Parsimony & overfitting
Slides are licensed under CC BY-NC-SA 4.0
Why not use a standard linear regression?
Normal distribution has a support of (-∞,∞), but we know the outcome variable takes on only two values.
Under some circumstances, results can be interpreted as proportions or probabilities, but this can lead to predicted values less than zero or more than one.
Replace Norm(μ, σ)with Bernoulli(p)
But now we need a “link” function With normal distribution, μ could take on any value, but p is restricted to [0,1]
Takes values between 0 and 1, and turns them into values between -∞ and ∞.
Takes values between -∞ and ∞, and turns them into values between 0 and 1.
⇔
Inverse Logit transformation
Why this model instead of the model we built in the first week of class?
Logistic regression allows us to include explanatory covariates.
Pr(α)
logit–1(Pr(α))
James Spader in Pretty in Pink