Mixed Logit - Random Taste Variation

Random Taste Variation

The standard logit model's "taste" cofficients, or 's, are fixed, which means the 's are the same for everyone. Mixed logit has different 's for each person (i.e., each decision maker.)

In the standard logit model, the utility of person n for alternative i is:

with

~ iid extreme value

For the mixed logit model, this specification is generalized by allowing to be random. The utility of person n for alternative i in the mixed logit model is:

with

~ iid extreme value

where θ are the parameters of the distribution of 's over the population, such as the mean and variance of .

Conditional on, the probability that person n chooses alternative i is the standard logit formula:

However, since is random and not known, the (unconditional) choice probability is the integral of this logit formula over the density of .

This model is also called the random coefficient logit model since is a random variable. It allows the slopes of utility (i.e., the marginal utility) to be random, which is an extension of the random effects model where only the intercept was stochastic.

Any probability density function can be specified for the distribution of the coefficients in the population, i.e., for . The most widely used distribution is normal, mainly for its simplicity. For coefficients that take the same sign for all people, such as a price coefficient that is necessarily negative or the coefficient of a desirable attribute, distributions with support on only one side of zero, like the lognormal, are used. When coefficients cannot logically be unboundedly large or small, then bounded distributions are often used, such as the or triangular distributions.