[R-sig-ME] Does the “non-independent" data structure defined in mixed models follow the “independency” defined by probability theory?

[Poe, John]

They are assumed to be independent across levels but you can deal with the
assumption by specifying the dependence as part of the model. You can add
in fixed effects or additional random effects for starters.

In practice having correlation across groups seems to distort the
distribution of the random effect causing some groups to be clustered. In
extreme cases the random effect can become multimodal. This doesn't seem to
matter much for linear models but it can badly damage generalized linear
models depending on how you approximate random effects.

On Sep 5, 2016 3:54 PM, <joaquin.aldabe at gmail.com> wrote:

> I have a related doubt. Do levels of a grouping variable have to be
> independent? Eg. Sites from where i take non independient samples?
> Thanks in advanced
> Joaquín
>
> Enviado desde mi iPad
>
> > El 5 set. 2016, a las 3:51 p.m., Ben Bolker <bbolker at gmail.com>
> escribió:
> >
> >> On Mon, Sep 5, 2016 at 4:08 AM, Chen, Chun <chun.chen at wur.nl> wrote:
> >> Dear all,
> >>
> >> I am bit puzzled by definition of the “nested data” or “non-independent
> data” structure in the mixed model.
> >>
> >>> From the statistical point of view, independency is defined as the
> probabilities of selecting two observations are not influencing each other.
> In this case, if I design an experiment where I on purposely select two
> observations from the same group (or strata), then later on we can say
> these two observations are dependent. However, if I am doing a sampling
> with replacement and by coincidence I selected one observations twice (e.g.
> throw a dice twice and by coincidence we get both a “6” each time). The
> probability of selecting these two observations are indeed not influencing
> each other and they are independent.
> >>
> >> My questions are:
> >>
> >> What’s the definition of the “non-independent data” that is often
> referred in mixed modeling? Is it the same concept as “independency”
> defined by probability theory, which is relevant by how the observations
> are selected, rather than how the observations look alike in the final
> sample
> >
> >   (You say "questions" here, but there really seems to be only one
> > question here.)
> >
> >  Yes, mixed modeling defines grouping variables based on
> > experimental/observational design.  That is, grouping variables are
> > identifiers that are believed *a priori* to be associated with
> > non-independence of observations with the same identifier values.
> >
> >  Ben Bolker
> >
> > _______________________________________________
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> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
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