Simulation
Unfortunately there is no closed form for the integral that enters the choice probability, and so the researcher must simulate Pn. Fortunately for the researcher, simulating Pn can be very simple. There are four basic steps to follow
1. Take a draw from the probability density function that you specified for the 'taste' coefficients. That is, take a draw from and label the draw, for representing the first draw.
2. Calculate . (The conditional probability.)
3. Repeat many times, for .
4. Average the results
Then the formula for the simulation look like the following,
where R is the total number of draws taken from the distribution, and r is one draw.
Once this is done you will have a value for the probability of each alternative i for each respondent n.
Read more about this topic: Mixed Logit
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