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
where
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.
After setting
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.