Regression model

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Basics & Definition
Epidemiology
Odds in statistics and Odds in a horse race
Collider bias
Data distribution
Statistical test
Regression model
Multivariate analysis
Marginal effects
Prediction and decision
Table-related commands in STATA
Missing data and imputation

Classification of Regression models

Independent variable (exposure)
Monovariable (single variable) Multivariable (multiple variables)
Dependent
variable
(outcome)
Continuous
  • Simple linear regression
[math]\displaystyle{ Y = a + bX }[/math]
  • Multiple† linear regression
[math]\displaystyle{ Y = a + b_1X_1 + b_2X_2 + b_3X_3 + \cdots }[/math]
Binary
  • Simple binary logistic regression
[math]\displaystyle{ \log Y = a + bX }[/math]
where [math]\displaystyle{ Y }[/math] is odds of outcome
  • Multiple† binary logistic regression
[math]\displaystyle{ \log Y = a + b_1X_1 + b_2X_2 + b_3X_3 + \cdots }[/math]
where [math]\displaystyle{ Y }[/math] is odds of outcome
Multinominal
≥ 3
  • Simple multinominal logistic regression
  • Multiple† multinominal logistic regression
Ordinal
  • Simple ordinal logistic regression
  • Multiple† ordinal logistic regression
Survival time
  • Multiple proportional hazard regression
    = Cox hazard regression
[math]\displaystyle{ \log h(T) = \log h_0(T) + b_1X_1 + b_2X_2 + b_3X_3 + \cdots }[/math]
where [math]\displaystyle{ h(T) }[/math] is the hazard at time [math]\displaystyle{ T }[/math]
and [math]\displaystyle{ h_0(T) }[/math] is the baseline hazard at time [math]\displaystyle{ T }[/math]

†'Multiple' can be rephrased as 'Multivariable'; NOT 'Multivariate'!!