Approximating an AL profile

1. Replace the derivative with a finite difference of the CP profiles to remove the effect of all variables other than $X^j$ (works for models without interactions).

$$q^j(\underline{x}^{j|=v})dv \approx f(\underline{x}^{j|=v+dv})-f(\underline{x}^{j|=v})$$

2. Consider a partition of the range of observed values $x_{i}^j$ of variable $X^j$ into $K$ intervals.

$$N_j(k)=\left(z_{k-1}^j,z_k^j\right] \qquad (k=1,\ldots,K)$$