[R-sig-ME] Dependency structure

[Malcolm Fairbrother]

Hi,

John Poe’s response to this just now is very helpful.

Yashree, you may find it helpful to look at some code I wrote to run simulations effectively implementing what John suggests (distinguishing between from within effects). A paper presenting the simulations is here <https://doi.org/10.1017/psrm.2013.24>, and the R code is in the supplementary material linked from that website. I used the “rmsn” function to generate random intercepts that are correlated with a group-level covariate—which I take it is the issue you want to deal with.

Other than using a “REWB” specification (see also https://doi.org/10.1007/s11135-018-0802-x), I’m not sure there’s much you can do.

Hope that helps,
Malcolm


Malcolm Fairbrother

Professor of Sociology, Umeå University<http://www.soc.umu.se/english/>
Researcher, Institute for Futures Studies<https://www.iffs.se/en/>
Sweden



Date: Thu, 25 Oct 2018 19:45:45 -0400
From: Ben Bolker <bbolker using gmail.com<mailto:bbolker using gmail.com>>
To: Yashree Mehta <yashree19 using gmail.com<mailto:yashree19 using gmail.com>>
Cc: "r-sig-mixed-models using r-project.org<mailto:r-sig-mixed-models using r-project.org>"
<r-sig-mixed-models using r-project.org<mailto:r-sig-mixed-models using r-project.org>>
Subject: Re: [R-sig-ME] Dependency structure
Message-ID: <a1cab4e4-514a-e18e-4e86-e52bc60afd1a using gmail.com<mailto:a1cab4e4-514a-e18e-4e86-e52bc60afd1a using gmail.com>>
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 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>
<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

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