Logistic regression: Difference between revisions

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===Maximum likelihood estimation (MLE)===

The regression coefficients are usually estimated using [[maximum likelihood estimation]].<ref name=Menard/><ref>{{cite journal |first1=Christian |last1=Gourieroux |first2=Alain |last2=Monfort |title=Asymptotic Properties of the Maximum Likelihood Estimator in Dichotomous Logit Models |journal=Journal of Econometrics |volume=17 |issue=1 |year=1981 |pages=83–97 |doi=10.1016/0304-4076(81)90060-9 }}</ref> Unlike linear regression with normally distributed residuals, it is not possible to find a closed-form expression for the coefficient values that maximize the likelihood function, so that an iterative process must be used instead; for example [[Newton's method]]. This process begins with a tentative solution, revises it slightly to see if it can be improved, and repeats this revision until no more improvement is made, at which point the process is said to have converged.<ref name="Menard" />

In some instances, the model may not reach convergence. Non-convergence of a model indicates that the coefficients are not meaningful because the iterative process was unable to find appropriate solutions. A failure to converge may occur for a number of reasons: having a large ratio of predictors to cases, [[multicollinearity]], [[sparse matrix|sparseness]], or complete [[Separation (statistics)|separation]].