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Introduction to Logistic Regression: Understanding Binary Response Variables

Logistic regression explains the relationship between a binary or discrete response variable and a set of explanatory variables. It utilizes probabilities to model outcomes, with coefficients interpreted in terms of odds. Although it differs from linear regression in terms of modeling, estimation, and inference, its practical use is similar. This approach allows for the analysis of risk measures, odds, and odds ratios, enabling comparisons of outcomes across different populations or conditions.

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Introduction to Logistic Regression: Understanding Binary Response Variables

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  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

  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.

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