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Logistic Regression

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Model

\log\left(\frac{p}{1-p}\right) = \beta_0 + \beta_1 x_1 + \cdots + \beta_k x_k

p = \frac{e^{\beta_0 + \beta_1 x_1 + \cdots}}{1 + e^{\beta_0 + \beta_1 x_1 + \cdots}}

Likelihood:

L(\beta) = \prod_{i: y_i=1} p_i \prod_{i: y_i=0} (1-p_i)

Maximized using IRLS (iteratively reweighted least squares).

Deviance: $-2 \ln(L)$ (compare to null model)
AIC: Deviance $+ 2p$
ROC curve: Plot TPR vs FPR. AUC = area under curve.
Confusion matrix: Accuracy, precision, recall, F1 Join Discord PreviousGeneralized Linear ModelsNextMixed Effects Models