Selecting a c

It is often chosen so that:

\[ E_{X^j}\left\{g_{AL}^{j}(X^j)\right\} = \int g_{AL}^{j}(x) p(X^j = x) dx = 0 \]

This ensures that the AL profile has an average effect of zero over the distribution of \(X^j\), making it easier to interpret changes relative to this baseline.