A Spatial and Statistical Approach for Imputing Origin-Destination Matrices from Household Travel Survey Data: A Sydney Case Study

Abstract

A Household Travel Survey (HTS) is a valuable instrument for collecting data suitable for studying the travel behaviour of a sample of households in a specific geographical context. One important output from the trip data after expansion to the population is a set of origin-destination (O-D) trip matrices for combinations of trip purpose, time of day and mode of transport. However, the O-D matrices generally take the form of sparse matrices (ie cell values are mostly zero). The degree of sparseness of these matrices is a function of sample size (a consequence of cost constraints), segmentation requirements and the spatial resolution of a geographical zoning system. Another factor contributing to the sparseness is the non-revelation of information in some cells in order to protect the privacy of households who live in those cells where their total amount of travel in a cell is less than a cut-off criterion (eg < 200 trips). Establishing an appropriate value to assign to a ‘zero value’ cell is a non-trivial task. There are two key issues to work through. The first is how to set up a classification rule to determine either if zero value cells have no travel related activity at all (ie genuine zeroes) or the travel values are truly missing. The second issue is the development of a trip allocation rule to assign the number of trips to each missing value cell within the constraint of a given total number of trips to be allocated to each missing value cell (given knowledge of marginals). This paper shows how spatial and statistical techniques can be implemented to estimate the number of missing value cells and the number of trips associated with each missing value cell. The classification rule is a spatial one in locating missing value cells for any travel activities between each origin and destination. It is driven by the mean trip length distribution of the origin and destination distance among traffic zones. The trip allocation rule is constructed to allocate the number of trips to missing value cells using a distribution assumption (such as the uniform). The two rules are then combined in a process based on the proportion of trip purposes and modes of travel for a whole sample of household travel records. We implement the method for Sydney for the period 1998- 2000 to obtain total passenger trip movements for linked trips by five purposes, six modes and six times of day.