Interpretation of lme output with correlation structure specification

Dear Andrew,

Thank you for suggesting the book. I went through the relevant parts of
the book which helped me clarify my third question.

But I still am not clear on phi. What I understood is that it is the
within group correlation (which is solved by the model?) whose value ranges
from -1 to 1. What I didn?t understand is as follows:
Q1: Is any value of phi acceptable since it is the correlation of the
within group observations which is taken into account by the model?
Q2: The AR1 parameter estimate (the ?value?) I provide while specifying
the model is calculated based on AR model. How does the phi value relate
with that? The book did not say much on it.

Any help will be appreciated!

Thanks
Udita Bansal

From: Andrew Robinson <apro at unimelb.edu.au>
Date: Saturday, 11 August 2018 at 11:16 PM
To: "r-sig-mixed-models at r-project.org" <r-sig-mixed-models at r-project.org>,
"Bansal, Udita" <udita.bansal17 at imperial.ac.uk>
Subject: Re: [R-sig-ME] Interpretation of lme output with correlation
structure specification


Hi Udita,

You should read the book cited in the package. It?s really worthwhile.

Best wishes,

Andrew

--
Andrew Robinson
Director, CEBRA, School of BioSciences
Reader & Associate Professor in Applied Statistics Tel: (+61) 0403 138 955
School of Mathematics and Statistics Fax: (+61) 03 8344 4599
University of Melbourne, VIC 3010 Australia
Email: apro at unimelb.edu.au
Website: http://cebra.unimelb.edu.au/
On 12 Aug 2018, 7:34 AM +1000, Bansal, Udita <
udita.bansal17 at imperial.ac.uk>, wrote:

Hi all,

I was modeling the laying date of bird nests against moving averages of
weather variables for several years of data. I used Durbin-Watson test and
found considerable amount of autocorrelation in the residuals of simple
linear and mixed effect models (with month as a random factor). So, I
decided to run lme models with correlation structure specified. When I
compare the AIC of the models with and without the correlation structure, I
find that the models with the correlation structure are better.
Question 1.: How can I interpret the phi (parameter estimate for
correlation structure) value in the model output?
Question 2.: Does the interpretation of phi affect the interpretation of
the random effect?
Question 3.: How can I interpret the random effect (since this is
different from what lmer output shows which I am used to of)?

An example output is as below:

Random effects:
Formula: ~1 | month
(Intercept) Residual
StdDev: 12.53908 5.009051

Correlation Structure: AR(1)
Formula: ~1 | month
Parameter estimate(s):
Phi
0.324984

I could not find much on the interpretation for these online. Any help
will be much appreciated.

Thanks
Udita Bansal

[[alternative HTML version deleted]]