[R] Phi parameter in corAR(1) in NLMEs

[Nelson, Kerrie P.]

Hello,
 
I have been fitting nonlinear models with random effects using nlme with the
corCAR1 correlation structure, as I have unequally spaced observations per
subject, and serially correlated errors.  My question is regarding the Phi
parameter.  
 
Example of output:
Correlation Structure: Continuous AR(1)
 Formula: ~day | subject 
 Parameter estimate(s):
      Phi 
0.8475842 
 
After reading the Pinheiro and Bates (2000), and Jones (1993) texts I am
uncertain whether the estimate of Phi given in the output is:
 
- the correlation between two observations one time unit apart, i.e. phi(t2-t1)
= phi(1) = 0.8475842
 
- or is the parameter in the exponential term, exp(-phi(t2-t1)), i.e the
correlation between two observations one unit apart is exp(-0.8475842*(t2-t1)) =
exp(-0.8475842*1) = 0.4284
 
- or if there is another interpretation altogether
 
Thank-you very much for any clarification on this, I appreciate your help!
 
Kerrie Nelson,
Biostatistics Unit,
MGH
 


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