[R-sig-ME] Dependency structure

Ben Bolker bbolker @ending from gm@il@com
Wed Oct 17 02:34:59 CEST 2018

> Hi,
> Is there literature on how to specify the dependency structure between the
> random intercept and the statistical noise error term in a random
> 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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