Use of Iterative Proportional Fitting Algorithm for Combining Traffic Count Data with Missing Dimensions

Abstract

This paper proposes a modified version of the iterative proportional fitting (IPF) algorithm that can be used to combine contingency tables with missing dimensions. In many situations data from more than one survey could be used to answer a certain question of interest. Although using only one of the data sets is the simplest approach, it is uneconomical because information contained in the other data sets is not used. When combining data from different sources, one often faces the problem that the data have not been collected in exactly the same way, so certain information is available only in some data sets. Dominici proposed a hierarchical Bayesian model for combining contingency tables with missing dimensions. Although this is an elegant theory, it has a number of shortcomings, the most important one being that it has a high time and memory complexity. In other words, this method is too slow to be useful for traffic count data in which the number of cells easily exceeds several thousands. The IPF algorithm proposed here consists of iterations whose time complexity is linear only in the number of cells, so it can easily be applied to huge contingency tables such as those obtained from traffic surveys.