[R-sig-ME] Bug in weights in lmer

[Doran, Harold]

I'm confused. When I run this, I get the exact same answers for all
three models for all variance components and for all fixed effects. See
my results below. Where is the bug?

> w<-rep(1,nrow(sleepstudy))
> w
  [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1
 [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1
 [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1
[112] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1
[149] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

> (fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy) )
Linear mixed-effects model fit by REML 
Formula: Reaction ~ Days + (Days | Subject) 
   Data: sleepstudy 
  AIC  BIC logLik MLdeviance REMLdeviance
 1754 1770 -871.8       1752         1744
Random effects:
 Groups   Name        Variance Std.Dev. Corr  
 Subject  (Intercept) 610.835  24.7151        
          Days         35.056   5.9208  0.067 
 Residual             655.066  25.5943        
number of obs: 180, groups: Subject, 18

Fixed effects:
            Estimate Std. Error t value
(Intercept)  251.405      6.820   36.86
Days          10.467      1.546    6.77

Correlation of Fixed Effects:
     (Intr)
Days -0.137
> (fm2 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy, weights =
w) )
Linear mixed-effects model fit by REML 
Formula: Reaction ~ Days + (Days | Subject) 
   Data: sleepstudy 
  AIC  BIC logLik MLdeviance REMLdeviance
 1754 1770 -871.8       1752         1744
Random effects:
 Groups   Name        Variance Std.Dev. Corr  
 Subject  (Intercept) 610.835  24.7151        
          Days         35.056   5.9208  0.067 
 Residual             655.066  25.5943        
number of obs: 180, groups: Subject, 18

Fixed effects:
            Estimate Std. Error t value
(Intercept)  251.405      6.820   36.86
Days          10.467      1.546    6.77

Correlation of Fixed Effects:
     (Intr)
Days -0.137
> (fm3 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy, weights =
w/sum(w)) )
Linear mixed-effects model fit by REML 
Formula: Reaction ~ Days + (Days | Subject) 
   Data: sleepstudy 
  AIC  BIC logLik MLdeviance REMLdeviance
 1754 1770 -871.8       1752         1744
Random effects:
 Groups   Name        Variance Std.Dev. Corr  
 Subject  (Intercept) 610.835  24.7151        
          Days         35.056   5.9208  0.067 
 Residual             655.066  25.5943        
number of obs: 180, groups: Subject, 18

Fixed effects:
            Estimate Std. Error t value
(Intercept)  251.405      6.820   36.86
Days          10.467      1.546    6.77

Correlation of Fixed Effects:
     (Intr)
Days -0.137 

> -----Original Message-----
> From: r-sig-mixed-models-bounces at r-project.org 
> [mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf 
> Of Nick Isaac
> Sent: Wednesday, April 23, 2008 8:39 AM
> To: R-sig-mixed-models at r-project.org
> Subject: [R-sig-ME] Bug in weights in lmer
> 
> I have unearthed a bug in the way lmer() deals with weights.
> 
> Adding weights causes an inflation of the variance estimates. 
> The phenomenon is easily demonstrated by comparing the 
> following models, all of which should be identical:
> 
> w<-rep(1,nrow(sleepstudy))
> (fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy) )
> (fm2 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy, 
> weights = w) )
> (fm3 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy, 
> weights = w/sum(w)) )
> 
> I have tried this with other datasets and models and find the 
> same general pattern. I find that the inflation factor is 
> correlated with
> sum(w) and is higher for cross-classified models than simple 
> nested ones.
> 
> The fixed effect estimates are also changed.
> 
> Best wishes, Nick
> 
> 
> > sessionInfo()
> R version 2.6.2 (2008-02-08)
> i386-apple-darwin8.10.1
> 
> locale:
> en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8
> 
> attached base packages:
> [1] stats     graphics  grDevices utils     datasets  methods   base
> 
> other attached packages:
> [1] lme4_0.999375-13  Matrix_0.999375-7 lattice_0.17-6
> 
> loaded via a namespace (and not attached):
> [1] grid_2.6.2
> 
> _______________________________________________
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