What is the Difference Between Logit and Logistic Regression?

Logit and logistic regression are the same thing.  However, they actually relate to generalized linear models.  In a generalized linear model, you have some features x, parameters \beta, response y, and link function g.  that relates E(y) to x and \beta.  The relationship is as follows:

(1)   \begin{align*} g(E(y))&=\beta^T x \end{align*}

One choice of g is the logit function \log\frac{x}{1-x}.  Its inverse, which is an activation function, is the logistic function \frac{1}{1+\exp(-x)}.  Thus logit regression is simply the GLM when describing it in terms of its link function, and logistic regression describes the GLM in terms of its activation function.

One Reply to “What is the Difference Between Logit and Logistic Regression?”

  1. Would it be possible to expand upon this?
    For example, when would it be more appropriate to use the logistic function instead of the logit function?
    Also, what does T represent?

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