Logit
Logit(p)
The Logit function is equal to
- [math]\displaystyle{ Logit(p) = \ln\left( p\over{1-p} \right) }[/math]
where [math]\displaystyle{ 0\lt p\lt 1 }[/math]. The logit is also called the log-odds of a probability [math]\displaystyle{ p }[/math].
The inverse of the Logit function is Sigmoid(x) (before Analytica 4.5, the function InvLogit was used, defined in the Generalized Regression library). Its first and second derivatives are
- [math]\displaystyle{ {{d \; logit(p)}\over{d p}} = {1\over p} + {1\over{1-p}} = {1 \over {p (1-p)}} }[/math]
- [math]\displaystyle{ {{d^2 \; logit(p)}\over{d p^2}} = {{2 p - 1} \over { p^2 (1-p)^2 }} }[/math]
- [math]\displaystyle{ {{d^n \; logit(p)}\over{d p^n}} = (n-1)! {{p^n - (-1)^n (1-p)^n } \over { p^n (1-p)^n }} }[/math]
The logit function is sometimes called the log-odds function.
Library
Advanced Math Functions
Complex numbers
When p < 0 or p > 1, a warning is issued and if the warning is ignored, the result is NaN. This is the case unless you have enabled complex numbers. If you have set the system variable EnableComplexNumbers to 1, then no warning is issued and Logit(p) returns a complex number.
History
Logit was introduced as a built-in function in Analytica 4.5. Before that, it was supplied as a function in the Generalized Regression library.
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