[R-sig-ME] Question on random effect

[Viechtbauer Wolfgang (SP)]

Another example where random effects are not assumed to be independent is phylogenetic models. Based on a phylogeny, we can construct a correlation matrix that indicates the phylogenetic relatedness of the species. Random effects for species are then assumed to be correlated accordingly.

Best,
Wolfgang

-- 
Wolfgang Viechtbauer, Ph.D., Statistician | Department of Psychiatry and    
Neuropsychology | Maastricht University | P.O. Box 616 (VIJV1) | 6200 MD    
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>-----Original Message-----
>From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces at r-project.org]
>On Behalf Of Thierry Onkelinx
>Sent: Wednesday, July 12, 2017 10:03
>To: Ben Bolker
>Cc: r-sig-mixed-models
>Subject: Re: [R-sig-ME] Question on random effect
>
>Dear Joaquin and Ben,
>
>AFAIK have most random effects a term which is i.i.d. The random effects
>in
>nlme and lme4 directly use the i.i.d. term: x_i ~ N(0, \sigma), hence the
>random effect itself is i.i.d. INLA has some other constructs available.
>e.g. a first order random walk where x_i - x_{i-1} ~ N(0, \sigma). Here
>the
>difference between to consecutive random effects is i.i.d. but the random
>effect itself isn't. The available options are listed at
>http://www.r-inla.org/models/latent-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
>
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>say
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>~ John Tukey
>
>2017-07-11 13:22 GMT+02:00 Ben Bolker <bbolker at gmail.com>:
>
>> Yes, the assumption is that the random effects are (conditionally)
>> independent.  It can help to specify covariates  (such as
>> latitude/longitude or eastings/northings, or environmental conditions
>> [temperature, elevation, etc.]) for sites to mop up some of the
>> independence. It is theoretically possible, although I don't know of
>> an easy off-the-shelf way to do it, to impose (e.g.) spatial
>> correlation structures at the level of the random effects ...  or you
>> could examine the spatial dependence of the conditional modes/random
>> effects and try to convince yourself it was weak ...
>>
>> On Tue, Jul 11, 2017 at 7:14 AM, Joaquín Aldabe
>> <joaquin.aldabe at gmail.com> wrote:
>> > Hi all, when working with mixed models, do the levels of the random
>> effect
>> > have to be independent? For example, if my random effect is the
>identity
>> of
>> > sites and it is associated to the intercept, do sites have to be
>> > independent?
>> >
>> > I appreciate comments and bibliographic references.
>> >
>> > Thank you very much in advanced,
>> >
>> > Joaquin
>> >
>> > --
>> > *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>