<s>
In	O
statistics	O
,	O
a	O
random	B-General_Concept
effects	I-General_Concept
model	I-General_Concept
,	O
also	O
called	O
a	O
variance	B-General_Concept
components	I-General_Concept
model	I-General_Concept
,	O
is	O
a	O
statistical	O
model	O
where	O
the	O
model	O
parameters	O
are	O
random	O
variables	O
.	O
</s>
<s>
It	O
is	O
a	O
kind	O
of	O
hierarchical	B-General_Concept
linear	I-General_Concept
model	I-General_Concept
,	O
which	O
assumes	O
that	O
the	O
data	O
being	O
analysed	O
are	O
drawn	O
from	O
a	O
hierarchy	O
of	O
different	O
populations	O
whose	O
differences	O
relate	O
to	O
that	O
hierarchy	O
.	O
</s>
<s>
A	O
random	B-General_Concept
effects	I-General_Concept
model	I-General_Concept
is	O
a	O
special	O
case	O
of	O
a	O
mixed	B-General_Concept
model	I-General_Concept
.	O
</s>
<s>
Random	B-General_Concept
effect	I-General_Concept
models	I-General_Concept
assist	O
in	O
controlling	O
for	O
unobserved	O
heterogeneity	O
when	O
the	O
heterogeneity	O
is	O
constant	O
over	O
time	O
and	O
not	O
correlated	O
with	O
independent	O
variables	O
.	O
</s>
<s>
Two	O
common	O
assumptions	O
can	O
be	O
made	O
about	O
the	O
individual	O
specific	O
effect	O
:	O
the	O
random	B-General_Concept
effects	I-General_Concept
assumption	O
and	O
the	O
fixed	B-General_Concept
effects	I-General_Concept
assumption	O
.	O
</s>
<s>
The	O
random	B-General_Concept
effects	I-General_Concept
assumption	O
is	O
that	O
the	O
individual	O
unobserved	O
heterogeneity	O
is	O
uncorrelated	O
with	O
the	O
independent	O
variables	O
.	O
</s>
<s>
The	O
fixed	B-General_Concept
effect	I-General_Concept
assumption	O
is	O
that	O
the	O
individual	O
specific	O
effect	O
is	O
correlated	O
with	O
the	O
independent	O
variables	O
.	O
</s>
<s>
If	O
the	O
random	B-General_Concept
effects	I-General_Concept
assumption	O
holds	O
,	O
the	O
random	B-General_Concept
effects	I-General_Concept
estimator	I-General_Concept
is	O
more	O
efficient	O
than	O
the	O
fixed	B-General_Concept
effects	I-General_Concept
model	I-General_Concept
.	O
</s>
<s>
In	O
this	O
model	O
Ui	O
is	O
the	O
school-specific	O
random	B-General_Concept
effect	I-General_Concept
:	O
it	O
measures	O
the	O
difference	O
between	O
the	O
average	O
score	O
at	O
school	O
i	O
and	O
the	O
average	O
score	O
in	O
the	O
entire	O
country	O
.	O
</s>
<s>
The	O
term	O
Wij	O
is	O
the	O
individual-specific	O
random	B-General_Concept
effect	I-General_Concept
,	O
i.e.	O
,	O
it	O
's	O
the	O
deviation	O
of	O
the	O
j-th	O
pupil	O
's	O
score	O
from	O
the	O
average	O
for	O
the	O
i-th	O
school	O
.	O
</s>
<s>
This	O
is	O
a	O
mixed	B-General_Concept
model	I-General_Concept
,	O
not	O
a	O
purely	O
random	B-General_Concept
effects	I-General_Concept
model	I-General_Concept
,	O
as	O
it	O
introduces	O
fixed-effects	B-General_Concept
terms	O
for	O
Sex	O
and	O
Parents	O
 '	O
Education	O
.	O
</s>
<s>
be	O
the	O
grand	B-General_Concept
average	I-General_Concept
.	O
</s>
<s>
These	O
"	O
expected	B-General_Concept
mean	I-General_Concept
squares	I-General_Concept
"	O
can	O
be	O
used	O
as	O
the	O
basis	O
for	O
estimation	O
of	O
the	O
"	O
variance	B-General_Concept
components	I-General_Concept
"	O
σ2	O
and	O
τ2	O
.	O
</s>
<s>
Random	B-General_Concept
effects	I-General_Concept
models	I-General_Concept
used	O
in	O
practice	O
include	O
the	O
Bühlmann	B-General_Concept
model	I-General_Concept
of	O
insurance	O
contracts	O
and	O
the	O
Fay-Herriot	O
model	O
used	O
for	O
small	O
area	O
estimation	O
.	O
</s>
