[R] Efficiency of random and fixed effects estimator

[Daniel Malter]

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
> 

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