<s>
Parallel	B-Algorithm
analysis	I-Algorithm
,	O
also	O
known	O
as	O
Horn	B-Algorithm
's	I-Algorithm
parallel	I-Algorithm
analysis	I-Algorithm
,	O
is	O
a	O
statistical	O
method	O
used	O
to	O
determine	O
the	O
number	O
of	O
components	O
to	O
keep	O
in	O
a	O
principal	B-Application
component	I-Application
analysis	I-Application
or	O
factors	O
to	O
keep	O
in	O
an	O
exploratory	B-Algorithm
factor	I-Algorithm
analysis	I-Algorithm
.	O
</s>
<s>
The	O
method	O
compares	O
the	O
eigenvalues	O
generated	O
from	O
the	O
data	O
matrix	O
to	O
the	O
eigenvalues	O
generated	O
from	O
a	O
Monte-Carlo	B-Algorithm
simulated	I-Algorithm
matrix	O
created	O
from	O
random	O
data	O
of	O
the	O
same	O
size	O
.	O
</s>
<s>
Parallel	B-Algorithm
analysis	I-Algorithm
is	O
regarded	O
as	O
one	O
of	O
the	O
more	O
accurate	O
methods	O
for	O
determining	O
the	O
number	O
of	O
factors	O
or	O
components	O
to	O
retain	O
.	O
</s>
<s>
Since	O
its	O
original	O
publication	O
,	O
multiple	O
variations	O
of	O
parallel	B-Algorithm
analysis	I-Algorithm
have	O
been	O
proposed	O
.	O
</s>
<s>
Other	O
methods	O
of	O
determining	O
the	O
number	O
of	O
factors	O
or	O
components	O
to	O
retain	O
in	O
an	O
analysis	O
include	O
the	O
scree	B-Application
plot	I-Application
,	O
Kaiser	O
rule	O
,	O
or	O
Velicer	O
's	O
MAP	O
test	O
.	O
</s>
<s>
Anton	O
Formann	O
provided	O
both	O
theoretical	O
and	O
empirical	O
evidence	O
that	O
parallel	B-Algorithm
analysis	I-Algorithm
's	O
application	O
might	O
not	O
be	O
appropriate	O
in	O
many	O
cases	O
since	O
its	O
performance	O
is	O
influenced	O
by	O
sample	O
size	O
,	O
item	O
discrimination	O
,	O
and	O
type	O
of	O
correlation	O
coefficient	O
.	O
</s>
<s>
Parallel	B-Algorithm
analysis	I-Algorithm
has	O
been	O
implemented	O
in	O
JASP	B-Application
,	O
SPSS	B-Algorithm
,	O
SAS	B-Language
,	O
STATA	B-Algorithm
,	O
and	O
MATLAB	B-Language
and	O
in	O
multiple	O
packages	O
for	O
the	O
R	B-Language
programming	I-Language
language	I-Language
,	O
including	O
the	O
psych	O
multicon	O
,	O
hornpa	O
,	O
and	O
paran	O
packages	O
.	O
</s>
