1. Introduction to logistic regression a.k.a. Varbrul
Christopher Manning
Ling 236, 2002

2. Logistic regression
Describes association of binary (or discrete) response variable with set of explanatory variables (often, but not necessarily discrete)
Mean of binary response is probability
So, probability is related to regression-like model
Interpretation of coefficients is in terms of odds
Model, estimation and inference differ from linear regression, but use in practice is similar

3. GLMs: models for statistical analysis
Randomness
Link function
Explanatory
Model
Normal
Identity
Continuous
Linear regression
Categorical
Anal. of variance
Bernoulli
Logit
Mixed
Logistic regression
Poisson
Log
Loglinear
Multinomial
Generalized logit
Multinomial log. regress.

4. Risk measures
Odds
Odds ratio : ratio of odds (focus: risk indicator, covariate)
odds in target group / odds in control group [reference category]: ratio of favourable outcomes in target group over ratio in control group. The odds ratio measures the ‘belief’ in a given outcome in two different populations or under two different conditions. If the odds ratio is one, the two populations or conditions are similar.