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