Multinomial Choice Models Flashcards
What is the estimation of discrete choice models called?
Maximum Likelihood estimation
This looks for the value of p that maximises LL
What is the formula for the likelihood function of the binomial distribution?
What is the formula for the maximum likelihood function?
What is the formula for the log likelihood function?
Why do we calculate a likelihood function in terms of logs?
Because a computer may not be able to detect a very small number from the original likelihood function, so logs replace multiplication by summation to aid the software in finding the maximum value
What are the limitations of the logit model?
What are the properties of the Nested Logit model?
What is the cumulative distribution function for εn = (εn1, . . . , εnJ ) in the nested logit model?
What is the variance for εn = (εn1, . . . , εnJ ) in the nested logit model?
Which models of λk are consistent with utility maximisation?
What is the utility function for n facing j alternatives in the multinomial logit model?
What is the variance of the error term in the multinomial logit model?
π2/6
How do we find the probability of i in the multinomial logit model?
How do we find the probability of i given εni in the multinomial logit model?
How do we calculate εni in the multinomial logit model?
What is the simple formula for the probability of i in the multinomial logit model?
Collapses to this as long as you assume V(ε)=ℼ2/6
What are the properties of the logit probabilities? (3)
Probability functions for n choosing i, each person in the sample, the log-likelihood function, and the maximum of the likelihood function
What is a Direct Marginal Effect?
Direct Marginal Effect represents the change in the choice probability of an alternative given a unit change in a variable related to that same alternative.
What is the cross-marginal effect?
•Cross-Marginal Effect represents the change in the choice probability of an alternative given a unit change in a variable related to a competing alternative.
What is the direct elasticity?
•Direct elasticity measures the change in probability of choosing a particular alternative in the choice set with respect to a given percentage change in an attribute of that same alternative.
What is the cross elasticity?
•Cross-elasticity measures the change in probability of choosing a particular alternative in the choice set with respect to a given percentage change in an attribute of a competing alternative.
How do we calculate log likelihood ratio?
-2(LLbase – LLmodel) ~ χ2number of new parameters
How do we calculate pseudo R-squared?
Pseudo-R2 = 1 – (LLmodel /LLbase)
With J alternatives, how many alternative-specific constants can enter the model?
With J alternatives, at most J-1 alternative-specific constants can enter the model, with one of the constants normalised to zero.
What is the red bus, blue bus problem?
Relevant to Independence from Irrelevant Alternatives (IIA)
What is the variance of the error term in the ordered choice probit model?
1
What is the variance of the ordered choice logit model?
π2/3
How do we calculate the probability y* is within the range of mu(j-1) and (j)?
What are the probabilities for three ordered outcomes (when there are three mu’s, y*=0,1,2)?
What is the log likelihood function of the ordered choice model?
What is Willingness to Pay and how do we calculate it?
i.e. The WTP can be interpreted as follows: for males to be at the same level of
wellbeing as females they need to be compensated £X per year. Age is not
statistically significant so you would be interpreting that. With every
child, an individual would need to be compensated £X per year to be at the
same level of wellbeing as before.
