Logit, Probit and Tobit: Models for Categorical and Limited ...

Models for Polytomous Data
• B) Polytomous Case
– Here we need to distinguish between purely
nominal variables and really ordinal variables.
– When the variable is purely nominal, we can
extend the dichotomous logit g model, , using gone
of
the categories as reference and modeling the other
responses j=1,2,..m-1 compared to the reference.
• Example: In the case of 3 categories, using the 3rd category
as the reference, logit p1 = ln(p1/p3) and logit p2 = ln(p2/p3), which will give g two sets of parameter p estimates.
exp( β 1x
)
P(
y = 1)
=
1 + exp( β 1x
) + exp( β 2 x)
exp( β 2 x)
P ( y = 2 ) =
1 +
exp( β x)
+ exp( β x)
P(
y =
3)
=
1
1
1 + exp( β x)
+ exp( β x)
1
2
2