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Classification of Regression models
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Independent variable (exposure)
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| Univariable (single variable)
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Multivariable (multiple variables)
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How to derive coefficients [math]\displaystyle{ b_i }[/math]
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Dependent
variable
(outcome)
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Continuous
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- [math]\displaystyle{ Y = a + bX }[/math]
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- Multivariable† linear regression
- [math]\displaystyle{ Y = a + b_1X_1 + b_2X_2 + b_3X_3 + \cdots }[/math]
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Least squares method
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| Binary
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- Single binary logistic regression
- [math]\displaystyle{ \log Y = a + bX }[/math]
where [math]\displaystyle{ Y }[/math] is odds of outcome [math]\displaystyle{ \frac{p}{1-p} }[/math]
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- Multivariable† 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 [math]\displaystyle{ \frac{p}{1-p} }[/math]
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Maximum likelihood estimation method
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Multinominal
≥ 3
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- Single multinominal logistic regression
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- Multivariable† multinominal logistic regression
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| Ordinal
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- Single ordinal logistic regression
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- Multivariable† ordinal logistic regression
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| Rate ratio
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- Multivariable Poisson regression
- [math]\displaystyle{ \log Y = a + b_1X_1 + b_2X_2 + b_3X_3 + \cdots }[/math]
where [math]\displaystyle{ Y }[/math] is rate ratio [math]\displaystyle{ \frac{events_1/person \cdot time}{events_2/person \cdot time} }[/math]
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| Survival time
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- Multivariable 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]
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†'Multivariable' can be rephrased as 'Multiple'; Multivariable is NOT equal to 'Multivariate'!!
Penalized multivariable logistic regression model
Restricted cubic spline
