[R] AR1 covariance structure for lme object and R/SAS differences in model output

anord andreas.nord at biol.lu.se
Wed Feb 11 16:57:15 CET 2015


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






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