Commuting to School: A New Spatial Interaction Modelling Framework for the Education Sector

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Commuting to School A New Spatial Interaction
Modelling Framework for the Education Sector
School of Geography FACULTY OF ENVIRONMENT
Kirk Harland and John Stillwell

• Email k.harland98_at_leeds.ac.uk
• Research Methods Festival 2nd July 2008

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School of Geography FACULTY OF ENVIRONMENT

• Presentation
• Context
• Modelling methodology
• Model structure
• Study area
• Simulating the past
• Predicting the future
• Summary

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School of Geography FACULTY OF ENVIRONMENT

• Context
• 1988 ERA open market policy
• 28/02/2007 new school admissions code
• Has mandatory provisions
• Requires LAs to provide equitable access to
  schools for all

2004-based population projections by the
Government Actuary, England
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School of Geography FACULTY OF ENVIRONMENT
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School of Geography FACULTY OF ENVIRONMENT

• Context
• Education is a hot topic prompting a variety of
  research
• Social and ethnic segregation (Gibson and Asthana
  2000a, 2000b Gorard 1999, 2000, 2004 Johnston
  et al. 2004, 2005, 2006)
• Qualitative studies on school choice (Pooley et
  al. 2005 Gereluk, 2005)
• Pupil mobility at non-conventional times of year
  (Demie 2002 Dobson et al. 2000 Dobson and
  Pooley 2004, Wilson 2008)
• National Pupil Database (NPD) gateway hosted by
  the University of Bristol and the Department for
  Children, Schools and Families
• Limited research on pupil-school interactions and
  school role forecasting (Sven Muller, Dresden
  University)

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School of Geography FACULTY OF ENVIRONMENT

• Modelling Methodology
• Spatial interaction model equation produces a
  likely flow event using the mass of origins, the
  mass of destinations and the difference in
  relative locations in space. Typically

where is the predicted flow between i and
j Oi is the mass of origin zone i Dj is the mass
of destination zone j f(dij) is the distance
function k is a balancing factor or constraint
ensuring flows equate to a known value
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School of Geography FACULTY OF ENVIRONMENT

• Modelling Methodology Applications
• Spatial interaction models have been applied
  successfully in studies of, for example
• migration (Stillwell 1978)
• journey to work (Senior 1979)
• retail location planning (Fotheringham 1983
  Fotheringham and Trew 1993)
• commercial retail marketing (Birkin et al. 2004)
• Peculiarities of each market have demanded model
  innovations
• Education sector is no different it has its
  own challenges

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School of Geography FACULTY OF ENVIRONMENT

• Modelling Methodology Challenges in the
  Education Sector
• School capacities Schools have a maximum number
  of pupils the they can acceptBUT these do not
  have to be met
• Over-subscription policy Can differ between
  Local Authorities and schools
• Admissions criteria Some schools apply an
  admissions policy
• Data rich Collection and collation of over eight
  million individual pupil records each year (Jones
  and Elias 2006)
• School selection behaviour Differs between
  primary and secondary phases and also between
  families with different backgrounds
• Boundary effects Although sector is data rich,
  some data are not available to education planners
  when planning projects are undertaken
• How do we develop an appropriate equation that
  gives a good representation of the journey to
  school the factors that influence it?

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School of Geography FACULTY OF ENVIRONMENT

• Modelling Methodology
• Openshaw (1998, unpublished) and Diplock (1998)
  developed an approach for equation selection in
  the late 1990s
• Separation of the model equation from the model
  constraint(s) (Openshaw 1998) and
• Use of genetic algorithms for equation building
  (Diplock 1998, Openshaw unpublished)
• First stage of this approach can be achieved
  relatively easily by simply not applying the
  balancing factor or constraint in the initial
  spatial interaction model run, and then using a
  separate second stage to constrain the model
• WHY?
• The method of applying a constraint does not
  change unless you change the constraint
• It simplifies the model equation considerably

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School of Geography FACULTY OF ENVIRONMENT

• Modelling Methodology Constraint Separation
• An origin constrained model (Wilson 1971)

where ß is a calibrated distance decay
parameter Wj2 is an estimated destination
attractiveness factor
which can be expressed as

• This part of the equation calculates a
  probability of a flow occurring

• Multiplied by the known origin mass to give a
  predicted flow value

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School of Geography FACULTY OF ENVIRONMENT

• Modelling Methodology Constraint Separation
• Openshaw (1998) proposes separating the
  constraint and model equation into a two stage
  process
• Stage 1 produces an initial matrix of flows
• Stage 2 converts these relative flows into
  predicted flows by proportionally fitting the
  relative flows for each i to the known Oi value
• Although, Openshaw (1998) only shows the origin
  constraint derivation, this principle can be
  applied to total, destination and double
  constrained models

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School of Geography FACULTY OF ENVIRONMENT

• Modelling Methodology Equation Definition
• With a simplified model equation a genetic
  algorithm can be applied to breed a model
• First step is to think of the equation as a
  series of genes where each gene four parts
• data item
• parameter
• function
• operator

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School of Geography FACULTY OF ENVIRONMENT

• Modelling Methodology Equation Definition
• The simplified model is
• It has 2 genes representing Wj2 and exp(ßdij)
  with each gene having four parts
• Encoded equation is
• 2004 3124

Lookup tables
Wj2. exp(ßdij)
Data 2 3
Parameter 0 1
Function 0 2
Operator 4 4
Data Data
Origin 1
Destination 2
Distance 3
Parameter Parameter
None 0
Parameter 1
Operator Operator
Addition 1
Subtraction 2
Division 3
Multiplication 4
Function Function
None 0
Log10 1
Exp 2
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School of Geography FACULTY OF ENVIRONMENT

• Modelling Methodology Equation Definition
• Employing a genetic algorithm encoded equations
  can be used to create or breed new
  populations of equations to be calibrated and
  tested against observed data
• Genes can be recombined to create new equations

2004
3124
2104
3024

• and genes can be mutated

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School of Geography FACULTY OF ENVIRONMENT

• Modelling Methodology
• Equation Definition
• Genetic algorithm runs in two loops
• Inner loop runs and calibrates model equations
  until all the population equations have been run
• Outer loop breeds new generation populations from
  the best performing equations until either no new
  equations are generated, a convergence threshold
  is reached, or the maximum number of generations
  is reached

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School of Geography FACULTY OF ENVIRONMENT

• Modelling Methodology Equation Performance
• The genetic algorithm is used as a tool to find
  trends in equation performance
• Many outputs are nonsense and careful thought has
  to be applied to the results
• Revealed that the attractiveness of secondary
  schools in Leeds to be non-linear and that
  access to primary schools is very important

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School of Geography FACULTY OF ENVIRONMENT
Model structure
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School of Geography FACULTY OF ENVIRONMENT
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School of Geography FACULTY OF ENVIRONMENT

• Simulating the past
• School role simulation errors (observed vs.
  simulated school role numbers)
• Goodness of fit statistics

Year Predicted Role Error Predicted Role Error Percentage Percentage
Year gt20 20gt10 gt20 20gt10 Schools
2003/04 5 4 11.63 9.30 43
2004/05 0 6 0.00 14.63 41
2005/06 1 3 2.50 7.50 40
Year Output Areas Output Areas LLSOA LLSOA MLSOA MLSOA
Year SRMSE R2 SRMSE R2 SRMSE R2
2003/04 2.94 0.71 2.39 0.81 2.13 0.87
2004/05 2.83 0.72 2.27 0.82 2.03 0.88
2005/06 2.82 0.72 2.23 0.82 1.97 0.88
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School of Geography FACULTY OF ENVIRONMENT
Predicting the Future

• Using data on primary school pupils and
  progressing each cohort through to secondary
  school a fall in pupil numbers is observed
• These forecasts do not take into account that
  approximately 2 of each cohort enter private
  schools between year 6 and year 7
• Therefore, the fall in pupil numbers could be
  greater than predicted here

Year Pupils
2004 40,276
2005 41,538
2006 41,650
2007 41,422
2008 40,889
2009 40,304
2010 39,980
2011 39,778
2012 39,121
2013 38,486
change -1,790
change -4.44
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School of Geography FACULTY OF ENVIRONMENT
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School of Geography FACULTY OF ENVIRONMENT

• Summary
• Forecasting pupil numbers is becoming
  increasingly important
• Model development can be simplified by separating
  model equation and constraint into two stages
• Use of a genetic algorithm to breed models can
  give useful insight but results should be
  examined carefully
• Use of a series of spatial interaction models
  wrapped within a broader rule-based model
  controlling for specific features of each
  destination/school provides a good model for
  education planning
• Preference data is required to calibrate models,
  but not easily accessible

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School of Geography FACULTY OF ENVIRONMENT
Thank you for listening
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School of Geography FACULTY OF ENVIRONMENT
References Birkin, M., Clarke, G., Clarke, M.,
Culf, R. (2004). Using Spatial Models to Solve
Difficult Retail Location Problems, in Applied
GIS and Spatial Analysis, Eds Stillwell, J. and
Clarke, G. pp. 3554. John Wiley and Sons Ltd,
Chichester Demie, F. (2002). Pupil mobility and
education in schools an empirical analysis.
Educational Research 44(2)197 215 Diplock, G.
J. (1998). Building new spatial interaction
models by using genetic programming and a
supercomputer. Environment and Planning A
30(10)1893 1904 Dobson, J., Henthorne, K.,
Lynas, Z. (2000). Pupil Mobility in Schools
Final Report. Tech. rep., Department of
Geography, University College London Dobson, J.,
Pooley, C. E. (2004). Mobility, equality,
Diversity a study of pupil mobililty in the
secondary school system. Tech. rep., Department
of Geography, University College
London Fotheringham, A. S. (1983). A new set of
spatial interaction models the theory of
competing destinations. Environment and Planning
A 15(1)15 36 Fotheringham, A. S., Trew, R.
(1993). Chain image and store-choice modelling
the effects of income and race. Environment and
Planning A 25179 196 Gereluk, D. (2005).
Communities in a changing educational
environment. British Journal of Education
Studies 53(1)4 18 Gibson, A., Asthana, S.
(2000a). Local Markets and the polarization of
public-sector schools in England and Wales.
Transactions of the Institute of British
Geographers 25(3)303 319
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School of Geography FACULTY OF ENVIRONMENT
References Gibson, A., Asthana, S. (2000b).
Whats in a number? Commentary on Gorard and
Fitzs Investigating the determinants of
segregation between schools. Research Papers in
Education 15(2)133 153 Gorard, S. (1999).
Well. That about wraps it up for school choice
research a state of the art review. School
Leadership and Management 1925 47 Gorard, S.
(2000). Here we go again a reply to whats in
a number? by Gibson and Asthana. Research
Papers in Education 15(2)155 162 Gorard, S.
(2004). Comments on Modelling social
segregation by Goldstein and Noden. Oxford
Review of Education 30(3)435 440 Johnston, R.,
Wilson, D., Burgess, S. (2004). School
segregation in multiethnic England. Ethnicities
4(2)237 265 Johnston, R., Wilson, D., Burgess,
S. (2005). Englands multiethnic educational
system? a classification of secondary schools.
Environment and Planning A 3745 62 Johnston,
R., Burgess, S., Wilson, D., Harris, R. (2006).
School and Residential Ethnic Segregation An
Analysis of Variation across Englands Local
Education Authorities. Regional Studies
40(9)973 990 Jones, P., Elias, P. (2006).
Administrative data as a research resource a
selected audit. Economic Social Research
Council Regional Review Board Report 43/06,
Warwick Institute for Employment
Research Openshaw, S. (1998). Neural network,
genetic, and fuzzy logic models of spatial
interaction. Environment and Planning A
30(10)1857 1872 Openshaw, S. (unpublished). A
Model Breeder, University of Leeds, Leeds
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School of Geography FACULTY OF ENVIRONMENT
References Senior, M. L. (1979). From gravity
modelling to entropy maximizing a pedagogic
guide. Progress in Human Geography 3(2)175
210 Stillwell, J. C. H. (1978). Interzonal
migration some historical tests of
spatial-interaction models. Environment and
Planning A 10(10)1187 1200 Wilson, A. G.
(1971). A family of spatial interaction models,
and associated developments. Environment and
Planning 31 32