Origin-destination missing data estimation for freight transportation planning: a gravity model-based regression approach

This paper develops a log-linear regression approach to estimate missing data in a sparse origin-destination (O-D) matrix assuming the sampled or observed O-D trips follow a good gravity pattern. The approach is tested with randomly selected samples from the known portions of 1997, 2002, and 2007 US Commodity Flow Survey (CFS) O-D value and tonnage matrices and validated with 2007 US O-D tonnage matrix at the state level. The missing data are also estimated for the 2007 CFS tonnage matrix with the best intercept and coefficients obtained using all known entries of the matrix. The concept of the approach can be extended beyond the gravity model to any strong mathematical pattern embedded in the known set of a sparse O-D matrix to estimate its missing cells.