[R-sig-ME] Interpretation of lme output with correlation structure specification

[Bansal, Udita]

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 using unimelb.edu.au>
Date: Saturday, 11 August 2018 at 11:16 PM
To: "r-sig-mixed-models using r-project.org" <r-sig-mixed-models using r-project.org>, "Bansal, Udita" <udita.bansal17 using 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 using unimelb.edu.au
Website: http://cebra.unimelb.edu.au/
On 12 Aug 2018, 7:34 AM +1000, Bansal, Udita <udita.bansal17 using 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

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