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
>in
>nlme and lme4 directly use the i.i.d. term: x_i ~ N(0, \sigma), hence
>random effect itself is i.i.d. INLA has some other constructs
>e.g. a first order random walk where x_i - x_{i-1} ~ N(0, \sigma).
>the
>difference between to consecutive random effects is i.i.d. but the
>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
>than asking him to perform a post-mortem examination: he may be able
>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
>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
>> [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
>> 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, Joaqu?n Aldabe
>> <joaquin.aldabe at gmail.com> wrote:
>> > Hi all, when working with mixed models, do the levels of the
>> > have to be independent? For example, if my random effect is the
>> > 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
>> >
>> > --
>> > *Joaqu?n Aldabe*
>> >
>> > *Grupo Biodiversidad, Ambiente y Sociedad*
>> > Centro Universitario de la Regi?n Este, Universidad de la