>> >>>>>>>>>>>
>> >>>>>>>>>>>> Best regards,
>> >>>>>>>>>>>>
>> >>>>>>>>>>>>
>> >>>>>>>>>>>> ir. Thierry Onkelinx Instituut voor natuur- en bosonderzoek /
>> >>>>>>>>>>>> Research Institute
>> >>>>>>>>>>>>
>> >>>>>>>>>>> for Nature
>> >>>>>>>>>>>
>> >>>>>>>>>>>> and Forest team Biometrie & Kwaliteitszorg / team Biometrics
>> >>>>>>>>>>>> & Quality
>> >>>>>>>>>>>>
>> >>>>>>>>>>> Assurance
>> >>>>>>>>>>>
>> >>>>>>>>>>>> Kliniekstraat 25 1070 Anderlecht Belgium
>> >>>>>>>>>>>>
>> >>>>>>>>>>>> To call in the statistician after the experiment is done
>> >>>>>>>>>>>>
>> >>>>>>>>>>> may be no
>> >>>>>>>>>>>
>> >>>>>>>>>>>> more than asking him to perform a post-mortem examination:
>> >>>>>>>>>>>>
>> >>>>>>>>>>> he may be
>> >>>>>>>>>>>
>> >>>>>>>>>>>> able to say what the experiment died of. ~ Sir Ronald
>> >>>>>>>>>>>>
>> >>>>>>>>>>> Aylmer Fisher
>> >>>>>>>>>>>
>> >>>>>>>>>>>> The plural of anecdote is not data. ~ Roger Brinner The
>> >>>>>>>>>>>> combination of some data and an aching desire for an
>> >>>>>>>>>>>>
>> >>>>>>>>>>> answer does
>> >>>>>>>>>>>
>> >>>>>>>>>>>> not ensure that a reasonable answer can be extracted from a
>> >>>>>>>>>>>>
>> >>>>>>>>>>> given body
>> >>>>>>>>>>>
>> >>>>>>>>>>>> of data. ~ John Tukey
>> >>>>>>>>>>>>
>> >>>>>>>>>>>> 2016-06-23 10:07 GMT+02:00 Philipp Singer
>> >>>>>>>>>>>>
>> >>>>>>>>>>> <killver at gmail.com <mailto:killver at gmail.com>
>> >>>>>>>>>>> <mailto:killver at gmail.com <mailto:killver at gmail.com>>
>> >>>>>>>>>>>
>> >>>>>>>>>>>> <mailto:killver at gmail.com <mailto:killver at gmail.com>
>> >>>>>>>>>>>> <mailto:killver at gmail.com <mailto:killver at gmail.com>>>>:
>> >>>>>>>>>>>>
>> >>>>>>>>>>>> Dear group - I am currently fitting a Poisson glmer
>> >>>>>>>>>>>>
>> >>>>>>>>>>> where I have
>> >>>>>>>>>>>
>> >>>>>>>>>>>> an excess of outcomes that are zero (>95%). I am now
>> >>>>>>>>>>>>
>> >>>>>>>>>>> debating on
>> >>>>>>>>>>>
>> >>>>>>>>>>>> how to proceed and came up with three options:
>> >>>>>>>>>>>>
>> >>>>>>>>>>>> 1.) Just fit a regular glmer to the complete data. I am
>> >>>>>>>>>>>>
>> >>>>>>>>>>> not fully
>> >>>>>>>>>>>
>> >>>>>>>>>>>> sure how interpret the coefficients then, are they more
>> >>>>>>>>>>>>
>> >>>>>>>>>>> optimizing
>> >>>>>>>>>>>
>> >>>>>>>>>>>> towards distinguishing zero and non-zero, or also
>> >>>>>>>>>>>>
>> >>>>>>>>>>> capturing the
>> >>>>>>>>>>>
>> >>>>>>>>>>>> differences in those outcomes that are non-zero?
>> >>>>>>>>>>>>
>> >>>>>>>>>>>> 2.) Leave all zeros out of the data and fit a glmer to
>> >>>>>>>>>>>>
>> >>>>>>>>>>> only those
>> >>>>>>>>>>>
>> >>>>>>>>>>>> outcomes that are non-zero. Then, I would only learn about
>> >>>>>>>>>>>> differences in the non-zero outcomes though.
>> >>>>>>>>>>>>
>> >>>>>>>>>>>> 3.) Use a zero-inflated Poisson model. My data is quite
>> >>>>>>>>>>>> large-scale, so I am currently playing around with the EM
>> >>>>>>>>>>>> implementation of Bolker et al. that alternates between
>> >>>>>>>>>>>>
>> >>>>>>>>>>> fitting a
>> >>>>>>>>>>>
>> >>>>>>>>>>>> glmer with data that are weighted according to their zero
>> >>>>>>>>>>>> probability, and fitting a logistic regression for the
>> >>>>>>>>>>>>
>> >>>>>>>>>>> probability
>> >>>>>>>>>>>
>> >>>>>>>>>>>> that a data point is zero. The method is elaborated for
>> >>>>>>>>>>>>
>> >>>>>>>>>>> the OWL
>> >>>>>>>>>>>
>> >>>>>>>>>>>> data in:
>> >>>>>>>>>>>>
>> >>>>>>>>>>>>
>> >>>>>>>>>>>
>> https://groups.nceas.ucsb.edu/non-linear-modeling/projects/owls/WRITEUP/owls.pdf
>> >>>>>>>>>>> <
>> >>>>>>>>>>>
>> https://groups.nceas.ucsb.edu/non-linear-modeling/projects/owls/WRITEUP/owls.pdf
>> >>>>>>>>>>> >
>> >>>>>>>>>>>
>> >>>>>>>>>> I am not fully sure how to interpret the results for the
>> >>>>>>>
>> >>>>>>>> zero-inflated version though. Would I need to interpret the
>> >>>>>>>>>>>> coefficients for the result of the glmer similar to as
>> >>>>>>>>>>>>
>> >>>>>>>>>>> I would do
>> >>>>>>>>>>>
>> >>>>>>>>>>>> for my idea of 2)? And then on top of that interpret the
>> >>>>>>>>>>>> coefficients for the logistic regression regarding whether
>> >>>>>>>>>>>> something is in the perfect or imperfect state? I am
>> >>>>>>>>>>>>
>> >>>>>>>>>>> also not
>> >>>>>>>>>>>
>> >>>>>>>>>>>> quite sure what the common approach for the zformula is
>> >>>>>>>>>>>>
>> >>>>>>>>>>> here. The
>> >>>>>>>>>>>
>> >>>>>>>>>>>> OWL elaborations only use zformula=z~1, so no random
>> >>>>>>>>>>>>
>> >>>>>>>>>>> effect; I
>> >>>>>>>>>>>
>> >>>>>>>>>>>> would use the same formula as for the glmer.
>> >>>>>>>>>>>>
>> >>>>>>>>>>>> I am appreciating some help and pointers.
>> >>>>>>>>>>>>
>> >>>>>>>>>>>> Thanks! Philipp
>> >>>>>>>>>>>>
>> >>>>>>>>>>>> _______________________________________________
>> >>>>>>>>>>>> R-sig-mixed-models at r-project.org
>> >>>>>>>>>>>> <mailto:R-sig-mixed-models at r-project.org>
>> >>>>>>>>>>>> <mailto:R-sig-mixed-models at r-project.org>
>> >>>>>>>>>>>>
>> >>>>>>>>>>> <mailto:R-sig-mixed-models at r-project.org
>> >>>>>>>>>>> <mailto:R-sig-mixed-models at r-project.org>>
>> >>>>>>>>>>>
>> >>>>>>>>>>>> <mailto:R-sig-mixed-models at r-project.org
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>> >>>>>>>>>>>>
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