Binary outcomes

Binary outcomes are outcome variables with only two possible values, e.g.:

• Failure or success
• No or yes
• Fail or pass
• Employed or unemployed
• Depressed or not depressed

To represent the binary outcome numerically, we must represent one level as 0 and the other as 1. The level that we represent as 1 is the level that we want the logistic regression model to estimate the probability/log-odds of.

For example:

• Failure or success
  • Failure = 0
  • Success = 1
  • The model will estimate the log-odds of success
• No or yes
  • No = 0
  • Yes = 1
  • The model will estimate the log-odds of a “Yes” response
• Fail or pass
  • Fail = 0
  • Pass = 1
  • The model will estimate the log-odds of a pass
• Employed or unemployed
  • Employed = 0
  • Unemployed = 1
  • The model will estimate the log-odds of being unemployed
• Depressed or not depressed
  • Depressed = 0
  • Not depressed = 1
  • The model will estimate the log-odds of not being depressed

Note: although both use 0s and 1s, binary outcomes are not the same thing as a treatment-coded predictor, and binary outcomes have no reference level.