[R-sig-ME] Within group estimate of autocorrelation

[Ben Bolker]

On 14-09-22 02:39 PM, PATRICK, Samantha wrote:
> Hi

> I have a model which fits an corAR1 autocorrelation structure and
>  the code tells the model that time is nested within individual:

> fit0<-lme(Respone~1,
> random=~1|indiv,
> correlation=corAR1(form=~time|indiv),
> data=Data2, method = "REML")

>>From this I get a Phi single estimate of the autocorrelation.
  However I want to have an estimate of the autocorrelation for each
  individual.  I have checked but can not find any code to extract
  this value.

The model assumes that autocorrelation structure is homogeneous
across individuals.

>  So my first question is: Is it possible to extract an estimate of
> autocorrelation per individual or does the model not save/calculate
> this?

  So, the answer is: no/correct.

> And second, if it isn't possible, I wondered if there is any way to
  use the weights function to group individuals.

>  If I add the code: weights=varIdent(form=~1|group), I can fit
> multiple residual variance terms so I wondered if this could be used
> to estimate a Phi value per group, by somehow structuring the model
> so it fits an autocorrelation for each residual variance group?


> The solution does not need to be lme necessarily - I’m open to any
  suggestions!


Perhaps just use acf() along with your favourite by-group tool
in R (plyr, aggregate, dplyr, data.table, for loop ...)
to compute/extract the first-order autocorrelation parameter for each
individual?  Or you could use

gls(Response~1,correlation=corAR1(form~time),...)

for each individual and similarly return the autocorrelation parameter
per individual.

  I hope you have a reasonably large number of observations per
individual ...