GLM - Binary Target

Question 1

Bernoulli Distribution

Answer 1

Can only take two possible values: 0 or 1
Probability the random variable = 1 is also the variables mean (mu)

probability of success = mu
Odds of success = mu/(1-mu) - how many times is mu bigger than (1-mu)
mu= odds/(1+odds)

Link functions - all difficult to understand, but logit link easiest of the three
-logit link = ln(mu/(1-mu)) - logit link is the natural log of the success odds
-probit link = Phi-1 (mu)
-complementary log-log link = ln[-ln(1-mu)]

Question 2

Logistic Regression

Answer 2

GLM with binomial target and logit link

Given the logit link, the interpretation of b_j is:
->for every unit increase in x_j, the predicted odds changes by a factor of e^(b_j), assuming all other predictors are held constant for j=1, …, p

As a predicted probability is denoted by mu^, let a target prediction be denoted by y^. The cutoff is the predicted probability value that separates the target predictions; an observation with a mu^ above the cutoff is predicted to be a positive observations (i.e. y^ = 1)