Logit, probit and linear probability

Question 2

When should you use a logit? Are the errors heteroskedastic or homoskedastic?

Answer 2

Binary outcomes. 0 is failure, 1 is success

Note that we actually expect heteroskedastic errors, with D_i over [0,1] since X can take only two values the errors are dependent on X.

Question 3

What are key weaknesses of linear probability model? Strenghts?

Answer 3

1) Predicted probability of success/failure can be outside the [0,1] internal
2) We are guaranteed heteroskedasticity in the residuals
3) Strength is ease of interpretation

Question 4

When is MLE more efficient than OLS?

Answer 4

Yes for large samples and bernoulli variables. For binary outcome variables, linear probability model (OLS) is not most efficient, it’s logit/probit because they can be put into the MLE funciton.

Question 5

What is a major drawback of the logit and probit models?

Answer 5

Difficult to interpret coefficients.

Question 6

What is an ordered multinominal logit or probit?

Answer 6

You have an outcome variable that has more than 2 mutually exclusive categories with some natural ordering (ex. health rated on a 1-5 scale).

Question 7

What is an ordered LPM or an ordered Probit?

Answer 7

Bins (ex. income range) for outcomes

Question 8

What is interval regression?

Answer 8

When you have a continuous dependent variable that is divided into intervals, eg reporting income ranges which can be solved using the MLE technique.

Question 9

What is an unordered multnomial outcome model?

Answer 9

Your outcome can be divided into mutually exclusive categories that do not have any ordering, such as where to get dinner.

Question 10

How can you fix the problems with heteroskedastic errors in LPM?

Answer 10

1) Robust standards errors (usually not still efficient though)
2) Perform weighted least squares using 1/V[ei|Xi]

Only problem is, we can’t give observations negative weight of a weight greater than one so any observations with predicted values outside the unit interval (0,1) must be dropped from the weighted regression so omission will bias our estimates unless there’s few/no observations outside the (0,1) interval.

Question 11

What is the difference between the multinomial, conditional and mixed conditional logit models?

Answer 11

1) Multinomial logit has only individual (Xi)-specific covariates
2) Conditional logit model has only option-specific covariates (so restaurant-specific characteristics, for example)
3) Mixed conditional logit model has both option-specific and individual-specific covariates