Compound Symmetry Covariance structure

  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 at gmail.com
<mailto:bbolker at 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 at gmail.com

    <mailto:yashree19 at 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]]
    >>
    >> _______________________________________________
    >> R-sig-mixed-models at r-project.org

    <mailto:R-sig-mixed-models at r-project.org> mailing list

    >> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
    >>

    >
    >