[R-sig-ME] Compound Symmetry Covariance structure

[Ben Bolker]

  I don't think a compound-symmetric specification would do anything in
this case (i.e. when only the intercept varies among groups), because
there are no explicit correlation parameters to model. Does the model
actually change (e.g. are the log-likelihoods of the original and the
compound-symmetrized models the same)?

On 2018-12-09 3:37 p.m., Yashree Mehta wrote:
> Hi Ben, Joaquin and John,
> 
> First of all, thank you very much for your responses. They are all very
> helpful.
> 
> Yes, I understand now that there is an induced compound -symmetry
> covariance structure in random effects model in nlme as default. I was
> wondering if now, if I explicitly initialize the correlation and impose
> compound symmetry in the model code (learnt from the example in Pinheiro
> and Bates):
> 
> First, I estimate the intra-class correlation coefficient and the value
> is 0.908. Then, I estimate the standard LME model,
> 
> model <- maize ~ "covariates" + random = ~ 1|HOUSEHOLD_ID, data=farm
> 
> Then, I impose compound symmetry explicitly:
>  
> dependency<-corCompSymm(value=0.908, form=~1|HOUSEHOLD_ID)
> cs<-Initialize( dependency  , data=farm)
> new_model<-update(model, correlation=cs)
> 
> Is this fundamentally correct or is it double accounting for compound
> symmetry since there already is default in lme function?
> 
> Thank you very much.
> 
> Regards,
> Yashree
> 
> On Sun, Dec 9, 2018 at 8:24 PM Ben Bolker <bbolker using gmail.com
> <mailto:bbolker using gmail.com>> wrote:
> 
> 
>       A quick example of the induced covariance structure.
> 
>       Suppose you set up the simplest possible (linear) mixed model, which
>     has an overall intercept B; a group-level random effect on the intercept
>     e1_i with variance v1; and a residual error e0_ij with variance v0. The
>     value of x_{ij} = B + e1_i + e0_ij.  The variance of any observation
>     (E[(x_{ij}-B)^2]) is v0+v1.  The covariance of observations in the same
>     group is E[(x_{ij}-B)(x_{kj}-B)] = v1. The covariance of observations in
>     *different* groups is 0.  If we write out the correlation matrix for the
>     whole data set (assuming the observations are written out with samples
>     from the same group occurring contiguously), it will consist of a
>     block-diagonal matrix with correlation v1/(v0+v1) within each block; the
>     rest of the matrix will be zero.  This is a form of induced
>     compound-symmetric covariance structure.
> 
>       Presumably others can give good references to where this is explained
>     clearly in the literature (maybe even in Pinheiro and Bates, I don't
>     have access to my copy right now)
> 
>     On 2018-12-07 1:53 p.m., Poe, John wrote:
>     > Hi Yashree,
>     >
>     > Can you give the citation and page number for the panel data book?
>     >
>     > On Fri, Dec 7, 2018 at 1:15 PM Yashree Mehta <yashree19 using gmail.com
>     <mailto:yashree19 using gmail.com>> wrote:
>     >
>     >> Hi,
>     >>
>     >> I have a question about the random effects model (Specifically, a
>     random
>     >> intercept model) in its role in assuming a covariance structure in
>     >> estimation. In a panel data textbook, I read that by estimating a
>     random
>     >> effects model itself, there is an induced covariance structure.
>     >>
>     >> In nlme package, there are several types of covariance structures
>     such as
>     >> Compound Symmetry (which I assume in my model) but the default
>     value is 0.
>     >> I initialize it and proceed with the estimation.
>     >>
>     >> Does this mean that if I do not specify the compound symmetry
>     value in
>     >> nlme, the estimation is without a covariance assumption or there is
>     >> something I have missed in my understanding? That the " by
>     estimating a
>     >> random effects model itself, there is an induced covariance
>     structure"
>     >> confuses me a little.
>     >>
>     >> It would be very helpful to get an explanation on this.
>     >>
>     >> Thank you very much!
>     >>
>     >> Regards,
>     >> Yashree
>     >>
>     >>         [[alternative HTML version deleted]]
>     >>
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