Sorry to bother you. I am struggling in this issue for long time. Wish
somebody can help me.

I first used lmer to do the following analysis.
fullmodel=lmer(BMI~1+exposure+(age|ID),data, REML=FALSE)
          reducemodel=lmer(BMI~1+(age|ID),data, REML=FALSE)
          anova(full,red)
The "fullmodel" has AIC of 6874 and "reducemodel" has AIC of 7106, which
cause "anova" analysis giving the p-value< 2.2e-16 . This result is
definitely wrong

I then did the similar study by SAS.
The fullmodel is:
proc mixed;
class exposure;
model BMI=exposure;
random age /sub=id;
run;
The AIC is 7099.7, and type 3 test of fixed effect, exposure, got
p-value=0.74.

The reducemodel is:
proc mixed;
 class exposure;
 model BMI=;
 random age /sub=id;
 run;
 The AIC is 7101.2.

The SAS result is correct.

Could somebody help me to explain why lmer is wrong?

I do not even dare to use lmer now, since I can not trust its result. Thanks
in advance for any of your answer.

Best,
Yong
,

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