[R] Efficiency of random and fixed effects estimator

[Bert Gunter]

Daniel:

Your question should be addressed to R-sig-mixed-models, as it really
does not belong on r-help.

-- Bert


On Mon, Aug 22, 2011 at 5:11 PM, Daniel Malter <daniel at umd.edu> wrote:
> Small bugs in my simulated data (corrected code below). However, that does
> not affect my question:
>
> id<-rep(c(1:100),each=2)
> obs<-rep(c(0:1),100)
> d<-rep(sample(c(-1,1),100,replace=T),each=2)
> base.happy<-rep(rnorm(100),each=2)
> happy<-base.happy+1.5*d*obs+rnorm(200)
>
> data<-data.frame(id,obs,d,happy)
>
>
> Daniel Malter wrote:
>>
>> Hi all,
>>
>> I am statistically confused tonight. When the assumptions to a random
>> effects estimator are warranted, random effects should be the more
>> efficient estimator than the fixed effects estimator because it uses fewer
>> degrees of freedom (estimating just the variance parameter of the normal
>> rather than using one df for each included fixed effect, I thought).
>> However, I don't find this to be the case in this simulated example.
>>
>> For the sake of the example, assume you measure subjects' happiness before
>> exposing them to a happy or sad movie, and then you measure their
>> happiness again after watching the movie. Here, "id" marks the subject,
>> "obs" marks the pre- and post-treatment observations, "d" is the treatment
>> indicator (whether the subject watched the happy or sad movie),
>> "base.happy" is the ~N(0,1)-distributed individual effect a(i), happy is
>> the measured happiness for each subject pre- and post-treatment,
>> respectively, and the error term u(i,t) is also distributed ~N(0,1).
>>
>> id<-rep(c(1:100),each=2)
>> obs<-rep(c(0:1),100)
>> d<-rep(sample(c(-1,1),100,replace=T),each=2)
>> base.happy<-rep(rnorm(50),each=2)
>> happy<-base.happy+1.5*d*obs+rnorm(100)
>>
>> data<-data.frame(id,obs,d,happy)
>>
>> # Now run the random and fixed effects models
>>
>> library(lme4)
>> reg.re<-lmer(happy~factor(obs)*factor(d)+(1|id))
>>
>> reg.fe1<-lm(happy~factor(id)+factor(obs)*factor(d))
>> summary(reg.fe1)
>>
>> library(plm)
>> reg.fe2<-plm(happy~factor(obs)*factor(d),index=c('id','obs'),model="within",data=data)
>> summary(reg.fe2)
>>
>>
>>
>> I am confused why FE and RE models are virtually equally efficient in this
>> case. Can somebody lift my confusion?
>>
>> Thanks much,
>> Daniel
>>
>
> --
> View this message in context: http://r.789695.n4.nabble.com/Efficiency-of-random-and-fixed-effects-estimator-tp3761611p3761617.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
nt.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm