Standard Article

Iterative Proportional Fitting

  1. Terry P. Speed

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a10027

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Speed, T. P. 2005. Iterative Proportional Fitting. Encyclopedia of Biostatistics. 4.

Author Information

  1. University of California, Berkeley, CA, USA

Publication History

  1. Published Online: 15 JUL 2005


Iterative proportional fitting, also known as iterative proportional scaling, is an algorithm for constructing tables of numbers satisfying certain constraints. In its simplest form, the algorithm enables one to construct two-way tables with specified row and column margins and prescribed association, measured by a family of cross-ratios. The algorithm can be used to obtain maximum likelihood estimates of table entries under hierarchical loglinear models, and it can be used to adjust counts in survey sampling, where it is known as raking. Natural extensions exist to three and higher-way tables, and to more general exponential families.


  • cross-ratio;
  • hierarchical loglinear model;
  • marginals;
  • interactions;
  • I-divergence