Inverse Logit Transformation

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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 jth of J alternatives, the probability of choosing the jth 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