Generating Synthetic Populations Using Iterative Proportional Fitting (IPF) and Monte Carlo Techniques Martin Frick, IVT, ETH Zürich Kay W
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Generating Synthetic Populations using Iterative Proportional Fitting (IPF) and Monte Carlo Techniques Martin Frick, IVT, ETH Zürich Kay W. Axhausen, IVT ETH Zürich Conference paper STRC 2003 Session Model & Generation Swiss Transport Research Conference 3 rd STRC Monte Verità / Ascona, March 19-21, 2003 Swiss Transport Research Conference _______________________________________________________________________________ March 19-21, 2003 Generating Synthetic Populations using Itera- tive Proportional Fitting (IPF) and Monte Carlo Techniques Martin Frick IVT ETH Zürich 8093 Zürich Phone: 01-633 37 13 Fax: 01-633 10 57 e-Mail: [email protected] I Swiss Transport Research Conference _______________________________________________________________________________ March 19-21, 2003 Abstract The generation of synthetic populations represents a substantial contribution to the acquisition of useful data for large scale multi agent based microsimulations in the field of transport plan- ning. Basically, the observed data is available from censuses (microcensus) in terms of simple summary tables of demographics, such as the number of persons per household for census block group sized areas. Nevertheless, there is a need of more disaggregated personal data and thus another data source is considered. The Public Use Sample (PUS), often used in transportation studies, is a 5% representative sample of almost complete census records for each individual, missing addresses and unique identifiers, including missing items. The problem is, to generate a large number of individual agents (~ 1Mio.) with appropriate characteristic values of the demo- graphic variables for each agent, interacting in the microsimulation. Due to the fact that one is faced with incomplete multivariate data it is useful to consider multiple data imputation tech- niques. In this paper an overview is given over existing methods such as Iterative Proportional Fitting (IPF), the Maximum Likelihood method (MLE) and Monte-Carlo (MC) techniques. To exemplify the generation of synthetic populations the Swiss PUS's from 1970, 1980 and 1990 as well as Swiss microcensus data is used to generate a large number (~1.5 Mio) of synthetic agents, representing the people in the Glattal, which is a fast developing area north of Zürich. The data sources are fused together using IPF and Monte Carlo technique to estimate the joint distribution of demographic characteristics such as age, sex, car ownership, drivers licence ownership, vehicle miles, car availability, etc. for each agent. In a further step the generation of representative households for the Glattal area is addressed. Keywords Synthetic Population Generation – IPF – MCMC – Imputing missing Data – Glattal – 3rd Swiss Transport Research Conference – STRC 2003 – Monte Verità II Swiss Transport Research Conference _______________________________________________________________________________ March 19-21, 2003 1. Introduction In recent years, the computing power of distributed computing has increased significantly. Therefore it is now possible to do traffic simulations on a microscopic scale for large metro- politan areas with more than 1 million habitants. Microscopic means that each entity in the simulation is an object, e.g. travellers, roads, vehicles, traffic lights, etc. The TRANSIMS sys- tem, e. g. explained in Smith et al., (1995) is an existing implementation. For an implementa- tion for Switzerland see Voellmy et al. (2001). For a 1 day simulation of 1 million intelligent agents, one need about 5 hours computing time on a cluster with 64 CPU’s, from scratch. For the microsimulation one needs different modules for different tasks. Figure 1 shows the most important modules. Figure 1 Traffic Microsimulation, Schema 1 Swiss Transport Research Conference _______________________________________________________________________________ March 19-21, 2003 The reason why people move from one point in space and time to another is assumed to be that people starts activities due to personal needs. For details about activity based transport models see for example Axhausen and Gärling, 1991 or Gärling et al., 1994. Therefore in the simulation there is a module called activity generation module, which provides each agent with a daily plan of activities witch should be executed. Once the agent has the activities for the day, the mode- and route choice module relates a particular route and vehicle modes to each agent depending on the individual activities. The next step is to execute these choices for all agents simultaneously within the traffic microsimulation module. The algorithm behind the traffic microsimulation module is similar to molecular dynamics method, well known from physics, except for the fact that the agents (particles) are simulated on a road net. If an incon- sistency occurs within the daily plans of some agents, the interaction module is responsible for adapting the plans and run the procedure as long as all agent plans are consistent. This is usually the case after about 50 iterations. In a first and important step it is necessary to gener- ate the needed number of agents with individual demographic properties as an initial dataset for the microsimulation. This module is called Synthetic Population Generation Module. The purpose of this paper is to describe in detail the IPF method used for synthetic population generation and to present the obtained first results for the Kanton Zürich in Switzerland. The task is to generate agents, which reflects the demographic structure and the travel behav- iour of the real people. Almost all information, which is easily available about people and their travel behaviour, comes from empirical data obtained by surveys. Due to the fact that there exist laws to protect the privacy of people, not all desired information about people could be obtained. In general the situation is as follows: The more information we get from an individual traveller about his demographics (e.g. age, sex, income, employment, car owner- ship, etc.) the less we know about his residency, i.e. the spatial resolution of where he or she lives. On the other hand, if we have a good spatial resolution for the e.g. residence of the trav- eller, i.e. the municipality, the hectare data or the street address of that particular traveller, we do not have information about the other sociodemographics of that individual traveller but usually we have 1D or 2D summary tables for various demographics instead. To overcome the situation described above, one can use methods for disaggregating and syn- chronizing the data given to public. One method, which has been used in traffic research be- fore is called Iterative Proportional Fitting (IPF), e.g. (Papacostas and Prevedouros, 1993). The present paper describe some modifications to the original method, and shows how high dimensional contingency tables can be obtained with this method. As an example the method 2 Swiss Transport Research Conference _______________________________________________________________________________ March 19-21, 2003 is adapted to the Kanton Zürich, witch is a metropolitan area with about 1 million residents in Switzerland. First results will be presented. 3 Swiss Transport Research Conference _______________________________________________________________________________ March 19-21, 2003 2. Census Data One of the main problems in generating synthetic populations is the spatial disaggragation and synchronization of the available census data. In this approach the census 2000 from Swit- zerland as well as the microcensuses from 1989 to 2000 (BFS and ARE, 2001) are used to de- termine the synthetic population. First of all, it is necessary to choose a set of demographic variables of interest. For example this may be residence, age, sex, income, car ownership, working place, etc. These demograph- ics are available in different resolutions in each data source. In particular the residence varies from Kanton level down to municipality level and even hectare grid or exact xy-coordinates are possible. To obtain the best spatial resolution for residence or work place the process of generating synthetic agents is divided into two major steps. Starting from the 1-dimensional (1D) marginal distributions of the demographics for each municipality the data for each demographic variable is aggregated to the low spatial resolution level which is here the Kanton Zürich, to obtain 1D, 2D, etc. distributions for each demo- graphic or a combination of demographics except for the residence. The Tables 1-4 show the 1D distribution of age and sex for the municipality Aeugst am Albis and the aggregated re- sults for the Kanton Zürich, respectively. More tables for other demographics and cross- classified tables are possible but not presented here. Furthermore, Figure 2 and 3 shows a chart of the aggregated distributions for age and sex. Table 1 Sex Distribution for the Municipality Aeugst am Albis, 2000 Sex 1 = male 2 = female Frequency 771 773 4 Swiss Transport Research Conference _______________________________________________________________________________ March 19-21, 2003 Table 2 Age distribution for the Municipality Aeugst am Albis, 2000 Age (categories) 1 2 3 4 5 6 Frequency 17 67 104 109 78 75 Age (categories) 7 8 9 10 11 12 Frequency 58 108 132 184 147 121 Age (categories) 13 14 15 16 17 18 Frequency 109 75 59 44 35 10 Age (categories) 19 20 21 22 23 Frequency 10 2 0 0 0 Labels 1 = 0 years, 2 = 1-4 years, 3 = 5-9 years,…, 22 = 100-104 years, 23 = >105 years Table