The relation between baseline logit and conditional logit models¶
Baseline-category logit models can be expressed as particular form of conditional logit models. In a conditional logit model (without random effects) the probability that individual chooses alternative from choice set is
In a baseline-category logit model, the set of alternatives is the same for all individuals that is and the linear part of the model can be written like:
where the coefficients in the equation for baseline category are all zero, i.e.
we have for the log-odds:
where , , etc.
That is, the baseline-category logit model is translated into a conditional logit model where the alternative-specific values of the attribute variables are interaction terms composed of alternativ-specific dummes and individual-specific values of characteristics variables.
Analogously, the random-effects extension of the baseline-logit model can be translated into a random-effects conditional logit model where the random intercepts in the logit equations of the baseline-logit model are translated into random slopes of category-specific dummy variables.