[R-sig-ME] correlated samples
Highland Statistics Ltd
highstat at highstat.com
Wed Jul 13 10:14:37 CEST 2016
Joaquin,
I don;t know where you get the first Vi from. My final pdf shows an Y_i,
as you can see in the snapshot below.
However....downloading the pdf seems that the online version of the book
does have a V_i. I guess the editing company of Springer messed up the
text (or I didn't double check their corrections good enough).
Thierry is right in stating that the equations are for a linear mixed
effects model with a random intercept. If there are two random
intercepts then the equations change (See Chapter 20 in the same book).
I did look at similar expressions for the intraclass correlation for (1
way nested and 2-way nested) Poisson GLMM. They are given in our 2012
book. You can also find them in Nzoufras (2009). I tried to derive them
for ZIP models, but that was quite difficult. The following two papers
do simulation to calculate the intra-class correlation for Bernoulli GLMMs:
Goldstein H, Browne W, Rasbash J (2002) Partitioning Variation in
Multilevel Models.
Understanding Statistics 1: 223–231.
Browne WJ, Subramanian SV, Jones K (2005) Variance partitioning in
multilevel logistic models that
exhibit overdispersion. Journal Royal Statistical Society. Series A 168:
599–613.
I'm sure there will be some more recent material on intraclass
correlations for complicated GLMMs.
Alain
On 13/07/2016 17:50, Thierry Onkelinx wrote:
> Dear Joaquin,
>
> You can derive eqn. 5.13 from the assumptions in eqn. 5.8, which
> assumes that Yi follows a normal distribution.
>
> Note that the example is use in a chapter which introduces **linear**
> mixed models. Hence a normal distribution is assumed for the sake of
> simplicity.
>
> 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
>
> 2016-07-12 19:42 GMT+02:00 Joaquín Aldabe <joaquin.aldabe at gmail.com
> <mailto:joaquin.aldabe at gmail.com>>:
>
> By the way..I don´t see why it is relatively easy to show that Yi
> is normally distributed..(in fact, the Y variable is count so it
> should be poisson). This is in section 5.4 (p. 112) of Zuur et al
> (2009).
> Thanks,
> joaquín.
>
> 2016-07-12 10:52 GMT-03:00 Thierry Onkelinx
> <thierry.onkelinx at inbo.be <mailto:thierry.onkelinx at inbo.be>>:
>
> Dear Joaquin,
>
> Yes. I think you have found a typo. The prior to equation 5.13
> should read "It is relatively easy to show that $Y_i$ is
> normally distributed ..."
>
> 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
>
> 2016-07-11 21:36 GMT+02:00 Joaquín Aldabe
> <joaquin.aldabe at gmail.com <mailto:joaquin.aldabe at gmail.com>>:
>
> Sorrry, I hadn´t copied the whole group. Here it goes:
> Thanks Thierry, I´ve been there a couple of times.
> I´ll try again. I think there is a mistake in page 112
> when says: It is relatively easy to show that Vi is
> normally distributed with mean X i × β and variance V
> i in mathematical notation...
>
> It should say Yi instead of Vi, right?
>
> Cheers,
> Joaquín .
>
> 2016-07-08 9:02 GMT-03:00 Thierry Onkelinx
> <thierry.onkelinx at inbo.be
> <mailto:thierry.onkelinx at inbo.be>>:
>
> Dear Joaquin,
>
> I'd recommend Zuur et al 2009, section 5.4
>
> 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
>
> 2016-07-07 20:17 GMT+02:00 Joaquín Aldabe
> <joaquin.aldabe at gmail.com
> <mailto:joaquin.aldabe at gmail.com>>:
>
> Dear all, I´m a basic user of mixed models but
> there are things that I´ve
> found hard to understand. On of these is how
> the model solves the
> correlations among samples taken in the same
> site or levels of other kind
> of grouping variable.
>
> I´ve consulted Bolker (2015) in G. Fox et al
> Ed., Zuur et al 2009 and part
> of Pinheiro and Bates (2000). But still don´t
> understand the way that GLMM
> include the correlation effect in the
> predictions of the model.
>
> I really appreciate any comment and/or
> bibliographic reference that help me
> understand this.
>
> Thanks in advanced,
> Joaquín.
>
> --
> *Joaquín Aldabe*
>
> *Grupo Biodiversidad, Ambiente y Sociedad*
> Centro Universitario de la Región Este,
> Universidad de la República
> Ruta 15 (y Ruta 9), Km 28.500, Departamento de
> Rocha
>
> *Departamento de Conservación*
> Aves Uruguay
> BirdLife International
> Canelones 1164, Montevideo
>
> https://sites.google.com/site/joaquin.aldabe
> <https://sites.google.com/site/perfilprofesionaljoaquinaldabe>
>
> [[alternative HTML version deleted]]
>
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>
>
>
>
> --
> *Joaquín Aldabe*
>
> /Grupo Biodiversidad, Ambiente y Sociedad/
> Centro Universitario de la Región Este, Universidad de
> la República
> Ruta 15 (y Ruta 9), Km 28.500, Departamento de Rocha
> /Departamento de Conservación/
> Aves Uruguay
> BirdLife International
> Canelones 1164, Montevideo
>
> https://sites.google.com/site/joaquin.aldabe
> <https://sites.google.com/site/perfilprofesionaljoaquinaldabe>
>
>
>
>
> --
> *Joaquín Aldabe*
>
> /Grupo Biodiversidad, Ambiente y Sociedad/
> Centro Universitario de la Región Este, Universidad de la
> República
> Ruta 15 (y Ruta 9), Km 28.500, Departamento de Rocha
> /Departamento de Conservación/
> Aves Uruguay
> BirdLife International
> Canelones 1164, Montevideo
>
> https://sites.google.com/site/joaquin.aldabe
> <https://sites.google.com/site/perfilprofesionaljoaquinaldabe>
>
>
>
>
>
> --
> *Joaquín Aldabe*
>
> /Grupo Biodiversidad, Ambiente y Sociedad/
> Centro Universitario de la Región Este, Universidad de la República
> Ruta 15 (y Ruta 9), Km 28.500, Departamento de Rocha
> /Departamento de Conservación/
> Aves Uruguay
> BirdLife International
> Canelones 1164, Montevideo
>
> https://sites.google.com/site/joaquin.aldabe
> <https://sites.google.com/site/perfilprofesionaljoaquinaldabe>
>
>
--
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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