[R-sig-ME] Covariance structure specification

[Ben Bolker]

Angelina Mukherjee <angelina.mukherjee88 at ...> writes:

> I have response measures corresponding to 2 patients. The structure is as
> follows:
> 
> Patient 1:  Region 1             Region 2              Region 3
>                S1 S2 S3 S4       S1 S2 S3 S4        S1 S2 S3 S4
> 
> Patient 2:  Region 1               Region 2            Region 3
>                 S1 S2 S3 S4       S1 S2 S3 S4        S1 S2 S3 S4


  Hmm.  Do you really have only two patients, i.e. a total of
24 response values?  I understand that you're trying to do a
variance decomposition here (no fixed effects, only random
effects), but your estimates of variance will be extremely
inaccurate based on only two patients (you might want to consider
making patient a fixed effect, then you would at least have
6 data points (5 df) for the patient:region variance ...
 
> Each patient has 3 regions and each region has 4 sub-regions. (nested
> design)
> 
> Fitting   *lme( Response ~ 1, random=~ Patient + Region +Subregion |
> Patient/Region/Subregion )*
> allows me to specify covariance structure for the 'sub-region' term.
> 
> But I'm trying to fit a random effects model of the form as I have only 1
> observation per 'sub-region':
> *lme( Response ~ 1, random=~ Patient + Region | Patient/Region )*
> 
> Is there a way I can specify a covariance structure like
> the auto-regressive (to specify that correlation decreases with distance as
> one moves from Subregion 1 to Subregion 4) for the 'sub-region' term only
> as it is not included in my random effects model but I'd like to account
> for the correlation in it?

   I would think that something like

lme(Response~1, random = ~1|Patient/Region,
   correlation=corAR1(~Subregion))

  But I also think you're fitting a more complicated model
than can really be supported by 24 data points ...

  Ben Bolker