Multinomial Logit model

Question 1

What is the dependent variable?

Answer 1

Choice i out of J alternatives

Question 2

Multinomial logit model

Answer 2

• explanatory variables vary across households/individuals

- not across alternatives (display/price)

Question 3

Conditional logit model

Answer 3

• explanatory variables can also vary across alternatives not choice always AB but also CD or BC

Question 4

Outcome based on…

Answer 4

Utility of consumer i for choice J. However utility is compared to the base, which is often “no choice” but it can also be another brand.

Question 5

Assumption of the outcome function

Answer 5

Outcome function = utility function. Assumption is that consumers maximize utility.

Question 6

Estimation via…

Answer 6

Maximum likelihood or minimizing the distance between the probability and choice.

Question 7

Useful descriptive statistics are:

Answer 7

1) Market share of J brand
2) Age
3) Household size
4) Gender

Question 8

Validation

Answer 8

Value of the likelihood or the log likelihood ratio test can be used for validation

Question 9

Prediction via the model

Answer 9

Compute utilities for each brand/option. Option with highest utility (or probability) will be chosen.

Question 10

Market share calculation

Answer 10

Calculating the binomial outcomes or via probabilities

Question 11

Do we need to prepare the data?

Answer 11

Often, yes! For each observation often a single row. However we need for each alternative for everyone a single row.

Question 12

Interpretation options

Answer 12

1) Coef. -> only usefull for direction
2) Odds -> very complicated; hence not useful
3) Marginal effects

Question 13

Marginal effects options

Answer 13

1) own marginal effect

2) cross marginal effect

Question 14

Own marginal effect

Answer 14

Effect of a IV on the increase for option i. So price increase on option A.

Question 15

Cross marginal effect

Answer 15

A price increase for option C, on the probability of choosing B.

Question 16

Assumption of the MNL model

Answer 16

The independence of irrelevant alternatives

Question 17

IIA explanation

Answer 17

Suppose probability of choosing a red bus or bike is 50%|50%. Now add a blue buss, logically odds should be 25%|25%|50%. However since MNL assumes independence among alternatives probabilities will be 33%|33%|33%.

Question 18

Test for the IIA

Answer 18

If IIA is violated the test will be significant. H0 is that they are independent from each other. If violated? -> MNProbit or Nested Logit

Question 19

How to compare models?

Answer 19

• AIC
• BIC
• Log likelihood test
• Log likelihood value
• R-square

Question 20

Nested Logit, wHaT iS iT?

Answer 20

Grouping alternatives (choice options) in nests. Similar alternatives within nests, difference across nests. IIA should hold within nests, but not across nests.