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.