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:

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

For example, $\mu =2\Rightarrow \mathrm{Pr}=0.8807971$

Multinomial logit

Where ${\mu }_j$ is the utility for the $j$th of $J$ alternatives, the probability of choosing the $j$th alternative is:

$\underset{j}{\mathrm{Pr}}=\frac{e^{{\mu }_j}}{\sum _{j^{\prime }=1}^J{e}^{{\mu }_{j^{\prime }}}}$

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