Computes the logit transformation, including its inverse.
Syntax
LOGIT(X, Lo, Hi, Return)
 X
 is the real value(s) for which we compute the transformation. It may be a single value or a onedimensional array of cells (e.g., rows or columns)).
 Lo
 is the xdomain lower bound. If missing, Lo is assumed to be 0.
 Hi
 is the xdomain upper bound. If missing, Hi is assumed to be 1.
 Return
 is a number that determines the type of return value: 0 (or missing) = Logit, 1 = Inverse Logit.
Return Description 0 or omitted Logit Transform 1 Inverse of Logit transform
Remarks
 The X value(s) must be between Lo and Hi (exclusive).
 The original Logit function is very commonly used for parameters that lie in the unit interval. Numerical values of theta close to 0 or 1 or out of range result in #VALUE! or #N/A.
 The Logit transformation is defined as follows:
$$y=\textit{Logit}(x)=\ln{\frac{x}{1x}}$$ And,
$$x=\textit{Logit}^{1}(y)=\frac{e^y}{e^y+1}$$
Where:
 $x_{t}$ is the input value of the input time series at time $t$. X must be between 0 and 1, exclusive.
 $y_{t}$ is the transformed Logit value at time $t$.
 $\textit{Logit}^{1}$ is the inverse Logit transformation.
 To support a generic interval (Lo, Hi), we perform the following mapping:
$$z=\frac{x  Lo}{Hi  Lo}$$ So, the new transform and its inverse (i.e., $\textit{Logit}^{1}$) are defined as follows:
$$y = ln{\frac{x  Lo}{Hi  x}}$$ $$x =\textit{Logit}^{1}(y)= \frac{Lo+Hi\times{e^y}}{1+{e^y}}$$  In essence, the Logit converts a bounded xrange from (Lo, Hi) to $(\infty, \infty)$:
 The Logit function accepts a single value or an array of values for X.
 The first order derivative of the Logit transform is defined as follows:
$$\frac{dy}{dx}=\frac{HiLo}{({xLo})({Hix})}$$  The first derivative is positive for all xvalues in (Lo, Hi), but as x approaches Lo or Hi, the derivative goes to infinity.
Examples
Example 1:


Files Examples
Related Links
References
 John H. Aldrich, Forrest D. Nelson; Linear Probability, Logit, and Probit Models; SAGE Publications, Inc; 1st Edition(Nov 01, 1984), ISBN: 0803921330.
 Hilbe, Joseph M. (2009), Logistic Regression Models, CRC Press, p. 3, ISBN 9781420075779.
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