<s>
In	O
statistics	O
,	O
the	O
Goldfeld	B-General_Concept
–	I-General_Concept
Quandt	I-General_Concept
test	I-General_Concept
checks	O
for	O
homoscedasticity	B-General_Concept
in	O
regression	O
analyses	O
.	O
</s>
<s>
The	O
Goldfeld	B-General_Concept
–	I-General_Concept
Quandt	I-General_Concept
test	I-General_Concept
is	O
one	O
of	O
two	O
tests	O
proposed	O
in	O
a	O
1965	O
paper	O
by	O
Stephen	O
Goldfeld	O
and	O
Richard	O
Quandt	O
.	O
</s>
<s>
Both	O
a	O
parametric	O
and	O
nonparametric	B-General_Concept
test	I-General_Concept
are	O
described	O
in	O
the	O
paper	O
,	O
but	O
the	O
term	O
"	O
Goldfeld	B-General_Concept
–	I-General_Concept
Quandt	I-General_Concept
test	I-General_Concept
"	O
is	O
usually	O
associated	O
only	O
with	O
the	O
former	O
.	O
</s>
<s>
The	O
parametric	B-General_Concept
test	I-General_Concept
is	O
accomplished	O
by	O
undertaking	O
separate	O
least	B-Algorithm
squares	I-Algorithm
analyses	O
on	O
two	O
subsets	O
of	O
the	O
original	O
dataset	O
:	O
these	O
subsets	O
are	O
specified	O
so	O
that	O
the	O
observations	O
for	O
which	O
the	O
pre-identified	O
explanatory	O
variable	O
takes	O
the	O
lowest	O
values	O
are	O
in	O
one	O
subset	O
,	O
with	O
higher	O
values	O
in	O
the	O
other	O
.	O
</s>
<s>
The	O
parametric	B-General_Concept
test	I-General_Concept
assumes	O
that	O
the	O
errors	O
have	O
a	O
normal	O
distribution	O
.	O
</s>
<s>
There	O
is	O
an	O
additional	O
assumption	O
here	O
,	O
that	O
the	O
design	B-Algorithm
matrices	I-Algorithm
for	O
the	O
two	O
subsets	O
of	O
data	O
are	O
both	O
of	O
full	O
rank	O
.	O
</s>
<s>
The	O
test	B-General_Concept
statistic	I-General_Concept
used	O
is	O
the	O
ratio	O
of	O
the	O
mean	O
square	O
residual	O
errors	O
for	O
the	O
regressions	O
on	O
the	O
two	O
subsets	O
.	O
</s>
<s>
This	O
test	B-General_Concept
statistic	I-General_Concept
corresponds	O
to	O
an	O
F-test	B-General_Concept
of	I-General_Concept
equality	I-General_Concept
of	I-General_Concept
variances	I-General_Concept
,	O
and	O
a	O
one	O
-	O
or	O
two-sided	O
test	O
may	O
be	O
appropriate	O
depending	O
on	O
whether	O
or	O
not	O
the	O
direction	O
of	O
the	O
supposed	O
relation	O
of	O
the	O
error	O
variance	O
to	O
the	O
explanatory	O
variable	O
is	O
known	O
.	O
</s>
<s>
Increasing	O
the	O
number	O
of	O
observations	O
dropped	O
in	O
the	O
"	O
middle	O
"	O
of	O
the	O
ordering	O
will	O
increase	O
the	O
power	B-General_Concept
of	O
the	O
test	O
but	O
reduce	O
the	O
degrees	O
of	O
freedom	O
for	O
the	O
test	B-General_Concept
statistic	I-General_Concept
.	O
</s>
<s>
As	O
a	O
result	O
of	O
this	O
tradeoff	O
it	O
is	O
common	O
to	O
see	O
the	O
Goldfeld	B-General_Concept
–	I-General_Concept
Quandt	I-General_Concept
test	I-General_Concept
performed	O
by	O
dropping	O
the	O
middle	O
third	O
of	O
observations	O
with	O
smaller	O
proportions	O
of	O
dropped	O
observations	O
as	O
sample	O
size	O
increases	O
.	O
</s>
<s>
The	O
second	O
test	O
proposed	O
in	O
the	O
paper	O
is	O
a	O
nonparametric	B-General_Concept
one	I-General_Concept
and	O
hence	O
does	O
not	O
rely	O
on	O
the	O
assumption	O
that	O
the	O
errors	O
have	O
a	O
normal	O
distribution	O
.	O
</s>
<s>
The	O
test	B-General_Concept
statistic	I-General_Concept
used	O
to	O
test	O
for	O
homogeneity	O
is	O
the	O
number	O
of	O
peaks	O
in	O
this	O
list	O
:	O
ie	O
.	O
</s>
<s>
Critical	O
values	O
for	O
this	O
test	B-General_Concept
statistic	I-General_Concept
are	O
constructed	O
by	O
an	O
argument	O
related	O
to	O
permutation	B-General_Concept
tests	I-General_Concept
.	O
</s>
<s>
The	O
parametric	O
Goldfeld	B-General_Concept
–	I-General_Concept
Quandt	I-General_Concept
test	I-General_Concept
offers	O
a	O
simple	O
and	O
intuitive	O
diagnostic	O
for	O
heteroskedastic	B-General_Concept
errors	O
in	O
a	O
univariate	O
or	O
multivariate	O
regression	O
model	O
.	O
</s>
<s>
However	O
some	O
disadvantages	O
arise	O
under	O
certain	O
specifications	O
or	O
in	O
comparison	O
to	O
other	O
diagnostics	O
,	O
namely	O
the	O
Breusch	B-General_Concept
–	I-General_Concept
Pagan	I-General_Concept
test	I-General_Concept
,	O
as	O
the	O
Goldfeld	B-General_Concept
–	I-General_Concept
Quandt	I-General_Concept
test	I-General_Concept
is	O
somewhat	O
of	O
an	O
ad	O
hoc	O
test	O
.	O
</s>
<s>
Primarily	O
,	O
the	O
Goldfeld	B-General_Concept
–	I-General_Concept
Quandt	I-General_Concept
test	I-General_Concept
requires	O
that	O
data	O
be	O
ordered	O
along	O
a	O
known	O
explanatory	O
variable	O
.	O
</s>
<s>
The	O
parametric	B-General_Concept
test	I-General_Concept
orders	O
along	O
this	O
explanatory	O
variable	O
from	O
lowest	O
to	O
highest	O
.	O
</s>
<s>
If	O
the	O
error	O
structure	O
depends	O
on	O
an	O
unknown	O
variable	O
or	O
an	O
unobserved	O
variable	O
the	O
Goldfeld	B-General_Concept
–	I-General_Concept
Quandt	I-General_Concept
test	I-General_Concept
provides	O
little	O
guidance	O
.	O
</s>
<s>
For	O
example	O
,	O
when	O
faced	O
with	O
a	O
quadratic	O
function	O
mapping	O
the	O
explanatory	O
variable	O
to	O
error	O
variance	O
the	O
Goldfeld	B-General_Concept
–	I-General_Concept
Quandt	I-General_Concept
test	I-General_Concept
may	O
improperly	O
accept	O
the	O
null	O
hypothesis	O
of	O
homoskedastic	B-General_Concept
errors	O
.	O
</s>
<s>
Unfortunately	O
the	O
Goldfeld	B-General_Concept
–	I-General_Concept
Quandt	I-General_Concept
test	I-General_Concept
is	O
not	O
very	O
robust	O
to	O
specification	O
errors	O
.	O
</s>
<s>
The	O
Goldfeld	B-General_Concept
–	I-General_Concept
Quandt	I-General_Concept
test	I-General_Concept
detects	O
non-homoskedastic	O
errors	O
but	O
cannot	O
distinguish	O
between	O
heteroskedastic	B-General_Concept
error	O
structure	O
and	O
an	O
underlying	O
specification	O
problem	O
such	O
as	O
an	O
incorrect	O
functional	O
form	O
or	O
an	O
omitted	O
variable	O
.	O
</s>
<s>
Jerry	O
Thursby	O
proposed	O
a	O
modification	O
of	O
the	O
Goldfeld	B-General_Concept
–	I-General_Concept
Quandt	I-General_Concept
test	I-General_Concept
using	O
a	O
variation	O
of	O
the	O
Ramsey	B-General_Concept
RESET	I-General_Concept
test	I-General_Concept
in	O
order	O
to	O
provide	O
some	O
measure	O
of	O
robustness	O
.	O
</s>
<s>
Herbert	O
Glejser	O
,	O
in	O
his	O
1969	O
paper	O
outlining	O
the	O
Glejser	B-General_Concept
test	I-General_Concept
,	O
provides	O
a	O
small	O
sampling	B-Algorithm
experiment	I-Algorithm
to	O
test	O
the	O
power	B-General_Concept
and	O
sensitivity	O
of	O
the	O
Goldfeld	B-General_Concept
–	I-General_Concept
Quandt	I-General_Concept
test	I-General_Concept
.	O
</s>
<s>
His	O
results	O
show	O
limited	O
success	O
for	O
the	O
Goldfeld	B-General_Concept
–	I-General_Concept
Quandt	I-General_Concept
test	I-General_Concept
except	O
under	O
cases	O
of	O
"	O
pure	O
heteroskedasticity	B-General_Concept
"	O
—	O
where	O
variance	O
can	O
be	O
described	O
as	O
a	O
function	O
of	O
only	O
the	O
underlying	O
explanatory	O
variable	O
.	O
</s>
<s>
In	O
R	B-Language
,	O
the	O
Goldfeld-Quandt	B-General_Concept
Test	I-General_Concept
can	O
be	O
implemented	O
using	O
the	O
gqtest	O
function	O
of	O
the	O
lmtest	O
package	O
(	O
parametric	O
F	O
test	O
only	O
)	O
,	O
or	O
using	O
the	O
goldfeld_quandt	O
function	O
of	O
the	O
skedastic	O
package	O
(	O
both	O
parametric	O
F	O
test	O
and	O
nonparametric	B-General_Concept
peaks	O
test	O
)	O
.	O
</s>
