[R-sig-ME] Compound Symmetry Covariance structure

[Yashree Mehta]

Hi Ben,

the log-likelihoods of the original and the
compound-symmetrized models are the same. However, there is a shift in the
location of the kernel density plots of the random intercept when I compare
the ones from the original and the compound-symmetrized models. I
understand that there are no correlation parameters to model and so the the
log-likelihoods of the original and the
compound-symmetrized models are the same. I was wondering whether the
explicit accounting for compound symmetry by updating the original model is
necessary or simply a random intercept specification is enough for inducing
a compound symmetric covariance structure?

Thank you very much,

Regards,
Yashree

On Mon, Dec 10, 2018 at 1:10 AM Ben Bolker <bbolker using gmail.com> wrote:

>
>   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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> >     >>
> >     >
> >     >
> >
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>

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