21 Lecture 12 - 2019
21.1 Relative and absolute effects
Effect sizes two ways
- Relative effect scale: parameters have relative differences in their effect
- Absolute effect scale: used for predictions
Proportional odds eg treatment 4 and 2
post ← extract.samples
mean
0.9 = 90% of previous odds
Therefore 2→4 expects reduction of odds by 10%
But this disregards base rate
Risk of relative effects like proportional odds is they don’t consider absolute likelihood
Relative shark vs absolute deer - need both
21.2 Logistic regression
0, 1 trials (Bernoulli trials)
Aggregate binomial: aggregated from each 0, 1 to counts for each category
Example - UC Berkeley 1970s
Gender → Department → Acceptance, Gender → Acceptance
Recall: regressions are very literal to exactly the question you are asking
Model 1
Acceptance ~ Binomial(N, p)
logit(p) = alpha [gender]
Statistical question: what are the average probabilities of admission by gender across all departments?
Causal question: what is the total causal influence of gender?
It’s asking for the total effect, not the discrimination effect
Therefore, all paths are in play (Gender → Department → Acceptance, Gender → Acceptance)
Model 2
Close the backdoor.
Acceptance ~ Binomial(N, p)
logit(p) = alpha [gender] + beta department
Statistical question: what is the average difference in probability of admission for genders within department?
Causal question: what is the direct influence of gender?
These are equally valid, but different questions.