General Models
As mentioned earlier, calculation and justification of choice probabilities rely on the properties of the error (i.e. the unobservables) distribution function the researcher specifies. Here is the quick overview of frequently used models that each differs in specification
1. Logit:
- Assumes unobserved factors have the same variance with zero correlation across alternatives.
- iid extreme value unobserved factors
- The cumulative distribution of difference in extreme values is Logistics function
- Logistics function has a closed form solution => No simulation necessary.
2. GEV (Generalized extreme value distribution)
- Allows correlation in unobserved factors across alternatives.
- iid extreme value unobserved factors
- The cumulative distribution of difference in extreme values is Logistics function
- Logistics function has a closed form solution => No simulation necessary.
3. Probit
- Unobserved factors have a jointly normal distribution.
- No closed form for the cumulative distribution of normal distribution. Simulation necessary.
4. Mixed logit
- Allows any distribution in unobserved factors
- No closed form for the cumulative distribution of normal distribution. Simulation necessary.
Read more about this topic: Choice Model Simulation
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