Logistic regression is considered a generalized linear model because the outcome always depends on the sum of the inputs and parameters.
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Card 1 of 276. Answer: Logistic regression is considered a generalized linear model because the outcome always depends on the sum of the inputs and parameters.
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Yes. Logistic regression is a linear model because it computes a linear combination of the inputs, w·x + b, and the decision boundary where the predicted probability equals 0.5 is the hyperplane w·x + b = 0. It belongs to the family of generalized linear models.
The sigmoid on top is what confuses people. It squashes the linear score into a probability between 0 and 1, so the output is a non-linear function of x, but the log-odds, log(p / (1 − p)), is exactly linear in x. That is the sense in which the model is linear: in the parameters and in the log-odds, not in the probability.
The practical consequence is that logistic regression can only separate classes with a straight line or flat hyperplane. To fit curved boundaries you add features yourself, such as polynomial terms or interactions, or switch to a non-linear model like a tree ensemble or a neural network.
