[R-sig-ME] Dependency structure

[Ben Bolker]

  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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