mixed zero-inflated Poisson regression model (Dieter Anseeuw)

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Today's Topics:

    1. mixed zero-inflated Poisson regression model (Dieter Anseeuw)
    2. Effect size for lmer and glmer (Hamada Elsayed Ali)

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Message: 1
Date: Wed, 8 Oct 2014 14:37:49 +0000
From: Dieter Anseeuw <dieter.anseeuw at inagro.be>
To: "r-sig-mixed-models at r-project.org"
	<r-sig-mixed-models at r-project.org>
Subject: [R-sig-ME] mixed zero-inflated Poisson regression model
Message-ID:
	<72E5B92E710560479A262E2C2C6443911F8FDEC5 at BEXCPS01.inagrp.local>
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Dear all,
I have only limited experience in processing count data and would like to improve my statistical skills by addressing to the r-sig-mixed mailing list to handle the challenge (to me it is) below.

We did an experiment in which we would like to look at the effect of six treatments (+ 1 control) on the presence of leaf miners in Hippocastanum tree leaves.  Unfortunately the data are unbalanced: for two treatments we looked at 10 trees; for the other 4 + the control we looked only at 5 trees. For each tree 100 leaves were collected for which the number of mines (created by the life miners) were counted. In total we had 47 trees, 100 leaves per tree, this brings up 4700 observations.

To analyse this dataset, I need to use a zero inflated Poisson regression model, but I also may need to include the factor 'tree' as a random effect.
Why do you think you need to do zero inflated models? So...just to make 
sure I understand it properly....you count the number of bugs on 100 
leaves (which is potentially  Poisson)...or are you counting how many 
leaves have bugs (this is potentially binomial).
According to what I found in the r-sig-mixed list for comparable problems, this is where I got with my current code:
(whereby tellingen=count observations on a leaf (4700 observations); boom=unique tree code (47 trees); behandeling=treatment (7 levels))
I would choose the random effect structure based on how/what/where you 
expect a dependency structure in your data. And refrain from testing 
whether you need the random effects. Start with the Poisson GLMM and see 
whether this model does the job. If it does, then you are finished.
Poisson Regression:
summary(mod1<-glm(tellingen~behandeling, family="poisson", data=finalcounts))

Zero Inflated Poisson Regression:
summary(admod1<-glmmadmb(tellingen~behandeling, data=finalcounts, family="poisson", zeroInflation=TRUE))

Zero Inflated Poisson Regression, with tree as random effect:
summary(admixmod1<-glmmadmb(tellingen~behandeling, data=finalcounts, family="poisson", zeroInflation=TRUE, random=~(1|boom)))
The latter takes quite some computational time.

Any comments on my approach that may improve my insight are warmly welcomed.
Questions:

1.       Which test should I use to compare these three models (to decide whether or not I should use the simple or a more complex model)
See above. Start with a Poisson GLMM...check for 
overdispersion...patterns in residuals...etc.
2.       So far, I did not specifically take into account the difference in observed trees per treatment (10 versus 5 trees). Problematic? How can I address this?

3.       How should I perform pairwise comparisons among treatments?
Same way as in linear regression.

Alain
Dr. Alain F. Zuur

First author of:
1. Beginner's Guide to GAMM with R (2014).
2. Beginner's Guide to GLM and GLMM with R (2013).
3. Beginner's Guide to GAM with R (2012).
4. Zero Inflated Models and GLMM with R (2012).
5. A Beginner's Guide to R (2009).
6. Mixed effects models and extensions in ecology with R (2009).
7. Analysing Ecological Data (2007).

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