Logistic regression: why MLE and not OLS?

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Answer

$Y \in {0, 1} \to OLS predicts outside [0, 1] and residuals are heteroscedastic (Var = p(1-p)).$
$y_{i}$
$No closed form \to IRLS or gradient descent.$
$Softmax = generalization to k classes.$
$\operatorname{exp}({\beta}_{j})\; = \;\mathrm{odds}$
$Foundation of most tabular binary classifiers and the top layer of neural nets.$

Check yourself — multiple choice

Use OLS
OLS predicts outside [0,1] with heteroscedastic residuals; logistic: MLE of Bernoulli with σ(x'β); $\operatorname{exp}({\beta}_{j})\; = \;\mathrm{odds}$ ratio for a unit change
Same as OLS
Requires normality

Logistic: MLE (Bernoulli); $\operatorname{exp}({\beta}_{j})\; = \;\mathrm{odds}$ ratio.

#regression#glm

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