[R-sig-ME] Dependency structure

[Yashree Mehta]

Hi,

Regarding the question on dependency structure, is there a way to allow for
the possibility of the error term and random intercept being correlated? I
need to define the covariance matrix between these two terms and estimate
the values which should go into this matrix.

Thank you

Regards,
Yashree

On Wed, Oct 17, 2018 at 2:37 AM Ben Bolker <bbolker using gmail.com> wrote:

>
> > Hi,
> >
> > Is there literature on how to specify the dependency structure between
> the
> > random intercept and the statistical noise error term in a random
> intercept
> > model?
> > It would be useful to also know how to implement using R...
>
>
>   Can you be more specific about what you want?  Suppose you have
> observations j within groups i, and you have an epsilon_{0,ij} for each
> observation (error term) and an epsilon_"1,i} for each group (random
> intercept).  Typically the epsilon_{0,ij} values are iid with
> homogeneous variance sigma_0^2, and epsilon_{1,i} are iid with variance
> sigma_1^2.  What kind of correlation structure are you looking for?
>
> While we're at it, you previously asked:
>
> ===
> I am working with a random intercept model. I have the usual "X" vector
> of covariates and one id variable which will make up the random
> intercept. For example,
>
> Response variable: Production of maize
> Covariate: Size of plot
> ID variable: Household_ID
>
> I need to acknowledge that there is correlation between the FIXED EFFECT
> coefficient of plot size and the estimated random intercept. It is my
> model assumption.
>
> Does lme4 assume this correlation or do I have to make changes in the
> formula so that it gets considered?
> ===
>
>   The short answer to this one is "no", I think -- I don't know that
> there's a way to allow for correlation between fixed effect coefficients
> and random intercepts. (This actually seems like a weird question to me;
> in the frequentist world, as far as I know, you can only specify
> correlation models for *random variables* within the model.  In the
> context of LMM fitting, I don't think parameters are random effects in
> this sense.
>
> On 2018-10-16 01:03 PM, Yashree Mehta wrote:
>
> >
> > Thank you
> >
> > Yashree
> >
> >       [[alternative HTML version deleted]]
> >
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> >
>
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