[R-sig-ME] Question on random effect

[Anthony R. Ives]

I find that the easiest way to think about this is in terms of the covariance matrix of the residuals. For LMMs, the random effects (which themselves are independent) produce block-diagonal covariance matrices, with positive covariances among residuals within the same level of a random effect. Phylogenetic relationships will also produce positive off-diagonal elements in the covariance matrix. Focusing on the structure of the covariance matrix of residuals often gives the clearest picture of the overall assumptions of a model.

Cheers, Tony

On 7/12/17, 3:43 AM, "R-sig-mixed-models on behalf of Viechtbauer Wolfgang (SP)" <r-sig-mixed-models-bounces at r-project.org on behalf of wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:

    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    
    Maastricht, The Netherlands | +31 (43) 388-4170 | http://www.wvbauer.com    
    
    >-----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
    >
    >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
    >
    >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>
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