Editing Logistic function (section)

==== Logistic regression ====
{{Main|Logistic regression}}

Logistic functions are used in [[logistic regression]] to model how the probability <math>p</math> of an event may be affected by one or more [[explanatory variables]]: an example would be to have the model

<math display="block">p = f(a + bx),</math>

where <math>x</math> is the explanatory variable, <math>a</math> and <math>b</math> are model parameters to be fitted, and <math>f</math> is the standard logistic function.

Logistic regression and other [[log-linear model]]s are also commonly used in [[machine learning]]. A generalisation of the logistic function to multiple inputs is the [[softmax activation function]], used in [[multinomial logistic regression]].

Another application of the logistic function is in the [[Rasch model]], used in [[item response theory]]. In particular, the Rasch model forms a basis for [[maximum likelihood]] estimation of the locations of objects or persons on a [[Continuum (theory)|continuum]], based on collections of [[categorical variable|categorical data]], for example the abilities of persons on a continuum based on responses that have been categorized as correct and incorrect.