R help - Aug 2011 - Efficiency of random and fixed effects estimator

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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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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