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How do you interpret a logistic regression coefficient as an odds ratio?

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Answer

  • In log(odds)  =  wT\operatorname{log}(\mathrm{odds})\; = \;w^{T} x, a one-unit increase in xjx_{j} multiplies the odds by exp(wj)\operatorname{exp}(w_{j}). exp(wj)\operatorname{exp}(w_{j}) is the odds ratio: 1.5 means a 50% relative increase in odds per unit of xjx_{j}.
  • Positive w    oddsw\; \to \;\mathrm{odds} ratio  >  1    outcome\mathrm{ratio}\; > \;1\; \to \;\mathrm{outcome} more likely; negative w -> < 1    less1\; \to \;\mathrm{less} likely.
  • For a categorical predictor with a reference level, exp(w)\operatorname{exp}(w) is the odds ratio between that category and the reference.
Check yourself — multiple choice
  • exp(wj)\operatorname{exp}(w_{j}) is the change in probability per unit of xjx_{j}
  • exp(wj)\operatorname{exp}(w_{j}) is the odds ratio: multiplier on the odds for a one-unit increase in xjx_{j}
  • exp(wj)\operatorname{exp}(w_{j}) equals R2R^{2}
  • wjw_{j} is the direct change in probability

exp(wj)  =  odds\operatorname{exp}(w_{j})\; = \;\mathrm{odds} ratio (multiplier on odds), not on the probability directly.

#logistic-regression#interpretability

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