DERIVATIVES OF FLOWS IN A DOUBLY CONSTRAINED GRAVITY MODEL

For many practical applications it is important to know how the flows in a doubly constrained gravity model react to slight variations in the predetermined marginal totals. The first-order approximation of these variations is a linear function on the set of feasible variations of marginal totals, i.e., the set of variations not violating the consistency constraint of the model. Several methods to find a matrix describing this linear function are developed and compared with former contributions to this issue. Finally, applicability of the methods to sensitivity and error propagation analysis is demonstrated.