Iterative proportional fitting

Iterative Proportional Fitting (IPF) are disaggregation methods to obtain doubly constrained matrix cell values Xij proportional to a given strictly positive interaction measure (aka proxy) Cij given restrictions on row an column totals Ti. and T.j.

We introduce ai and bj to express Xij as aibjCij.

It follows that:

\[a_i := \frac{T_{i}}{\sum\limits_{j}{b_j C_{ij}}}\]


\[b_j := \frac{T_{j}}{\sum\limits_{i}{a_i C_{ij}}}\]

An IPF is used to solve the Continuous Allocation of the earlier versions of the Land Use Scanner by using eβ**si**j as proxy.

applications of IPF

  • Doubly Constrained Gravity Models of Spatial Interaction
  • Trip Distribution in Transport modelling is often modelled as doubly constrained gravity model
  • Continuous Allocation where land units are sources and claims for land use are destinations.

more Links

- IPF] RIVM/PBL paper (in Dutch)