introduction to spatial microsimulation dr kirk harland

Introduction to Spatial Microsimulation

Dr Kirk Harland

What is a Spatial Microsimulation?Static Spatial Microsimulation• Deterministic Reweighting• Conditional Probabilities• Simulated AnnealingDynamic Microsimulation

This Session

What is Spatial Microsimulation

There are two types of Spatial Microsimulation1. Static spatial microsimulation - creates a micro-level

population from aggregate data2. Dynamic spatial microsimulation – moves a population

through space and time

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 includingobesity (Smith et al., 2009)

diabetes (Smith et al., 2005)

smoking prevalence (Tomintz and Clarke, 2008)

Static Spatial Microsimulation

• Several different static microsimulation methods1. Deterministic reweighting – large iterative proportional

fitting algorithm2. Conditional probabilities – calculates the probability of a

person appearing in a zone give there characteristics3. Simulated annealing – combinatorial optimisation

algorithm originally designed to simulate the cooling properties of metals

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

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 Zones

Male – gender constraint counts

Male – gender synthesised population counts

Static Spatial MicrosimulationFit statistic used is normally Total Absolute Error (TAE)

TAE = ∑i∑j|Tij – Eij|

WhereTij is the sum of the observed counts for the cell ijEij is the sum of the expected counts for the cell ij

Williamson et al 1998

Static Spatial Microsimulation – Deterministic Reweighting

A very big iterative proportional fitting algorithm

Stage 1 – calculate weights for each individual

Smith et al 2009

Static Spatial Microsimulation – Deterministic Reweighting

Stage 2 - proportionally fit each weight to the population

Smith et al 2009

Static Spatial Microsimulation – Deterministic Reweighting

Iterate over the reweighting process until:a. the fit statistic does not improve any furtherb. A threshold set on the fit statistic to indicate

convergence is reachedMove to next zone

This algorithm has been widely used in health studies.

Static Spatial Microsimulation – Conditional Probabilities

Birking and Clarke 1988

Stage 1 – calculate conditional probabilities for all possible combinations of individuals

Static Spatial Microsimulation – Conditional Probabilities

Birking and Clarke 1988

Stage 2 – Assign synthetic characteristics applying conditional probabilities

Static Spatial Microsimulation – Conditional Probabilities

Birking and Clarke 1988

Stage 3 – Constrain weights to constraint table distributions

Static Spatial Microsimulation – Conditional Probabilities

Birking and Clarke 1988

Stage 4 – Calculate TAEStage 5 – Iterate over previous stages until no

further reduction in TAEStage 6 – Move to next zone

Particular strength of the algorithm is that it does not require an input population

Static Spatial Microsimulation – Simulated Annealing

sample population

constraint 1 constraint n…

synthetic population

zone x

aggregation 1aggregation

n…

calculate fitness - TAE

Harland et al. 2012

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

What do we mean by taking backwards steps?

Crossing the valley between say point A to reach point B

Static Spatial Microsimulation – Simulated Annealing

Comparing the Approaches

Harland et al 2012

Not any more…

Dynamic Spatial MicrosimulationTakes a population, whether synthesised or real world

data, and moves it through space and timeUses derived probabilities to determine outcomes for

individuals at each time-stepIndividuals can typically

DieBe bornMigrateGet marriedGet divorced… and any number of other actions for which probabilities can be derived

Dynamic Spatial Microsimulation

Time step 0

Time step 1

Time step 2

Transition matrices

Transition matrices

Dynamic Spatial MicrosimulationSeems 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

A Word on Model EvaluationAll too often not dealt with sufficiently in the literature.Williamson and Voas (1998) presented work into model

evaluation and assessmentHarland et al. (2012) examined three different model

approaches evaluating the algorithm performanceEvaluation of large models is very difficult and time

consuming but for reliable results it needs to be doneDifferent levels of statistics provide information about

different areas of the modelCell level – fine grained (often not presented)Attribute level – medium detail (often not presented)Constraint level – high level model assessment

Microsimulation Vs Agent-Based Modelling

Great deal of similarity between the two approachesBoth operate at the individual levelDynamic microsimulation moves individuals through time as

does ABMCould argue for simple behaviour in dynamic microsimulationBoth are very data hungry

Also several differencesABMs are enhanced by interaction of individuals with their

environmentBehaviour in ABM not restricted to simple transitional

probabilitiesABMs cannot handle the volumes of data… yet!

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

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

ReferencesBallas, 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