<s>
In	O
multivariate	B-General_Concept
statistics	I-General_Concept
,	O
exploratory	B-Algorithm
factor	I-Algorithm
analysis	I-Algorithm
(	O
EFA	O
)	O
is	O
a	O
statistical	O
method	O
used	O
to	O
uncover	O
the	O
underlying	O
structure	O
of	O
a	O
relatively	O
large	O
set	O
of	O
variables	O
.	O
</s>
<s>
When	O
developing	O
a	O
scale	O
,	O
researchers	O
should	O
use	O
EFA	O
first	O
before	O
moving	O
on	O
to	O
confirmatory	B-Algorithm
factor	I-Algorithm
analysis	I-Algorithm
(	O
CFA	O
)	O
.	O
</s>
<s>
The	O
maximum	O
likelihood	O
method	O
has	O
many	O
advantages	O
in	O
that	O
it	O
allows	O
researchers	O
to	O
compute	O
of	O
a	O
wide	O
range	O
of	O
indexes	O
of	O
the	O
goodness	O
of	O
fit	O
of	O
the	O
model	O
,	O
it	O
allows	O
researchers	O
to	O
test	O
the	O
statistical	B-General_Concept
significance	I-General_Concept
of	O
factor	O
loadings	O
,	O
calculate	O
correlations	O
among	O
factors	O
and	O
compute	O
confidence	O
intervals	O
for	O
these	O
parameters	O
.	O
</s>
<s>
ML	O
is	O
the	O
best	O
choice	O
when	O
data	O
are	O
normally	O
distributed	O
because	O
“	O
it	O
allows	O
for	O
the	O
computation	O
of	O
a	O
wide	O
range	O
of	O
indexes	O
of	O
the	O
goodness	O
of	O
fit	O
of	O
the	O
model	O
 [ and ] 	O
permits	O
statistical	B-General_Concept
significance	I-General_Concept
testing	O
of	O
factor	O
loadings	O
and	O
correlations	O
among	O
factors	O
and	O
the	O
computation	O
of	O
confidence	O
intervals	O
”	O
.	O
</s>
<s>
These	O
include	O
Kaiser	O
's	O
(	O
1960	O
)	O
eigenvalue-greater-than-one	O
rule	O
(	O
or	O
K1	O
rule	O
)	O
,	O
Cattell	O
's	O
(	O
1966	O
)	O
scree	B-Application
plot	I-Application
,	O
Revelle	O
and	O
Rocklin	O
's	O
(	O
1979	O
)	O
very	O
simple	O
structure	O
criterion	O
,	O
model	O
comparison	O
techniques	O
,	O
Raiche	O
,	O
Roipel	O
,	O
and	O
Blais	O
's	O
(	O
2006	O
)	O
acceleration	O
factor	O
and	O
optimal	O
coordinates	O
,	O
Velicer	O
's	O
(	O
1976	O
)	O
minimum	O
average	O
partial	O
,	O
Horn	O
's	O
(	O
1965	O
)	O
parallel	B-Algorithm
analysis	I-Algorithm
,	O
and	O
Ruscio	O
and	O
Roche	O
's	O
(	O
2012	O
)	O
comparison	O
data	O
.	O
</s>
<s>
In	O
an	O
attempt	O
to	O
overcome	O
the	O
subjective	O
weakness	O
of	O
Cattell	O
's	O
(	O
1966	O
)	O
scree	B-Application
test	I-Application
,	O
presented	O
two	O
families	O
of	O
non-graphical	O
solutions	O
.	O
</s>
<s>
Recent	O
simulation	O
studies	O
in	O
the	O
field	O
of	O
psychometrics	O
suggest	O
that	O
the	O
parallel	B-Algorithm
analysis	I-Algorithm
,	O
minimum	O
average	O
partial	O
,	O
and	O
comparative	O
data	O
techniques	O
can	O
be	O
improved	O
for	O
different	O
data	O
situations	O
.	O
</s>
<s>
The	O
goal	O
of	O
factor	O
rotation	O
is	O
to	O
rotate	B-Algorithm
factors	O
in	O
multidimensional	O
space	O
to	O
arrive	O
at	O
a	O
solution	O
with	O
best	O
simple	O
structure	O
.	O
</s>
<s>
There	O
are	O
two	O
main	O
types	O
of	O
factor	O
rotation	O
:	O
orthogonal	B-Application
and	O
oblique	O
rotation	O
.	O
</s>
<s>
Orthogonal	B-Application
rotations	O
constrain	O
factors	O
to	O
be	O
perpendicular	O
to	O
each	O
other	O
and	O
hence	O
uncorrelated	O
.	O
</s>
<s>
An	O
advantage	O
of	O
orthogonal	B-Application
rotation	O
is	O
its	O
simplicity	O
and	O
conceptual	O
clarity	O
,	O
although	O
there	O
are	O
several	O
disadvantages	O
.	O
</s>
<s>
In	O
the	O
social	O
sciences	O
,	O
there	O
is	O
often	O
a	O
theoretical	O
basis	O
for	O
expecting	O
constructs	O
to	O
be	O
correlated	O
,	O
therefore	O
orthogonal	B-Application
rotations	O
may	O
not	O
be	O
very	O
realistic	O
because	O
they	O
do	O
not	O
allow	O
this	O
.	O
</s>
<s>
Also	O
,	O
because	O
orthogonal	B-Application
rotations	O
require	O
factors	O
to	O
be	O
uncorrelated	O
,	O
they	O
are	O
less	O
likely	O
to	O
produce	O
solutions	O
with	O
simple	O
structure	O
.	O
</s>
<s>
Varimax	B-Algorithm
rotation	I-Algorithm
is	O
an	O
orthogonal	B-Application
rotation	O
of	O
the	O
factor	O
axes	O
to	O
maximize	O
the	O
variance	O
of	O
the	O
squared	O
loadings	O
of	O
a	O
factor	O
(	O
column	O
)	O
on	O
all	O
the	O
variables	O
(	O
rows	O
)	O
in	O
a	O
factor	O
matrix	O
,	O
which	O
has	O
the	O
effect	O
of	O
differentiating	O
the	O
original	O
variables	O
by	O
extracted	O
factor	O
.	O
</s>
<s>
A	O
varimax	B-Algorithm
solution	O
yields	O
results	O
which	O
make	O
it	O
as	O
easy	O
as	O
possible	O
to	O
identify	O
each	O
variable	O
with	O
a	O
single	O
factor	O
.	O
</s>
<s>
This	O
is	O
the	O
most	O
common	O
orthogonal	B-Application
rotation	O
option	O
.	O
</s>
<s>
Quartimax	O
rotation	O
is	O
an	O
orthogonal	B-Application
rotation	O
that	O
maximizes	O
the	O
squared	O
loadings	O
for	O
each	O
variable	O
rather	O
than	O
each	O
factor	O
.	O
</s>
<s>
Equimax	O
rotation	O
is	O
a	O
compromise	O
between	O
varimax	B-Algorithm
and	O
quartimax	O
criteria	O
.	O
</s>
<s>
These	O
rotations	O
may	O
produce	O
solutions	O
similar	O
to	O
orthogonal	B-Application
rotation	O
if	O
the	O
factors	O
do	O
not	O
correlate	O
with	O
each	O
other	O
.	O
</s>
<s>
The	O
so-called	O
unrotated	O
solution	O
is	O
in	O
fact	O
an	O
orthogonal	B-Application
rotation	O
that	O
maximizes	O
the	O
variance	O
of	O
the	O
first	O
factors	O
.	O
</s>
<s>
This	O
may	O
be	O
useful	O
if	O
many	O
variables	O
are	O
correlated	O
with	O
each	O
other	O
,	O
as	O
revealed	O
by	O
one	O
or	O
a	O
few	O
dominating	O
eigenvalues	O
on	O
a	O
scree	B-Application
plot	I-Application
.	O
</s>
