GAMs can also be used in situations where Y is qualitative. For simplicity, here we will assume Y takes on values zero or one, and let $p(X) = Pr(Y = 1 \mid X)$ be the conditional probability (given the predictors) that the response equals one. Recall the logistic regression model: $log(\frac{p(X)}{1−p(X)}) = \beta_0 + \beta_1X_1 + \beta_2X_2 +···+ \beta_pX_p$ Note that this logit is the log of the odds of $P(Y =1 \mid X)$ versus $P(Y =0 \mid X)$. With GAMs, we have a new model: $log(\frac{p(X)}{1−p(X)}) = \beta_0 + \beta_1 f(X_1) + \beta_2 f(X_2) +···+ \beta_p f(X_p)$.