[R-sig-ME] Dependency structure

[Poe, John]

Here's a link to my previous post on the topic of model specification and
endogeneity (correlation between X and the grouping structure). You
basically either do group mean centering or group varying coefficients.
However,  those aren't bullet proof depending on your data structure.

Also, i did a thread on twitter a while back that is related and links some
additional readings. I have a link to my advanced multilevel syllabus for
the icpsr program on the Twitter thead and it has a pretty decent reading
list on there.

https://stat.ethz.ch/pipermail/r-sig-mixed-models/2016q4/025150.html

https://twitter.com/DavidPoe223/status/1009485620337692674?s=09



On Thu, Oct 25, 2018, 8:05 PM Ben Bolker <bbolker using gmail.com> wrote:

>
>   Please keep r-sig-mixed-models in the Cc: .
>
>   I don't immediately see any way to allow a correlation between the
> intercept terms and the X-covariates, nor even why that would
> necessarily make sense.  I do recall that there's some stuff in the
> causal inference literature (of special interest to economists)
> surrounding this assumption, and how one can center covariates by group
> to address the issue, but I can't remember where it is/point you to it
> at the moment.  Perhaps someone else on the mailing list can help ...
>
>
>
> On 2018-10-25 12:04 p.m., Yashree Mehta wrote:
> > Hi Ben,
> >
> > Thanks for your response. For the second question in your reply to this
> > email, it is my mistake. I meant to incorporate correlation between the
> > random intercept and X-covariates, not their beta coefficients. Is there
> > a way to do that?
> >
> > Regards
> > Yashree-
> >
> > On Wed, Oct 17, 2018 at 2:37 AM Ben Bolker <bbolker using gmail.com
> > <mailto: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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