<s>
In	O
statistics	O
,	O
a	O
generalized	B-General_Concept
linear	I-General_Concept
mixed	I-General_Concept
model	I-General_Concept
(	O
GLMM	B-General_Concept
)	O
is	O
an	O
extension	O
to	O
the	O
generalized	O
linear	O
model	O
(	O
GLM	O
)	O
in	O
which	O
the	O
linear	O
predictor	O
contains	O
random	B-General_Concept
effects	I-General_Concept
in	O
addition	O
to	O
the	O
usual	O
fixed	B-General_Concept
effects	I-General_Concept
.	O
</s>
<s>
They	O
also	O
inherit	O
from	O
GLMs	O
the	O
idea	O
of	O
extending	O
linear	B-General_Concept
mixed	I-General_Concept
models	I-General_Concept
to	O
non-normal	O
data	O
.	O
</s>
<s>
GLMMs	B-General_Concept
provide	O
a	O
broad	O
range	O
of	O
models	O
for	O
the	O
analysis	O
of	O
grouped	O
data	O
,	O
since	O
the	O
differences	O
between	O
groups	O
can	O
be	O
modelled	O
as	O
a	O
random	B-General_Concept
effect	I-General_Concept
.	O
</s>
<s>
Here	O
and	O
are	O
the	O
fixed	B-General_Concept
effects	I-General_Concept
design	O
matrix	O
,	O
and	O
fixed	B-General_Concept
effects	I-General_Concept
respectively	O
;	O
and	O
are	O
the	O
random	B-General_Concept
effects	I-General_Concept
design	O
matrix	O
and	O
random	B-General_Concept
effects	I-General_Concept
respectively	O
.	O
</s>
<s>
To	O
understand	O
this	O
very	O
brief	O
definition	O
you	O
will	O
first	O
need	O
to	O
understand	O
the	O
definition	O
of	O
a	O
generalized	O
linear	O
model	O
and	O
of	O
a	O
mixed	B-General_Concept
model	I-General_Concept
.	O
</s>
<s>
Generalized	B-General_Concept
linear	I-General_Concept
mixed	I-General_Concept
models	I-General_Concept
are	O
a	O
special	O
cases	O
of	O
hierarchical	O
generalized	O
linear	O
models	O
in	O
which	O
the	O
random	B-General_Concept
effects	I-General_Concept
are	O
normally	O
distributed	O
.	O
</s>
<s>
has	O
no	O
general	O
closed	O
form	O
,	O
and	O
integrating	O
over	O
the	O
random	B-General_Concept
effects	I-General_Concept
is	O
usually	O
extremely	O
computationally	O
intensive	O
.	O
</s>
<s>
via	O
Gauss	B-Algorithm
–	I-Algorithm
Hermite	I-Algorithm
quadrature	I-Algorithm
)	O
,	O
methods	O
motivated	O
by	O
Laplace	O
approximation	O
have	O
been	O
proposed	O
.	O
</s>
<s>
doubly	O
iterative	O
)	O
a	O
weighted	O
normal	O
mixed	B-General_Concept
model	I-General_Concept
with	O
a	O
working	O
variate	O
,	O
is	O
implemented	O
by	O
various	O
commercial	O
and	O
open	O
source	O
statistical	O
programs	O
.	O
</s>
<s>
Fitting	O
GLMMs	B-General_Concept
via	O
maximum	O
likelihood	O
(	O
as	O
via	O
AIC	O
)	O
involves	O
integrating	O
over	O
the	O
random	B-General_Concept
effects	I-General_Concept
.	O
</s>
<s>
Various	O
approximate	O
methods	O
have	O
been	O
developed	O
,	O
but	O
none	O
has	O
good	O
properties	O
for	O
all	O
possible	O
models	O
and	O
data	B-General_Concept
sets	I-General_Concept
(	O
e.g.	O
</s>
<s>
For	O
this	O
reason	O
,	O
methods	O
involving	O
numerical	B-Algorithm
quadrature	I-Algorithm
or	O
Markov	B-General_Concept
chain	I-General_Concept
Monte	I-General_Concept
Carlo	I-General_Concept
have	O
increased	O
in	O
use	O
,	O
as	O
increasing	O
computing	O
power	O
and	O
advances	O
in	O
methods	O
have	O
made	O
them	O
more	O
practical	O
.	O
</s>
<s>
Estimates	O
of	O
AIC	O
for	O
GLMMs	B-General_Concept
based	O
on	O
certain	O
exponential	O
family	O
distributions	O
have	O
recently	O
been	O
obtained	O
.	O
</s>
<s>
Several	O
contributed	O
packages	O
in	O
R	B-Language
provide	O
GLMM	B-General_Concept
functionality	O
,	O
including	O
lme4	O
and	O
glmm	B-General_Concept
.	O
</s>
<s>
MATLAB	B-Language
also	O
provides	O
a	O
function	O
called	O
"	O
fitglme	O
"	O
to	O
fit	O
GLMM	B-General_Concept
models	O
.	O
</s>
<s>
The	O
Julia	O
package	O
MixedModels.jl	O
provides	O
a	O
function	O
called	O
GeneralizedLinearMixedModel	O
that	O
fits	O
a	O
GLMM	B-General_Concept
to	O
provided	O
data	O
.	O
</s>
