Discussion:
[R-sig-ME] zero-inflated-count-data?
C. AMAL D. GLELE
2018-02-25 12:08:15 UTC
Permalink
Hi, dear all.
From which proportion of zero a count should be considered as zero-inflated
(in order to use a zero-inflated model for it's modelling)?
In advance, thanks for your replies.
Best,

<https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail>
Garanti
sans virus. www.avast.com
<https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail>
<#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>

[[alternative HTML version deleted]]
Ben Bolker
2018-02-25 18:05:35 UTC
Permalink
There is no set proportion. (For example, a Poisson distribution with
a mean of 0.01 is expected to be about 99% zeros, even without
zero-inflation.) There's a little bit of (bare-bones) discussion of
how to test for zero-inflation here:
https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#zero-inflation

On Sun, Feb 25, 2018 at 7:08 AM, C. AMAL D. GLELE <***@gmail.com> wrote:
> Hi, dear all.
> From which proportion of zero a count should be considered as zero-inflated
> (in order to use a zero-inflated model for it's modelling)?
> In advance, thanks for your replies.
> Best,
>
> <https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail>
> Garanti
> sans virus. www.avast.com
> <https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail>
> <#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-mixed-***@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
C. AMAL D. GLELE
2018-02-25 21:45:40 UTC
Permalink
Hi, Ben
Many thanks to you for your very helpful reply.
Best and regards,

2018-02-25 19:05 GMT+01:00 Ben Bolker <***@gmail.com>:

> There is no set proportion. (For example, a Poisson distribution with
> a mean of 0.01 is expected to be about 99% zeros, even without
> zero-inflation.) There's a little bit of (bare-bones) discussion of
> how to test for zero-inflation here:
> https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#zero-inflation
>
> On Sun, Feb 25, 2018 at 7:08 AM, C. AMAL D. GLELE <***@gmail.com>
> wrote:
> > Hi, dear all.
> > From which proportion of zero a count should be considered as
> zero-inflated
> > (in order to use a zero-inflated model for it's modelling)?
> > In advance, thanks for your replies.
> > Best,
> >
> > <https://www.avast.com/sig-email?utm_medium=email&utm_
> source=link&utm_campaign=sig-email&utm_content=webmail>
> > Garanti
> > sans virus. www.avast.com
> > <https://www.avast.com/sig-email?utm_medium=email&utm_
> source=link&utm_campaign=sig-email&utm_content=webmail>
> > <#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>
> >
> > [[alternative HTML version deleted]]
> >
> > _______________________________________________
> > R-sig-mixed-***@r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>

[[alternative HTML version deleted]]
Jonathan Judge
2018-02-25 22:55:51 UTC
Permalink
The pscl package offers the (somewhat controversial) Vuong test for this purpose and is a good ZI/hurdle resource in general.

Jonathan

> On Feb 25, 2018, at 3:45 PM, C. AMAL D. GLELE <***@gmail.com> wrote:
>
> Hi, Ben
> Many thanks to you for your very helpful reply.
> Best and regards,
>
> 2018-02-25 19:05 GMT+01:00 Ben Bolker <***@gmail.com>:
>
>> There is no set proportion. (For example, a Poisson distribution with
>> a mean of 0.01 is expected to be about 99% zeros, even without
>> zero-inflation.) There's a little bit of (bare-bones) discussion of
>> how to test for zero-inflation here:
>> https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#zero-inflation
>>
>> On Sun, Feb 25, 2018 at 7:08 AM, C. AMAL D. GLELE <***@gmail.com>
>> wrote:
>>> Hi, dear all.
>>> From which proportion of zero a count should be considered as
>> zero-inflated
>>> (in order to use a zero-inflated model for it's modelling)?
>>> In advance, thanks for your replies.
>>> Best,
>>>
>>> <https://www.avast.com/sig-email?utm_medium=email&utm_
>> source=link&utm_campaign=sig-email&utm_content=webmail>
>>> Garanti
>>> sans virus. www.avast.com
>>> <https://www.avast.com/sig-email?utm_medium=email&utm_
>> source=link&utm_campaign=sig-email&utm_content=webmail>
>>> <#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>
>>>
>>> [[alternative HTML version deleted]]
>>>
>>> _______________________________________________
>>> R-sig-mixed-***@r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-mixed-***@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
Thierry Onkelinx
2018-02-26 08:16:55 UTC
Permalink
Another option is the fit the model using a distribution without
zero-inflation. Then simulate data from that model and count the number of
zero's. Repeat this several times so that you get a distribution of the
number of zero's. In case of zero-inflation the number of zero's in the
data is much higher that those from the simulated data.

Best regards,


ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
***@inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be

///////////////////////////////////////////////////////////////////////////////////////////
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
///////////////////////////////////////////////////////////////////////////////////////////

<https://www.inbo.be>

2018-02-25 23:55 GMT+01:00 Jonathan Judge <***@outlook.com>:

> The pscl package offers the (somewhat controversial) Vuong test for this
> purpose and is a good ZI/hurdle resource in general.
>
> Jonathan
>
> > On Feb 25, 2018, at 3:45 PM, C. AMAL D. GLELE <***@gmail.com>
> wrote:
> >
> > Hi, Ben
> > Many thanks to you for your very helpful reply.
> > Best and regards,
> >
> > 2018-02-25 19:05 GMT+01:00 Ben Bolker <***@gmail.com>:
> >
> >> There is no set proportion. (For example, a Poisson distribution with
> >> a mean of 0.01 is expected to be about 99% zeros, even without
> >> zero-inflation.) There's a little bit of (bare-bones) discussion of
> >> how to test for zero-inflation here:
> >> https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#zero-inflation
> >>
> >> On Sun, Feb 25, 2018 at 7:08 AM, C. AMAL D. GLELE <
> ***@gmail.com>
> >> wrote:
> >>> Hi, dear all.
> >>> From which proportion of zero a count should be considered as
> >> zero-inflated
> >>> (in order to use a zero-inflated model for it's modelling)?
> >>> In advance, thanks for your replies.
> >>> Best,
> >>>
> >>> <https://www.avast.com/sig-email?utm_medium=email&utm_
> >> source=link&utm_campaign=sig-email&utm_content=webmail>
> >>> Garanti
> >>> sans virus. www.avast.com
> >>> <https://www.avast.com/sig-email?utm_medium=email&utm_
> >> source=link&utm_campaign=sig-email&utm_content=webmail>
> >>> <#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>
> >>>
> >>> [[alternative HTML version deleted]]
> >>>
> >>> _______________________________________________
> >>> R-sig-mixed-***@r-project.org mailing list
> >>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >
> > [[alternative HTML version deleted]]
> >
> > _______________________________________________
> > R-sig-mixed-***@r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
> _______________________________________________
> R-sig-mixed-***@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>

[[alternative HTML version deleted]]
C. AMAL D. GLELE
2018-02-26 13:57:00 UTC
Permalink
Hi, dear all.
Many thanks to you all for your very helpful answers.
Jonathan,
I've started fitting a model using zeroinfl function from pscl package, but
I'm having the following

difficulty according to one of my regressors, let be H_var (categorical
with 8 levels):
as regressors, I have 7 categorical variables (with a total of 26 levels)
and two numerical

variables;
1) when I fit the model like follows,
model1<-zeroinfl(countdata~var1+H_var+var3+var4+var5+var6+var7+var8num

+var9num,dist="negbin",data=mydata)
, I receive the error message below:
"Error in solve.default(as.matrix(fit$hessian)) :
system is computationally singular: reciprocal condition number =
7.05621e-21
In addition: Warning message:
glm.fit: fitted probabilities numerically 0 or 1 occurred
"
2)
but, if I remove H_var from the count component and fits model2 loke
follows,
model2<-zeroinfl(countdata~var1+var3+var4+var5+var6+var7+var8num+
var9num|H_var,dist="negbin",data=mydata)
the model fits well and I do not receive error message anymore.
3)
If use H_var in both component of the model, like follows,
model3<-zeroinfl(countdata~var1+var3+var4+var5+var6+var7+var8num+
var9num+H_var|H_var,dist="negbin",data=mydata)
I receive the following error message:
"Error in solve.default(as.matrix(fit$hessian)) :
system is computationally singular: reciprocal condition number =
4.2618e-20
"
Question:
Does someone have any idea about probables causes of the problems posed
at points 1) and 3) ?
Thierry,
can you, please, provide me details (some ways to do it) and/or lead about
simulating data from a fitted model?

In advance, thanks for your answers.
Best,

2018-02-25 23:55 GMT+01:00 Jonathan Judge <***@outlook.com>:

> The pscl package offers the (somewhat controversial) Vuong test for this
> purpose and is a good ZI/hurdle resource in general.
>
> Jonathan
>
> > On Feb 25, 2018, at 3:45 PM, C. AMAL D. GLELE <***@gmail.com>
> wrote:
> >
> > Hi, Ben
> > Many thanks to you for your very helpful reply.
> > Best and regards,
> >
> > 2018-02-25 19:05 GMT+01:00 Ben Bolker <***@gmail.com>:
> >
> >> There is no set proportion. (For example, a Poisson distribution with
> >> a mean of 0.01 is expected to be about 99% zeros, even without
> >> zero-inflation.) There's a little bit of (bare-bones) discussion of
> >> how to test for zero-inflation here:
> >> https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#zero-inflation
> >>
> >> On Sun, Feb 25, 2018 at 7:08 AM, C. AMAL D. GLELE <
> ***@gmail.com>
> >> wrote:
> >>> Hi, dear all.
> >>> From which proportion of zero a count should be considered as
> >> zero-inflated
> >>> (in order to use a zero-inflated model for it's modelling)?
> >>> In advance, thanks for your replies.
> >>> Best,
> >>>
> >>> <https://www.avast.com/sig-email?utm_medium=email&utm_
> >> source=link&utm_campaign=sig-email&utm_content=webmail>
> >>> Garanti
> >>> sans virus. www.avast.com
> >>> <https://www.avast.com/sig-email?utm_medium=email&utm_
> >> source=link&utm_campaign=sig-email&utm_content=webmail>
> >>> <#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>
> >>>
> >>> [[alternative HTML version deleted]]
> >>>
> >>> _______________________________________________
> >>> R-sig-mixed-***@r-project.org mailing list
> >>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >
> > [[alternative HTML version deleted]]
> >
> > _______________________________________________
> > R-sig-mixed-***@r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>

[[alternative HTML version deleted]]
Highland Statistics Ltd
2018-02-26 10:25:50 UTC
Permalink
------------------------------

Message: 5
Date: Mon, 26 Feb 2018 09:16:55 +0100
From: Thierry Onkelinx <***@inbo.be>
To: Jonathan Judge <***@outlook.com>
Cc: "C. AMAL D. GLELE" <***@gmail.com>, R SIG Mixed Models
<r-sig-mixed-***@r-project.org>
Subject: Re: [R-sig-ME] zero-inflated-count-data?
Message-ID:
<CAJuCY5yAvWYG2YA8FgVV1urK7Q8E55eNuR=***@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"

Another option is the fit the model using a distribution without
zero-inflation. Then simulate data from that model and count the number of
zero's. Repeat this several times so that you get a distribution of the
number of zero's. In case of zero-inflation the number of zero's in the
data is much higher that those from the simulated data.





I think that Thierry's suggestion is indeed the best option. It not only allows you to check whether
the model can cope with the observed number of zeros, but it also shows you to check whether the model can cope with other
aspects of the observed data. For example, you can calculate the frequency table for each of the 1000 simulated data sets,
and calculate somehow and average frequency table. And the compare this with the frequency table of the observed data.

Kind regards,
Alain










Best regards,


ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
***@inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be

///////////////////////////////////////////////////////////////////////////////////////////
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
///////////////////////////////////////////////////////////////////////////////////////////

<https://www.inbo.be>


------------------------------

End of R-sig-mixed-models Digest, Vol 134, Issue 36
***************************************************

--

Dr. Alain F. Zuur
Highland Statistics Ltd.
9 St Clair Wynd
AB41 6DZ Newburgh, UK
Email: ***@highstat.com
URL: www.highstat.com

And:
NIOZ Royal Netherlands Institute for Sea Research,
Department of Coastal Systems, and Utrecht University,
P.O. Box 59, 1790 AB Den Burg,
Texel, The Netherlands



Author of:
1. Beginner's Guide to Spatial, Temporal and Spatial-Temporal Ecological Data Analysis with R-INLA. (2017).
2. Beginner's Guide to Zero-Inflated Models with R (2016).
3. Beginner's Guide to Data Exploration and Visualisation with R (2015).
4. Beginner's Guide to GAMM with R (2014).
5. Beginner's Guide to GLM and GLMM with R (2013).
6. Beginner's Guide to GAM with R (2012).
7. Zero Inflated Models and GLMM with R (2012).
8. A Beginner's Guide to R (2009).
9. Mixed effects models and extensions in ecology with R (2009).
10. Analysing Ecological Data (2007).
Chris Stride
2018-06-16 11:01:49 UTC
Permalink
Hi

I'm trying to fit a mixed effects exponential decay model, in which I
have random effects for the initial value (init), the asymptote (asymp),
and the rate (rate).

The catch is that I'd also like to estimate the correlation between init
and asymp, but not between init and rate, or asymp and rate.

Now using  random = pdDiag(init + asymp + rate ~ 1) has none of the
random effects correlated

And using  random = pdSymm(init + asymp + rate ~ 1) has all three of the
random effects correlated

How do I specify just the correlation I want?

cheers

Chris
Highland Statistics Ltd
2018-02-26 17:26:02 UTC
Permalink
----------------------------------------------------------------------

Message: 1
Date: Mon, 26 Feb 2018 14:57:00 +0100
From: "C. AMAL D. GLELE" <***@gmail.com>
To: Jonathan Judge <***@outlook.com>
Cc: Ben Bolker <***@gmail.com>, R SIG Mixed Models
<r-sig-mixed-***@r-project.org>
Subject: Re: [R-sig-ME] zero-inflated-count-data?
Message-ID:
<CANrzCv0SZxAXjoftdkN7v5M4g6wrd3GM7qx23dFB=***@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"

Hi, dear all.
Many thanks to you all for your very helpful answers.
Jonathan,
I've started fitting a model using zeroinfl function from pscl package, but
I'm having the following

difficulty according to one of my regressors, let be H_var (categorical
with 8 levels):
as regressors, I have 7 categorical variables (with a total of 26 levels)
and two numerical

variables;
1) when I fit the model like follows,
model1<-zeroinfl(countdata~var1+H_var+var3+var4+var5+var6+var7+var8num

+var9num,dist="negbin",data=mydata)
, I receive the error message below:
"Error in solve.default(as.matrix(fit$hessian)) :
system is computationally singular: reciprocal condition number =
7.05621e-21
In addition: Warning message:
glm.fit: fitted probabilities numerically 0 or 1 occurred
"
2)
but, if I remove H_var from the count component and fits model2 loke
follows,
model2<-zeroinfl(countdata~var1+var3+var4+var5+var6+var7+var8num+
var9num|H_var,dist="negbin",data=mydata)
the model fits well and I do not receive error message anymore.
3)
If use H_var in both component of the model, like follows,
model3<-zeroinfl(countdata~var1+var3+var4+var5+var6+var7+var8num+
var9num+H_var|H_var,dist="negbin",data=mydata)
I receive the following error message:
"Error in solve.default(as.matrix(fit$hessian)) :
system is computationally singular: reciprocal condition number =
4.2618e-20
"
Question:
Does someone have any idea about probables causes of the problems posed
at points 1) and 3) ?






Without seeing the data......simplify your model? Collinearity? Start simple and build up the complexity of the model.
Maybe start with a Poisson GLM and figure out whether you really need a ZIP/ZINB? Why are you actually do a ZINB?






can you, please, provide me details (some ways to do it) and/or lead about
simulating data from a fitted model?





See step 10 in:

A protocol for conducting and presenting results of regression-type analyses (2016).
Zuur & Ieno.

http://onlinelibrary.wiley.com/doi/10.1111/2041-210X.12577/abstract

and see Figure 8 from that paper for an example. R code is somewhere online as well.


Alain







 In advance, thanks for your answers.
Best,

2018-02-25 23:55 GMT+01:00 Jonathan Judge <***@outlook.com>:
--

Dr. Alain F. Zuur
Highland Statistics Ltd.
9 St Clair Wynd
AB41 6DZ Newburgh, UK
Email: ***@highstat.com
URL: www.highstat.com

And:
NIOZ Royal Netherlands Institute for Sea Research,
Department of Coastal Systems, and Utrecht University,
P.O. Box 59, 1790 AB Den Burg,
Texel, The Netherlands



Author of:
1. Beginner's Guide to Spatial, Temporal and Spatial-Temporal Ecological Data Analysis with R-INLA. (2017).
2. Beginner's Guide to Zero-Inflated Models with R (2016).
3. Beginner's Guide to Data Exploration and Visualisation with R (2015).
4. Beginner's Guide to GAMM with R (2014).
5. Beginner's Guide to GLM and GLMM with R (2013).
6. Beginner's Guide to GAM with R (2012).
7. Zero Inflated Models and GLMM with R (2012).
8. A Beginner's Guide to R (2009).
9. Mixed effects models and extensions in ecology with R (2009).
10. Analysing Ecological Data (2007).
Ben Bolker
2018-02-27 01:17:14 UTC
Permalink
For some model types (unfortunately not pscl::zeroinlf(), it looks
like) you can just
use the simulate() method ...

By the way, Amal (hope that's a reasonable way to address you) - folks
are really helpful here (as
you will have noticed), but the list is primarily for questions about
*mixed* (hierarchical/multilevel/whatever) models.
At present your questions are more generic questions about
zero-inflation and generalized linear modeling.
I do recommend the books by Alain and his co-authors as a good way to
get started on the fairly
complex stuff you're attempting here.

On Mon, Feb 26, 2018 at 12:26 PM, Highland Statistics Ltd
<***@highstat.com> wrote:
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Mon, 26 Feb 2018 14:57:00 +0100
> From: "C. AMAL D. GLELE" <***@gmail.com>
> To: Jonathan Judge <***@outlook.com>
> Cc: Ben Bolker <***@gmail.com>, R SIG Mixed Models
> <r-sig-mixed-***@r-project.org>
> Subject: Re: [R-sig-ME] zero-inflated-count-data?
> Message-ID:
> <CANrzCv0SZxAXjoftdkN7v5M4g6wrd3GM7qx23dFB=***@mail.gmail.com>
> Content-Type: text/plain; charset="utf-8"
>
>
> Hi, dear all.
> Many thanks to you all for your very helpful answers.
> Jonathan,
> I've started fitting a model using zeroinfl function from pscl package, but
> I'm having the following
>
> difficulty according to one of my regressors, let be H_var (categorical
> with 8 levels):
> as regressors, I have 7 categorical variables (with a total of 26 levels)
> and two numerical
>
> variables;
> 1) when I fit the model like follows,
> model1<-zeroinfl(countdata~var1+H_var+var3+var4+var5+var6+var7+var8num
>
> +var9num,dist="negbin",data=mydata)
> , I receive the error message below:
> "Error in solve.default(as.matrix(fit$hessian)) :
> system is computationally singular: reciprocal condition number =
> 7.05621e-21
> In addition: Warning message:
> glm.fit: fitted probabilities numerically 0 or 1 occurred
> "
> 2)
> but, if I remove H_var from the count component and fits model2 loke
> follows,
> model2<-zeroinfl(countdata~var1+var3+var4+var5+var6+var7+var8num+
> var9num|H_var,dist="negbin",data=mydata)
> the model fits well and I do not receive error message anymore.
> 3)
> If use H_var in both component of the model, like follows,
> model3<-zeroinfl(countdata~var1+var3+var4+var5+var6+var7+var8num+
> var9num+H_var|H_var,dist="negbin",data=mydata)
> I receive the following error message:
> "Error in solve.default(as.matrix(fit$hessian)) :
> system is computationally singular: reciprocal condition number =
> 4.2618e-20
> "
> Question:
> Does someone have any idea about probables causes of the problems posed
> at points 1) and 3) ?
>
>
>
>
>
>
> Without seeing the data......simplify your model? Collinearity? Start simple
> and build up the complexity of the model.
> Maybe start with a Poisson GLM and figure out whether you really need a
> ZIP/ZINB? Why are you actually do a ZINB?
>
>
>
>
>
>
> can you, please, provide me details (some ways to do it) and/or lead about
> simulating data from a fitted model?
>
>
>
>
>
> See step 10 in:
>
> A protocol for conducting and presenting results of regression-type analyses
> (2016).
> Zuur & Ieno.
>
> http://onlinelibrary.wiley.com/doi/10.1111/2041-210X.12577/abstract
>
> and see Figure 8 from that paper for an example. R code is somewhere online
> as well.
>
>
> Alain
>
>
>
>
>
>
>
> In advance, thanks for your answers.
> Best,
>
> 2018-02-25 23:55 GMT+01:00 Jonathan Judge <***@outlook.com>:
> --
>
> Dr. Alain F. Zuur
> Highland Statistics Ltd.
> 9 St Clair Wynd
> AB41 6DZ Newburgh, UK
> Email: ***@highstat.com
> URL: www.highstat.com
>
> And:
> NIOZ Royal Netherlands Institute for Sea Research,
> Department of Coastal Systems, and Utrecht University,
> P.O. Box 59, 1790 AB Den Burg,
> Texel, The Netherlands
>
>
>
> Author of:
> 1. Beginner's Guide to Spatial, Temporal and Spatial-Temporal Ecological
> Data Analysis with R-INLA. (2017).
> 2. Beginner's Guide to Zero-Inflated Models with R (2016).
> 3. Beginner's Guide to Data Exploration and Visualisation with R (2015).
> 4. Beginner's Guide to GAMM with R (2014).
> 5. Beginner's Guide to GLM and GLMM with R (2013).
> 6. Beginner's Guide to GAM with R (2012).
> 7. Zero Inflated Models and GLMM with R (2012).
> 8. A Beginner's Guide to R (2009).
> 9. Mixed effects models and extensions in ecology with R (2009).
> 10. Analysing Ecological Data (2007).
>
> _______________________________________________
> R-sig-mixed-***@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
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