Multinomial Choice Models

Question 1

What is the estimation of discrete choice models called?

Answer 1

Maximum Likelihood estimation

This looks for the value of p that maximises LL

Question 2

What is the formula for the likelihood function of the binomial distribution?

Answer 2

Question 3

What is the formula for the maximum likelihood function?

Answer 3

Question 4

What is the formula for the log likelihood function?

Answer 4

Question 5

Why do we calculate a likelihood function in terms of logs?

Answer 5

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

Question 6

What are the limitations of the logit model?

Answer 6

Question 7

What are the properties of the Nested Logit model?

Answer 7

Question 8

What is the cumulative distribution function for ε_n = (ε_n1, . . . , ε_nJ ) in the nested logit model?

Answer 8

Question 9

What is the variance for ε_n = (ε_n1, . . . , ε_nJ ) in the nested logit model?

Answer 9

Question 10

Which models of λ_k are consistent with utility maximisation?

Answer 10

Question 11

What is the utility function for n facing j alternatives in the multinomial logit model?

Answer 11

Question 12

What is the variance of the error term in the multinomial logit model?

Answer 12

π²/6

Question 13

How do we find the probability of i in the multinomial logit model?

Answer 13

Question 14

How do we find the probability of i given ε_ni in the multinomial logit model?

Answer 14

Question 15

How do we calculate ε_ni in the multinomial logit model?

Answer 15

Question 16

What is the simple formula for the probability of i in the multinomial logit model?

Answer 16

Collapses to this as long as you assume V(ε)=ℼ²/6

Question 17

What are the properties of the logit probabilities? (3)

Answer 17

Question 18

Probability functions for n choosing i, each person in the sample, the log-likelihood function, and the maximum of the likelihood function

Answer 18

Question 19

What is a Direct Marginal Effect?

Answer 19

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.

Question 20

What is the cross-marginal effect?

Answer 20

•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.

Question 21

What is the direct elasticity?

Answer 21

•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.

Question 22

What is the cross elasticity?

Answer 22

•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.

Question 23

How do we calculate log likelihood ratio?

Answer 23

-2(LL_base – LL_model) ~ χ²_{number of new parameters}

Question 24

How do we calculate pseudo R-squared?

Answer 24

Pseudo-R² = 1 – (LL_model /LL_base)

Question 25

With J alternatives, how many alternative-specific constants can enter the model?

Answer 25

With J alternatives, at most J-1 alternative-specific constants can enter the model, with one of the constants normalised to zero.

Question 26

What is the red bus, blue bus problem?

Answer 26

Relevant to Independence from Irrelevant Alternatives (IIA)

Question 27

What is the variance of the error term in the ordered choice probit model?

Answer 27

1

Question 27

What is the variance of the ordered choice logit model?

Answer 27

π²/3

Question 28

How do we calculate the probability y\* is within the range of mu(j-1) and (j)?

Answer 28

Question 29

What are the probabilities for three ordered outcomes (when there are three mu's, y\*=0,1,2)?

Answer 29

Question 30

What is the log likelihood function of the ordered choice model?

Answer 30

Question 31

What is Willingness to Pay and how do we calculate it?

Answer 31

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.