Logit and Inverse-Logit Functions

Transform values to and from the logit scale. logit() calculates

Usage

logit(p)

invlogit(x)

Arguments

p

Values in the interval [0, 1]. Can be an atomic vector, a matrix, or an rvec.

x

Values in the interval (-Inf, Inf). Can be an atomic vector, a matrix, or an rvec.

Value

• A vector of doubles, if p or x is a vector.

• A matrix of doubles, if p or x is a matrix.

• An object of class rvec_dbl, if p or x is an rvec.

Details

$$x = \log \left(\frac{p}{1 - p}\right)$$

and invlogit() calculates

$$p = \frac{e^x}{1 + e^x}$$

To avoid overflow, invlogit() uses \(p = \frac{1}{1 + e^{-x}}\) internally for \(x\) where \(x > 0\).

In some of the demographic literature, the logit function is defined as

$$x = \frac{1}{2} \log \left(\frac{p}{1 - p}\right).$$

logit() and invlogit() follow the conventions in statistics and machine learning, and omit the \(\frac{1}{2}\).

Examples

p <- c(0.5, 1, 0.2)
logit(p)
#> [1]  0.000000       Inf -1.386294
invlogit(logit(p))
#> [1] 0.5 1.0 0.2