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

Philipp Singer killver at gmail.com
Mon Jun 27 16:17:47 CEST 2016 

Here is the fitted vs. residual plot for the observation-level poisson
model where the observation level has been removed as taken from:
https://stat.ethz.ch/pipermail/r-sig-mixed-models/2013q3/020817.html

So basically the prediction is always close to zero.

Note that this is just on a very small sample (1000 data points).

If I fit a nbinom2 to this smalle sample, I get predictions that are always
around ~20 (but never zero). Both plots are attached.

What I am wondering is whether I can do inference on a fixed parameter in
my model which is my main task of this study. The effect is similar in the
different models and in general I am only itnerested in whether it is
positive/negative and "significant" which it is. However, as can be seen,
the prediction looks not too good here.




2016-06-27 15:18 GMT+02:00 Philipp Singer <killver at gmail.com>:

> 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
>>> >>>>>>>>>>>> <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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