1. Introduction to Spatial Microsimulation Dr Kirk Harland

2. What is a Spatial Microsimulation? Static Spatial Microsimulation Deterministic Reweighting Conditional Probabilities Simulated Annealing Dynamic Microsimulation This Session

3. What is Spatial Microsimulation There are two types of Spatial Microsimulation 1. Static spatial microsimulation - creates a micro-level population from aggregate data 2. Dynamic spatial microsimulation – moves a population through space and time

4. Static Spatial Microsimulation Static spatial microsimulation synthesises individual level populations from aggregate information Does not move the population through space or time Alternative approach to joining two datasets spatially where no join is apparent, many health examples including obesity (Smith et al., 2009) diabetes (Smith et al., 2005) smoking prevalence (Tomintz and Clarke, 2008)

5. Static Spatial Microsimulation Several different static microsimulation methods 1. Deterministic reweighting – large iterative proportional fitting algorithm 2. Conditional probabilities – calculates the probability of a person appearing in a zone give there characteristics 3. Simulated annealing – combinatorial optimisation algorithm originally designed to simulate the cooling properties of metals

6. Static Spatial Microsimulation But they all attempt to do the same thing Turn a selection of aggregate constraint tables Into an individual level population allocated to spatial areas

7. Static Spatial Microsimulation While minimising the difference between the distribution of the constraint table attributes for each zone and the distribution of the attributes aggregated from the synthesised population… Zones Male – gender constraint counts Male – gender synthesised population counts

8. Static Spatial Microsimulation Fit statistic used is normally Total Absolute Error (TAE) TAE = ∑ i ∑ j |T ij – E ij | Where Tij is the sum of the observed counts for the cell ij Eij is the sum of the expected counts for the cell ij Williamson et al 1998

9. Static Spatial Microsimulation – Deterministic Reweighting A very big iterative proportional fitting algorithm Stage 1 – calculate weights for each individual Smith et al 2009

10. Static Spatial Microsimulation – Deterministic Reweighting Stage 2 - proportionally fit each weight to the population Smith et al 2009

11. Static Spatial Microsimulation – Deterministic Reweighting Iterate over the reweighting process until: a. the fit statistic does not improve any further b. A threshold set on the fit statistic to indicate convergence is reached Move to next zone This algorithm has been widely used in health studies.

12. Static Spatial Microsimulation – Conditional Probabilities Birking and Clarke 1988 Stage 1 – calculate conditional probabilities for all possible combinations of individuals

13. Static Spatial Microsimulation – Conditional Probabilities Birking and Clarke 1988 Stage 2 – Assign synthetic characteristics applying conditional probabilities

14. Static Spatial Microsimulation – Conditional Probabilities Birking and Clarke 1988 Stage 3 – Constrain weights to constraint table distributions

15. Static Spatial Microsimulation – Conditional Probabilities Birking and Clarke 1988 Stage 4 – Calculate TAE Stage 5 – Iterate over previous stages until no further reduction in TAE Stage 6 – Move to next zone Particular strength of the algorithm is that it does not require an input population

16. Static Spatial Microsimulation – Simulated Annealing sample population constraint 1constraint n… synthetic population zone x aggregation 1 aggregation n… calculate fitness - TAE Harland et al. 2012

17. A combinatorial optimisation algorithm well suited to static spatial microsimulation… Accurate, produces good results because it can take backwards steps Computationally intensive so care needed when implementing code Static Spatial Microsimulation – Simulated Annealing Harland et al. 2012

18. What do we mean by taking backwards steps? Crossing the valley between say point A to reach point B Static Spatial Microsimulation – Simulated Annealing

19. Comparing the Approaches Harland et al 2012 Not any more…

20. Dynamic Spatial Microsimulation Takes a population, whether synthesised or real world data, and moves it through space and time Uses derived probabilities to determine outcomes for individuals at each time-step Individuals can typically Die Be born Migrate Get married Get divorced … and any number of other actions for which probabilities can be derived

21. Dynamic Spatial Microsimulation Time step 0 Time step 1 Time step 2 Transition matrices

22. Dynamic Spatial Microsimulation Seems simple… Idea is simple but many complicating factors 1. Number of transitional probabilities dependent on number of attributes 2. Birth, death, migration, etc… not ubiquitous across zones 3. Derivation of probabilities become more complex and burdensome than the modelling process. 4. With large populations over longer time periods models can take time to setup and run, causing difficulties with calibration and evaluation

23. A Word on Model Evaluation All too often not dealt with sufficiently in the literature. Williamson and Voas (1998) presented work into model evaluation and assessment Harland et al. (2012) examined three different model approaches evaluating the algorithm performance Evaluation of large models is very difficult and time consuming but for reliable results it needs to be done Different levels of statistics provide information about different areas of the model Cell level – fine grained (often not presented) Attribute level – medium detail (often not presented) Constraint level – high level model assessment

24. Microsimulation Vs Agent-Based Modelling Great deal of similarity between the two approaches Both operate at the individual level Dynamic microsimulation moves individuals through time as does ABM Could argue for simple behaviour in dynamic microsimulation Both are very data hungry Also several differences ABMs are enhanced by interaction of individuals with their environment Behaviour in ABM not restricted to simple transitional probabilities ABMs cannot handle the volumes of data… yet!

25. Static spatial microsimulation synthesises an individual level population from aggregate data A variety of approaches have been used for static spatial microsimulation -iterative reweighting -statistical probabilities -combinatorial optimisation All have there benefits and there drawbacks… Summary

26. Dynamic microsimulation moves a population through time Has similarities to ABM but also major differences Static spatial microsimulation may have a role to play with both approaches One major complicating factor for dynamic microsimulation is the derivation of transitional probabilities… Summary

27. References Ballas, D., Clarke, G., Dorling, D., Eyre, H., Thomas, B., and Rossiter, D.(2005) SimBritain: a spatial microsimulation approach to population dynamics. Population, Space and Place 11, 13–34. Birkin, M. & Clarke, M. (1988). SYNTHESIS - a synthetic spatial information system for urban and regional analysis: methods and examples'' Environment and Planning A, 20, 1645 -1671. Harland K., Heppenstall A. J., Smith D., and Birkin, M. (2012) Creating Realistic Synthetic Populations at Varying Spatial Scales: A Comparative Critique of Population Synthesis Techniques Journal of Artificial Societies and Social Simulation 15 (1) 1 Smith M D, Clarke P G, Ransley J, Cade J. (2005). Food Access and Health : A Microsimulation Framework for Analysis. Studies in Regional Science. 35(4). 909 – 927 Smith D M, Clarke G P, Harland K, (2009), Improving the synthetic data generation process in spatial microsimulation models. Environment and Planning A 41(5) 1251 – 1268 Tomintz MN, GP Clarke, (2008) The geography of smoking in Leeds: estimating individual smoking rates and the implications for the location of stop smoking services. Area 40(3): 341-353 Williamson, P., Birkin, M., & Rees, P.H. (1998). The estimation of population microdata by using data from small area statistics and samples of anonymised records. Environment and Planning A, 30, 785-816. Wu, B., Birkin, M. and Rees P. (2008) A spatial microsimulation model with student agents. Computers, Environment and Urban Systems, 32 (6). pp. 440–453