Figures and tables in A fine grained hybrid spatial microsimulation technique for generating detailed synthetic individuals from multiple data sources: An application to walking and cycling

Abstract

We propose a hybrid static spatial microsimulation technique that combines simulated annealing and synthetic reconstruction (Monte-Carlo sampling), in order to generate a synthetic population of individuals as part of a model-based policy indicator. We focus on the following case: (i) the model must produce outputs at a fine spatial resolution; (ii) the individuals have many attributes the majority of which are found in an available micro-data survey, though some attributes are missing and need to be added from other sources. The hybrid method proposed uses simulated annealing to simulate the majority of the required attributes, and Monte-Carlo sampling to add the missing attributes. our paper expands the range of techniques which could produce this type of model. We test the hybrid technique on a UK example estimating the capability of individuals to make journeys by walking and cycling, in order to produce a novel indicator of resilience to the disruption of fuel availability. Additionally, the staged approach means that the intermediate steps in the spatial microsimulation modelling process generate data on bicycle availability and the need to escort children during commuting that are useful in their own right.

This article contains 7 figures and 9 tables.

Figures

**Figure 1.** The phases of the spatial microsimulation modelling process. In this paper we are concerned with proposing a hybrid technique for synthetic population generation.

**Figure 2.** The main steps in the algorithm.

**Figure 3.** Stage 2 of the hybrid microsimulation technique using Monte-Carlo sampling.

**Figure 4.** An estimate of the percentage indicator error resulting from the hybrid spatial micro simulation technique, showing Leeds and surrounds.

**Figure 5.** The indicator for Leeds Output Areas. The percentage of working individuals aged 16–74 in an Output Area capable of commuting to their current place of work by walking or cycling.

**Figure 6.** Percentage of working population in Leeds OAs with access to a bike.

**Figure 7.** Percentage of working population in Leeds OAs needing to escort children during the commute to work.

Tables

Table 1. Attributes and data sources used in Phase 1 (synthetic population generation) of the spatial-microsimulation modelling process.

Variable	Data source	Possible values	Constraint	Stage *
Physical activity (days in last 4 weeks with 30+mins vigorous activity)	HSE	0–28	N	1
Body Mass Index (kg/m²)	HSE	15–48	N	1
Age group	Census: Table CS028 Sex and Age (16–74) by Economic Activity & HSE	16–24, 25–34, 35–54, 55–64, 65–74.	Y	1
Gender	Census table CS028 & HSE	M/F	Y	1
Weight (kg)	HSE	32–130kg	N	1
Bicycle availability	NTS /(Anable, 2010)	Probability given age, gender and NSSEC	N	2
The need to escort children on commute	NTS / Children & Early Years Survey, 2010	Probability given age and gender	N	2
Current commute distance	Census table CAS120	Bins, 0, 0–2, 2–5, 5–10, 10–20, 20–40, 40–60, < 60, not fixed.	Y	2
Economic activity	Census table CS028 & HSE	Working, unemployed, student, economically inactive.	Y	1
LLTI	Census table CS021 and HSE	Y/N	Y	1
Highest educational qualification	Census table KS013 and HSE	6 categories	Y	1
NSSEC by sex	Census tables KS014 b and c. & HSE	10 NSSEC categories by gender	Y	1

Source: Health Survey for England, 2008 (HSE), National Travel Survey (NTS), UK Census, 2001, Limiting Long Term Illness (LLTI), National Statistics Socio-Economic Classification (NSSEC).

Notes: * The column ‘Stage’ refers to the simulated annealing Stage 1 or Monte-Carlo sampling Stage 2 of the synthetic population generation phase described in Section 4.

Table 2. Summary of how proposed technique is distinct from other techniques.

Technique	Comment on suitability for use on model of interest	How our proposed hybrid technique differs
Single-stage simulated annealing Deterministic reweighting Sample-based synthetic reconstruction	Not suitable because not all data in the model of interest is in one micro-data sample	Can deal with individual attribute data from multiple sources
Sample-free synthetic reconstruction	This may be suitable as it can handle data from multiple data sources and current developments mean it may be effective at simulating populations at the finest resolution	Specifically seeks to incorporate simulated annealing (rationale in text of Section 3.2)
Imputation using multiple existing synthetic populations	This may be suitable if it is accurate at simulating populations at the finest zones, and may be useful where there are existing synthetic populations	May be useful where suitable populations are not available
Imputation to better simulate under-represented individuals in a single micro-data sample	Not suitable on its own because not all data in model of interest is in one micro-data sample	Hybrid technique can deal with individual attribute data from multiple sources. We model stochastic variation in pedal power through cloning. Lymer, et al., 2009 also use a cloning approach which may inform future developments of our technique

Algorithm 1. Pseudocode.

1: Select reference population table

2: Calculate cell value based on frequencies:

3: Raw cell value / raw row total) * reference population total

4: Intergerise the decimal value from the previous step: Round the value up or down

6: If rounded value ≠ reference population total then

7: If reference population total < integerised row total then

8: subtract 1 from a random cell in the row

9: If reference population total > integerised row total then

10: add 1 to a random cell in the row.

11: Repeat until rounded value = reference population total

Algorithm 2. Pseudocode.

1: For N_total iterations

2: CREATE TABLE COMMUTE_DISTANCE_DRAW_N

3: For each gender by age group

4: For all individuals in EMPLOYEE table who are in this gender by age group

5: Set commute distance bin by drawing a random number between 0 and 1 and comparing it to the cumulative proportion in the cumulative distribution table

6: Set the commute distance =

7: minimum distance in bin + (random number [0–1] * maximum distance in bin).

8: For N_total iterations calculate the maximum distance the population can travel

9: CREATE TABLE MAXIMUM_DISTANCE_DRAW_N for iteration N

10: SELECT data from SAMPLEPOPULATION & EMPLOYEE (this table contains probability of bike availability given Stage 1 attributes and probability of escort trip given Stage 1 attributes)

11: WHERE the probability of having a bike > [random number between 0 and 1] set individual has bike = 1

12: WHERE the probability of having to escort children to school > [random number between 0 and 1] set individual has to escort children = 1

13: UPDATE MAXIMUM_DISTANCE_DRAW_N [Calculate maximum distance each individual is capable of travelling]

Algorithm 3. Pseudocode.

1: For N_total iterations

2: CREATE TABLE INDIVIDUAL_RESULT_DRAW_N

3: JOIN commute distance draw N and maximum distance draw N

4: For each individual

5: Capability to commute = 1 where maximum distance – commute distance >= 0

6: Capability to commute = 0 otherwise.

7: CREATE TABLE INDICATOR_result_draw_N (fields: Output Area ID, sum of people with capability to commute, % of employed population with capability to commute).

Table 3. Synthetic population outputs.

Output	Table	Attributes
N_total synthetic populations of individuals	INDIVIDUAL _RESULT_DRAW_N	Physical activity, BMI, age, gender, weight, bicycle availability, need to escort children on commute, pedalling power, maximum travel distance, commute distance, capability to commute by walking or cycling.
N_total summaries of the % of the working population in an Output Area capable of commuting by walking or cycling	INDICATOR_RESULT_DRAW_N	Zone code, % of population capable of commuting by walking or cycling
Summary of capability of all populations at Output Area resolution	INDICATOR_RESULT_DRAW_SUMMARY	Zone code, % of population capable of commuting by walking or cycling for each iteration, mean capability for all populations, standard deviation of capability for all populations

Table 4. Summary of internal validation tests.

Variable name	Percent cell error
Sex by age by economic activity	0.065
Education	0.065
LLTI	0.065
NSSEC with 3 categories	0.065
Commute distance by age by sex	0.76

Table 5. Results of external validation tests.

Unconstrained attribute	Results compared
BMI (Obesity used as a proxy)	% of adult population classified as obese
Public Health England (PHE) national estimate (HSE data, 2006 — 2008)	24.2
Synthetic population using hybrid technique	23.9
Bike availability	% of adult population with use of a bike
NTS, 2010 national estimate of bike availability amongst adults.	37.2
Synthetic population using hybrid technique	38.3
Physical activity	% of adult population with no participation in sport
Active People Survey (APS), people not doing 1x30 minutes sport per week	57.0
Synthetic population using hybrid technique	58.7

Table 6. Correlations of individual attributes with the indicator.

Attribute	Correlation with indicator value
Age	−0.33
% female	−0.58
BMI	−0.156
% obese	−0.132
Pedal power	0.247
% bike	−0.305
% escort	−0.082
Slope	−0.122
Commute distance	−0.267
Maximum travel distance	0.077