
Hi all, 
I don't know if anyone has any thoughts on this, I suspect it is a local convergence issue but am not sure. 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 time points. 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 parameter phi =   0.2782601, whereas SAS gives me an estimate of 0.3389 

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

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

Any ideas would be most welcome! 
 
Regards,
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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