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Econometrics > Multinomial Choice Models > Flashcards

Multinomial Choice Models Flashcards

1
Q

What is the estimation of discrete choice models called?

A

Maximum Likelihood estimation

This looks for the value of p that maximises LL

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2
Q

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

A
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3
Q

What is the formula for the maximum likelihood function?

A
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4
Q

What is the formula for the log likelihood function?

A
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5
Q

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

A

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

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6
Q

What are the limitations of the logit model?

A
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7
Q

What are the properties of the Nested Logit model?

A
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8
Q

What is the cumulative distribution function for εn = (εn1, . . . , εnJ ) in the nested logit model?

A
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9
Q

What is the variance for εn = (εn1, . . . , εnJ ) in the nested logit model?

A
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10
Q

Which models of λk are consistent with utility maximisation?

A
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11
Q

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

A
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12
Q

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

A

π2/6

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13
Q

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

A
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14
Q

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

A
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15
Q

How do we calculate εni in the multinomial logit model?

A
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16
Q

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

A

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

17
Q

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

A
18
Q

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

A
19
Q

What is a Direct Marginal Effect?

A

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.

20
Q

What is the cross-marginal effect?

A

•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.

21
Q

What is the direct elasticity?

A

•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.

22
Q

What is the cross elasticity?

A

•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.

23
Q

How do we calculate log likelihood ratio?

A

-2(LLbase – LLmodel) ~ χ2number of new parameters

24
Q

How do we calculate pseudo R-squared?

A

Pseudo-R2 = 1 – (LLmodel /LLbase)

25
Q

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

A

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

26
Q

What is the red bus, blue bus problem?

A

Relevant to Independence from Irrelevant Alternatives (IIA)

27
Q

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

A

1

27
Q

What is the variance of the ordered choice logit model?

A

π2/3

28
Q

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

A
29
Q

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

A
30
Q

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

A
31
Q

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

A

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.

Econometrics (10 decks)

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