[R-sig-ME] Dependency structure

[Yashree Mehta]

thanks for your reply. I read about prediction theory that in the
application of BLUP, one can try to reparameterize a model with non-zero
variance-covariance matrix between the error term and the random intercept
into an equivalent model containing the random intercept and error term as
uncorrelated. Is this possible?



On Tue, Nov 6, 2018 at 7:25 PM Poe, John <jdpo223 using g.uky.edu> wrote:

> Just to clarify, you mean that you want to specify a correlation structure
> between the individual level error term in the model (also called the
> residuals) and the random intercept or group-level error.
>
> This doesn't make a lot of sense to me because the random intercept is
> literally the product of a decomposition of the general model's error
> structure into the within group (R matrix) and between group (G matrix)
> components of the error. They are uncorrelated by construction. The only
> way that they could possibly be correlated would be if you had an
> exchangability problem in the random effects structure. You could have a
> fuzzy boundaries issue like US counties are correlated by space. But you
> wouldn't solve that by correlating the lower level error term with the
> random intercept. You'd build a group boundary spatial weights matrix and
> include it in the model.
>
> I must be missing something in the translation.
>
> On Tue, Nov 6, 2018 at 1:11 PM Yashree Mehta <yashree19 using gmail.com> wrote:
>
>> 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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>>
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>
>
> --
>
>
>
>
> Thanks,
> John
>
>
> John Poe, Ph.D.
> Postdoctoral Scholar / Research Methodologist
> Center for Public Health Services & Systems Research
> University of Kentucky
> www.johndavidpoe.com
>

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