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{L(\beta)} = \prod_{i=1}^np(x_i)^{y_i}(1-p(x_i))^{1-y_i}  \end{equation}  We could substitute the equation for \textit{p} from above but we will not here. Thie form of the likelihood function, which is the same as the distribution of the response, reflects the fact that we assume the response follows a \textit{binomial distribution}. Finding the parameters $\beta_i$ that maximizes the likelihood function involves numerical procedures that are outside the scope of this paper and not a concern of a modeler.