### Harland et al 2012

```Introduction to Spatial Microsimulation
Dr Kirk Harland
This Session
What is a Spatial Microsimulation?
Static Spatial Microsimulation
• Deterministic Reweighting
• Conditional Probabilities
• Simulated Annealing
Dynamic Microsimulation
What is Spatial Microsimulation
 There are two types of Spatial Microsimulation
Static spatial microsimulation - creates a micro-level
population from aggregate data
2. Dynamic spatial microsimulation – moves a population
through space and time
1.
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)
Static Spatial Microsimulation
• Several different static microsimulation methods
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
1.
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
Male – gender
constraint counts
Zones
Male – gender
synthesised
population counts
Static Spatial Microsimulation
 Fit statistic used is normally Total Absolute Error (TAE)
TAE = ∑i∑j|Tij – Eij|
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
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:
the fit statistic does not improve any further
b. A threshold set on the fit statistic to indicate
convergence is reached
a.
 Move to next zone
 This algorithm has been widely used in health studies.
Static Spatial Microsimulation –
Conditional Probabilities
 Stage 1 – calculate conditional probabilities for
all possible combinations of individuals
Birking and Clarke 1988
Static Spatial Microsimulation –
Conditional Probabilities
 Stage 2 – Assign synthetic characteristics
applying conditional probabilities
Birking and Clarke 1988
Static Spatial Microsimulation –
Conditional Probabilities
 Stage 3 – Constrain weights to constraint table
distributions
Birking and Clarke 1988
Static Spatial Microsimulation –
Conditional Probabilities
 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
Birking and Clarke 1988
Static Spatial Microsimulation –
Simulated Annealing
sample
population
constraint 1
constraint n…
calculate fitness
- TAE
synthetic
population
zone x
aggregation 1
aggregation
n…
Harland et al. 2012
Static Spatial Microsimulation –
Simulated Annealing
 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
Harland et al. 2012
Static Spatial Microsimulation –
Simulated Annealing
 What do we mean by taking backwards steps?
 Crossing the valley between say point A to reach point B
Comparing the Approaches
Not any more…
Harland et al 2012
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
Dynamic Spatial Microsimulation
Time step 0
Transition matrices
Time step 1
Transition matrices
Time step 2
Dynamic Spatial Microsimulation
 Seems simple…
 Idea is simple but many complicating factors
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
1.
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
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!
Summary
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…
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
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