[R-sig-ME] Autoregressive covariance structure for lme object and R/SAS

[Steve Candy]

Andreas
 You state:
> ...using AR1 instead of Variance Components in SAS, which fits the
observation that AIC values (in SAS) indicate both covariance structures fit
data equally well.

The lme model includes both random subject effects and an CAR1 process so
this last process is on the residuals adjusting for subject random effect
estimates. Is the SAS model equivalent? The above statement implies its
either random subject effects fitted or a CAR1 error process but not both
together. The summary(m2) in terms of the error model variance
component/parameters could be compared to the SAS output. Also you could
plot the sample/theoretical variograms with the R-code below. My experience
with lme suggested to me that you have to have subjects ("id") as a random
effect when fitting corCAR1(form=~x|id) but there may be a way around this
restriction. 

vg.01 <- Variogram(m2, form = ~ x|id)
plot(y= vg.01$variog , x= vg.01$dist)
# extract Phi (or set its value to output value)
# over-plot the fitted CAR1 model 
lines(y=(1-Phi^(seq(1,length(vg.01$dist)))), x=seq(1,length(vg.01$dist)),
lwd=2)


Dr Steven G. Candy
Director/Consultant
SCANDY STATISTICAL MODELLING PTY LTD


> Dear R users,
> We are working on a data set in which we have measured repeatedly a 
> physiological response variable (y) every 20 min for 12 h (time 
> variable; 'x') in subjects ('id') beloning to one of five groups 
> ('group'; 'A' to 'E'). Data are located at:
> https://www.dropbox.com/s/hf455aev3teb5e0/data.csv?dl=0
>
> We are interested to model if the response in y differences with time 
> (i.e. 'x') for the two groups. Thus:
> require(nlme)
> m1<-lme(y~group*x+group*I(x^2),random=~x|id,data=data.df,na.action=na.
> omit)
>
> But because data are collected repeatedly over short time intervals 
> for each subject, it seemed prudent to consider an autoregressive 
> covariance structure. Thus:
> m2<-update(m1,~.,corr=corCAR1(form=~x|id))
>
> AIC values indicate the latter (i.e. m2) as more appropriate:
>   anova(m1,m2)
> #   Model df      AIC      BIC       logLik        Test  L.Ratio
> p-value
> #m1     1 19 2155.996 2260.767 -1058.9981
> #m2     2 20 2021.944 2132.229  -990.9718 1 vs 2 136.0525  <.0001
>
> Fixed effects and test statistics differ between models. A look at 
> marginal ANOVA tables suggest inference might differ somewhat between
> models:
>
> anova.lme(m1,type="m")
> #              numDF denDF  F-value p-value
> #(Intercept)      1  1789 63384.80  <.0001
> #group             4    45      1.29  0.2893
> #x                   1  1789     0.05  0.8226
> #I(x^2)            1  1789     4.02  0.0451
> #group:x          4  1789     2.61  0.0341
> #group:I(x^2)   4  1789     4.37  0.0016
>
> anova.lme(m2,type="m")
> #             numDF denDF  F-value p-value
> #(Intercept)      1  1789 59395.79  <.0001
> #group             4    45      1.33  0.2725
> #x                    1  1789     0.04  0.8379
> #I(x^2)            1  1789     2.28  0.1312
> #group:x          4  1789     2.09  0.0802
> #group:I(x^2)  4  1789     2.81  0.0244
>
> Now, this is all well. But: my colleagues have been running the same 
> data set using PROC MIXED in SAS and come up with substantially 
> different results when comparing SAS default covariance structure 
> (variance
> components) and AR1. Specifically, there is virtually no change in 
> either test statistics or fitted values when using AR1 instead of 
> Variance Components in SAS, which fits the observation that AIC values 
> (in SAS) indicate both covariance structures fit data equally well.
>
> This is not very satisfactory to me, and I would be interesting to 
> know what is happening here. Realizing this might not be the correct 
> forum for this question, I would like to ask you all if anyone would 
> have any input as to what is going on here, e.g. am I setting up my 
> model erroneously, etc.?
>
> N.b. I have no desire to replicate SAS results, but I would most 
> certainly be interested to know what could possibly explain  such a 
> large discrepancy between the two platforms. Any suggestions greatly
welcomed.
>
> (Data are located at:
> https://www.dropbox.com/s/hf455aev3teb5e0/data.csv?dl=0)
>
> With all best wishes,
> Andreas
>
>         [[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list 
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>

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