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

Thierry Onkelinx thierry.onkelinx at inbo.be
Thu Jun 23 11:04:45 CEST 2016

```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 op 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
>
> 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
>
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