Interpretation of lme output with correlation structure specification
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