<s>
In	O
statistics	O
and	O
econometrics	O
,	O
the	O
multinomial	B-General_Concept
probit	I-General_Concept
model	I-Architecture
is	O
a	O
generalization	O
of	O
the	O
probit	B-Architecture
model	I-Architecture
used	O
when	O
there	O
are	O
several	O
possible	O
categories	O
that	O
the	O
dependent	O
variable	O
can	O
fall	O
into	O
.	O
</s>
<s>
As	O
such	O
,	O
it	O
is	O
an	O
alternative	O
to	O
the	O
multinomial	O
logit	O
model	O
as	O
one	O
method	O
of	O
multiclass	B-General_Concept
classification	I-General_Concept
.	O
</s>
<s>
It	O
is	O
not	O
to	O
be	O
confused	O
with	O
the	O
multivariate	O
probit	B-Architecture
model	I-Architecture
,	O
which	O
is	O
used	O
to	O
model	O
correlated	O
binary	O
outcomes	O
for	O
more	O
than	O
one	O
independent	O
variable	O
.	O
</s>
<s>
The	O
multinomial	B-General_Concept
probit	I-General_Concept
model	O
is	O
a	O
statistical	O
model	O
that	O
can	O
be	O
used	O
to	O
predict	O
the	O
likely	O
outcome	O
of	O
an	O
unobserved	O
multi-way	O
trial	O
given	O
the	O
associated	O
explanatory	O
variables	O
.	O
</s>
<s>
Multinomial	B-General_Concept
probit	I-General_Concept
is	O
often	O
written	O
in	O
terms	O
of	O
a	O
latent	O
variable	O
model	O
:	O
</s>
<s>
Note	O
that	O
this	O
model	O
allows	O
for	O
arbitrary	O
correlation	O
between	O
the	O
error	B-General_Concept
variables	I-General_Concept
,	O
so	O
that	O
it	O
does	O
n't	O
necessarily	O
respect	O
independence	O
of	O
irrelevant	O
alternatives	O
.	O
</s>
<s>
When	O
is	O
the	O
identity	O
matrix	O
(	O
such	O
that	O
there	O
is	O
no	O
correlation	O
or	O
heteroscedasticity	B-General_Concept
)	O
,	O
the	O
model	O
is	O
called	O
independent	O
probit	O
.	O
</s>
<s>
For	O
details	O
on	O
how	O
the	O
equations	O
are	O
estimated	O
,	O
see	O
the	O
article	O
Probit	B-Architecture
model	I-Architecture
.	O
</s>
