# Inverse Logit Transformation

The inverse logit transformation converts parameter estimates from Logit Models into probabilities.

## Binary logit

Where $\mu$ is the fitted value from a Binary Logit Model, the probability is computed as:

$\Pr = \frac{1}{1 + e^{-\mu}}$

For example, $\mu = 2 \Rightarrow \Pr = 0.8807971$

## Multinomial logit

Where $\mu_j$ is the utility for the $j$th of $J$ alternatives, the probability of choosing the $j$th alternative is:

$\Pr_j = \frac{e^{\mu_j}}{\sum^J_{j'=1} e^{\mu_{j'}}}$

For example, if in a MaxDiff experiment analyzed using a logit model the three alternatives, A, B and C, estimated parameters of 0, 0.5 and 0.9, the probability of choosing the first alternative is $\frac{e^{0.5}}{e^0 + e^{0.5} + e^{0.9}} = 0.3071959$. And, the probability of choosing B if only B and C were available is: $\frac{e^{0.5}}{e^{0.5} + e^{0.9}} = 0.3775407$

## Also known as

Logistic Transformation