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

The Logit and Probit Models
• When the transformation function F is the logistic
function, the response probabilities are given by
P(
y
i
= 1 |
x
i
)
=
• And, when the transformation function F is the
cumulative density function (cdf) of the standard
normal distribution, the response probabilities are
x ′ β
x ′ β
1
i
i
2
given by
1 − s
P ( yi
= 1 | xi
) = Φ ( xi′
β ) = ∫ Φ ( s ) ds = ∫ e 2
• The Logit and Probit models are almost identical (see
the Figure next slide) and the choice of the model is
arbitrary, bi although l h h llogit i model d l has h certain i
advantages (simplicity and ease of interpretation)
1+
x i e ′ i e
e
β
x′
β
i
− ∞
− ∞
2π
ds