[R] Repeated measures in nlme vs SAS Proc Mixed with AR1 correlation structure

[simontbate]

Hi all, 
I don't know if anyone has any thoughts on this. I have been trying to move
from SAS Proc Mixed to R nlme and have an unusual result.

I have several subjects measured at four timepoints. I want to model the
within-subject correlation using an autoregressive structure. I've attached
the R and SAS code I'm using along with the results from SAS.

With R lme I get an estimate of the autoregressive paramater phi =  
0.2782601, whereas SAS gives me an estimate of 0.3389

Intriguingly if I include a between subject factor or a covariate or delete
one of the observations, then the results appear to agree.

I'm suprised the seemingly simpler model if different between the two
packages whereas the more complex models agree.

Any ideas would be most welcome!
Simon


R Code:

library(nlme)
Response<-c(0.55,0.86,0.21,0.36,0.46,0.32,0.11,0.24,0.36,0.29,0.48,0.93,0.56,0.67,0.36,0.55,0.51,0.4,0.34,0.51,1,0.61,0.65,0.41,0.99,0.86,0.64,0.86,0.31,0.19,0.21,0.36,0.41,0.47,0.16,0.81,0.9,0.72,0.87,0.02)
Subject<-c(1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,10,10,10,10)
Day<-c(1,2,4,6,1,2,4,6,1,2,4,6,1,2,4,6,1,2,4,6,1,2,4,6,1,2,4,6,1,2,4,6,1,2,4,6,1,2,4,6)

sasdata<-data.frame(cbind(Response, Subject, Day))
sasdata$Time<-as.factor(sasdata$Day)

AR1<-lme(Response~Time, random=~1|Subject,
correlation=corAR1(form=~as.numeric(Time)|Subject, fixed =FALSE),
data=sasdata, na.action = (na.omit), method = "REML")
AR1


SAS Code:

proc mixed;
class Subject Day;
model Response = Day / outp=pout;
repeated Day / subject = Subject type=AR(1);
run;


SAS Results:


Model Information

Data Set	WORK.ALLDATA
Dependent Variable	Response
Covariance Structure	Autoregressive
Subject Effect	Subject
Estimation Method	REML
Residual Variance Method	Profile
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Between-Within


Class Level Information

Class	Levels	Values
Subject	10	1 10 2 3 4 5 6 7 8 9
Day	4	1 2 3 4


Dimensions

Covariance Parameters	2
Columns in X	5
Columns in Z	0
Subjects	10
Max Obs Per Subject	4


Number of Observations

Number of Observations Read	40
Number of Observations Used	40
Number of Observations Not Used	0


Iteration History

Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	14.67045653	
1	2	11.63168913	0.00000018
2	1	11.63168429	0.00000000


Convergence criteria met.



Covariance Parameter Estimates

Cov Parm	Subject	Estimate
AR(1)	Animal1	0.3389
Residual		0.06862




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