# [R-sig-ME] Question on random effect

Anthony R. Ives arives at wisc.edu
Wed Jul 12 13:07:26 CEST 2017

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*
>> >
>> > 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
>> >