Partial Matrix Techniques.

Partial matrix techniques are those in which gravity models are fitted to a partially observed matrix of trips and journey costs, and used to infer the trips in the unobserved cells. This paper reviews the theoretical basis from which such techniques have been developed, and demonstrates the need to pay careful attention to the - underlying assumptions, which in effect require that the model be a good fit to be observed data (and also a good 'fit' to the unobserved data). Circumstances are described in which the estimates for the unobserved cells may not be uniquely determined, and the effects of data structure on the reliability of the estimates (assuming these to be unique) are discussed. Ways are suggested in which further theoretical and empirical research might demonstrate whether a given pattern of observations would lead to particularly error-prone estimates.