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

[Bansal, Udita]

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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