L9 - Ordered Choice Models Flashcards
How do we translate latent utility into a discrete outcome?
- latent = unobserved
- we have a continuous scale that is broken up into chucks by different μi
- Each chunk is associate with a certain category that is labelled 1 through J
![](https://s3.amazonaws.com/brainscape-prod/system/cm/374/626/045/a_image_thumb.png?1645809896)
What does the underlying probability diagram look like for an order choice model?
- broken up into 3 chucks
![](https://s3.amazonaws.com/brainscape-prod/system/cm/374/631/383/a_image_thumb.png?1645810209)
What normalisations do I need to impose on the model parameter μ?
- like other models –> coefficients, like in other models, are once again uninformative –> including the sign or mangitude of it
![](https://s3.amazonaws.com/brainscape-prod/system/cm/374/632/202/a_image_thumb.png?1645810477)
What is the ordered probability?
- Converts into a cumulative function of the error term
![](https://s3.amazonaws.com/brainscape-prod/system/cm/374/632/699/a_image_thumb.png?1645810772)
How can we represented the order probability of three outcomes using a cumulative distribution function?
![](https://s3.amazonaws.com/brainscape-prod/system/cm/374/633/313/a_image_thumb.png?1645811284)
What is the log-likelihood function of this model?
- log function is summing across different categories and different individuals
![](https://s3.amazonaws.com/brainscape-prod/system/cm/374/633/415/a_image_thumb.png?1645811373)
Why are only 3 mu’s estimated for a 5 category choice order model?
- 4 mu’s needed to split model into 4 strips
- 1 mu is alwyas normalised to 0
- So only need to estimate 3
![](https://s3.amazonaws.com/brainscape-prod/system/cm/374/634/375/a_image_thumb.png?1645812329)
How do you calculate the partial effects of an order choice model?
- 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
- Can work these out in two different ways:
- how the probability changes when our explantory variable changes by 1 unit
- 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???
- Would leave you with a very small result
![](https://s3.amazonaws.com/brainscape-prod/system/cm/374/634/522/a_image_thumb.png?1645812397)
How do partial effect change the graph of the probabilities?
- 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
![](https://s3.amazonaws.com/brainscape-prod/system/cm/374/635/605/a_image_thumb.png?1645813252)
What are the three rules in determine the direction of a marginal effect?
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”)
What happens to the categories in the ‘tail’ of the order choice model distribution?
- usually there are so little people choosing the extreme values that researchers may combine them into a single category
Well-being analysis: example of data we would perform an ordered choice model on?
- 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
![](https://s3.amazonaws.com/brainscape-prod/system/cm/376/849/224/a_image_thumb.png?1647350973)
With the log-likelihood index (Goodness of Fit) what are we looking at in stata?
- 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
Well-being data: How do we interpret marginal effects?
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
- Report the probability from the base category (Gender is coded 1 for men, 0 for female so…)
![](https://s3.amazonaws.com/brainscape-prod/system/cm/376/850/392/a_image_thumb.png?1647352131)
What is Willingness to Pay (WTP) under order choice models?
- 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
- 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
- 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
*
- negative signs would be to paying to avoid
![](https://s3.amazonaws.com/brainscape-prod/system/cm/376/850/837/a_image_thumb.png?1647352523)