<s>
In	O
computational	O
biology	O
and	O
bioinformatics	O
,	O
analysis	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
–	O
simultaneous	O
component	O
analysis	O
(	O
ASCA	O
or	O
ANOVA	B-General_Concept
–	O
SCA	O
)	O
is	O
a	O
method	O
that	O
partitions	O
variation	O
and	O
enables	O
interpretation	O
of	O
these	O
partitions	O
by	O
SCA	O
,	O
a	O
method	O
that	O
is	O
similar	O
to	O
principal	B-Application
components	I-Application
analysis	I-Application
(	O
PCA	O
)	O
.	O
</s>
<s>
Analysis	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
(	O
ANOVA	B-General_Concept
)	O
is	O
a	O
collection	O
of	O
statistical	O
models	O
and	O
their	O
associated	O
estimation	O
procedures	O
used	O
to	O
analyze	O
differences	O
.	O
</s>
<s>
This	O
method	O
is	O
a	O
multivariate	B-General_Concept
or	O
even	O
megavariate	O
extension	O
of	O
analysis	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
(	O
ANOVA	B-General_Concept
)	O
.	O
</s>
<s>
The	O
variation	O
partitioning	O
is	O
similar	O
to	O
ANOVA	B-General_Concept
.	O
</s>
<s>
Because	O
even	O
the	O
effect	O
estimates	O
are	O
multivariate	B-General_Concept
,	O
interpretation	O
of	O
these	O
effects	O
estimates	O
is	O
not	O
intuitive	O
.	O
</s>
<s>
Because	O
of	O
this	O
,	O
most	O
traditional	O
multivariate	B-General_Concept
statistical	O
methods	O
cannot	O
be	O
applied	O
.	O
</s>
<s>
Let	O
X	O
be	O
a	O
matrix	B-Architecture
that	O
holds	O
the	O
data	O
.	O
</s>
<s>
Matrix	B-Architecture
E	O
holds	O
the	O
information	O
that	O
is	O
not	O
assigned	O
to	O
any	O
effect	O
.	O
</s>
<s>
Make	O
a	O
new	O
matrix	B-Architecture
of	O
the	O
same	O
size	O
of	O
X	O
and	O
place	O
the	O
calculated	O
averages	O
in	O
the	O
matching	O
rows	O
.	O
</s>
<s>
E''	O
is	O
the	O
residual	O
or	O
error	O
matrix	B-Architecture
.	O
</s>
<s>
Note	O
that	O
every	O
partition	O
has	O
its	O
own	O
error	O
matrix	B-Architecture
.	O
</s>
<s>
This	O
results	O
in	O
zero	O
errors	O
,	O
since	O
any	O
rank	O
1	O
matrix	B-Architecture
can	O
be	O
written	O
as	O
the	O
product	O
of	O
a	O
single	O
component	O
score	O
and	O
loading	O
vector	O
.	O
</s>
<s>
Because	O
'	O
time	O
 '	O
is	O
treated	O
as	O
a	O
qualitative	O
factor	O
in	O
the	O
ANOVA	B-General_Concept
decomposition	O
preceding	O
ASCA	O
,	O
a	O
nonlinear	O
multivariate	B-General_Concept
time	O
trajectory	O
can	O
be	O
modeled	O
.	O
</s>
