Ordered logit models

Question 1

Outcome variables

Answer 1

Similar as MNL in >2 outcomes. However choice is now ordered. For example:

• Low > Med > High
• Small > Med > Large

Question 2

Assumption of the model

Answer 2

Parallel lines assumption. For each level there is a separate regression line, those should be parallel.

Question 3

Separate regression lines..

Answer 3

• Only the intercepts are different

- All IV’s have the same coefficients in all equations

Question 4

Model specification

Answer 4

Yi is a latent variable i, individual i’s position on the latent scale. Yi is equal to a linear combination of parameters.

Question 5

Relation between the latent variable and the observed choice:

Answer 5

Yi = 1 if T0 < Yi <= T1
Yi = 2 if T1 < Yi <= T2
Yi = J if T0 < Yi <= TM
Yi = M if TM-1 < Yi <= TM
with;
M as the # of choices
J as a choice
T as the threshold values

Question 6

Estimation is via…

Answer 6

The maximum likelihood estimation.

Question 7

Interpretation is…

Answer 7

Only directly possible in terms of latent scale (not in terms of probabilities of choosing a certain category)

Question 8

Testing the assumption

Answer 8

Of lines… If the assumption does not hold:

• Try different link function (probit e.g.) instead of the standard logit function
• Collapse categories
• Eliminate non-critical IV’s
• Switch to Multi nomial Logit or probit, but you lose information on the ordering.