Local computations of the iterative proportional scaling procedure for hierarchical models

The maximum likelihood estimation of hierarchical models for contingency tables is often carried out by the iterative proportional scaling (IPS) procedure. In this paper, we propose local computations of the IPS procedure by partitioning generators. The proposed implementation, called IPSP for short, first partitions generators into several non-overlapping and non-empty blocks, and then adjusts marginal counts in each block locally. To find an approximation to the optimal partition resulting the least complexity, we apply the simulated annealing algorithm. Moreover, local computations can speed up the implementation of the IPS procedure using junction trees. Numerical experiments are presented to illustrate the efficiency of local computations.