L9 - Ordered Choice Models

Question 1

How do we translate latent utility into a discrete outcome?

Answer 1

• latent = unobserved
  
  • we have a continuous scale that is broken up into chucks by different μ_i
  • Each chunk is associate with a certain category that is labelled 1 through J

Question 2

What does the underlying probability diagram look like for an order choice model?

Answer 2

• broken up into 3 chucks

Question 3

What normalisations do I need to impose on the model parameter μ?

Answer 3

• like other models –> coefficients, like in other models, are once again uninformative –> including the sign or mangitude of it

Question 4

What is the ordered probability?

Answer 4

• Converts into a cumulative function of the error term

Question 5

How can we represented the order probability of three outcomes using a cumulative distribution function?

Answer 5

Question 6

What is the log-likelihood function of this model?

Answer 6

• log function is summing across different categories and different individuals

Question 7

Why are only 3 mu’s estimated for a 5 category choice order model?

Answer 7

• 4 mu’s needed to split model into 4 strips
  
  • 1 mu is alwyas normalised to 0
  • So only need to estimate 3

Question 8

How do you calculate the partial effects of an order choice model?

Answer 8

• partial effects can be marginal effects or elasticities –> we are just sticking to marginal
  
  • how the probability changes when our explantory variable changes by 1 unit
    
    • Can work these out in two different ways:
      
      • Take an average individual an compute
      • work out for all individuals and then average the final results –> recommended
• for dummy variables it is just the difference between probabilities
  
  • Would leave you with a very small result
    
    • Dummy variable is done by comparing one to the base category???

Question 9

How do partial effect change the graph of the probabilities?

Answer 9

• Top graph represents the average individual (with the average in each of the 5 categories)
• the partial effect lead to an increase/decrease in probabilities
  
  • This is represented in the graph by a change in the size of the category strips

Question 10

What are the three rules in determine the direction of a marginal effect?

Answer 10

DOESNT REALLY MAKE SENSE

• The effects is positive when:
  
  • •Increases in that variable will increase the probability in the highest cell and decrease the probability in the lowest cell.
  • •The sum of all the changes will be zero.
  • •There will be one sign change (“single-crossing feature”)

Question 11

What happens to the categories in the ‘tail’ of the order choice model distribution?

Answer 11

• usually there are so little people choosing the extreme values that researchers may combine them into a single category

Question 12

Well-being analysis: example of data we would perform an ordered choice model on?

Answer 12

• Data generated created a negatively skewed histogram with the median value of happiness being a 7/10
• Hardly any individuals choosing 0,1,2 and 3 –> can combine these into one category

Question 13

With the log-likelihood index (Goodness of Fit) what are we looking at in stata?

Answer 13

• Chi-squared of the MLE
  
  • Null: this model is not greater than an alternative model containing just a constant term
  • If it is greater than the critical value we reject the null OR if the P-value is less than 0.05 then we reject the null

Question 14

Well-being data: How do we interpret marginal effects?

Answer 14

Only focus on the most extreme categories (especially for the coursework)

• When one variable increases by one unit, (if it affect the probability positively)
  
  • The top category expands
  • The lowest shrinks
  • There is only one sign change
• Binary variables
  
  • Report the probability from the base category (Gender is coded 1 for men, 0 for female so…)
    
    • 0.74% of men are less likely to report on extreme happiness than women

Question 15

What is Willingness to Pay (WTP) under order choice models?

Answer 15

• Other way of interpretting the results of order choice models
• Also called marginal rate of substitution
  
  • Bottom variable has to be the coefficient of the variable denoted in monetary units e.g. income, price –> otherwise we wouldnt be able to calculate this
    
    • Both variables coefficients also need to be signficiant
• WTP measure are good as the scale of the coefficients is cancelled in the ratio
  
  • Criticism –> dont take this as an exact value individuals would pay, just an overall value
• Say WTP(marriage) is 137.673
  
  • Individuals are willing to pay £137,673 a year to stay married
  • This is can be used to compare different variables
    
    • negative signs would be to paying to avoid
      *