Introduction to logistic regression a.k.a. Varbrul

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Introduction to logistic regression a.k.a. Varbrul

• Christopher Manning
• Ling 236, 2002

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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

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