1. School of something FACULTY OF OTHER School of Geography FACULTY OF ENVIRONMENT Commuting to School: A New Spatial Interaction Modelling Framework for the Education Sector Email: k.harland98@leeds.ac.ukk.harland98@leeds.ac.uk Research Methods Festival 2 nd July 2008 Kirk Harland and John Stillwell

2. Presentation Context Modelling methodology Model structure Study area Simulating the past Predicting the future Summary School of Geography FACULTY OF ENVIRONMENT

3. 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

4. School of Geography FACULTY OF ENVIRONMENT

5. 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)

6. where is the predicted flow between i and j O i is the mass of origin zone i D j is the mass of destination zone j f(d ij ) is the distance function k is a balancing factor or constraint ensuring flows equate to a known value 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:

7. 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

8. 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 accept…BUT 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?

9. School of Geography FACULTY OF ENVIRONMENT Modelling Methodology Openshaw (1998, unpublished) and Diplock (1998) developed an approach for equation selection in the late 1990s 1.Separation of the model equation from the model constraint(s) (Openshaw 1998); and 2.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

10. where β is a calibrated distance decay parameter W j 2 is an estimated destination attractiveness factor School of Geography FACULTY OF ENVIRONMENT Modelling Methodology: Constraint Separation An origin constrained model (Wilson 1971) – 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

11. 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 O i value: Although, Openshaw (1998) only shows the origin constraint derivation, this principle can be applied to total, destination and double constrained models

12. 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 1.data item 2.parameter 3.function 4.operator

13. School of Geography FACULTY OF ENVIRONMENT Modelling Methodology: Equation Definition The simplified model is: It has 2 genes representing W j 2 and exp(βd ij ) with each gene having four parts: Encoded equation is: 2004 3124 Wj2.Wj2.exp(βd ij ) Data23 Parameter01 Function02 Operator44 Data Origin1 Destination2 Distance3 Parameter None0 Parameter1 Function None0 Log101 Exp2 Operator Addition1 Subtraction2 Division3 Multiplication4 Lookup tables

14. 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: School of Geography FACULTY OF ENVIRONMENT 20043004 and genes can be mutated: 20043124 21043024 21043124

15. 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

16. 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

17. School of Geography FACULTY OF ENVIRONMENT Model structure

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19. School of Geography FACULTY OF ENVIRONMENT Simulating the past School role simulation errors (observed vs. simulated school role numbers) Goodness of fit statistics Year Output AreasLLSOAMLSOA SRMSER2R2 R2R2 R2R2 2003/042.940.712.390.812.130.87 2004/052.830.722.270.822.030.88 2005/06 2.820.722.230.821.970.88 Year Predicted Role ErrorPercentage >20%20%>10%>20%20%>10%Schools 2003/045411.639.3043 2004/05060.0014.6341 2005/06132.507.5040

20. 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 YearPupils 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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22. 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

23. School of Geography FACULTY OF ENVIRONMENT Thank you for listening

24. 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. 35–54. 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 25:179 – 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

25. School of Geography FACULTY OF ENVIRONMENT References Gibson, A., Asthana, S. (2000b). ‘What’s in a number? Commentary on Gorard and Fitz’s ’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 19:25 – 47 Gorard, S. (2000). ‘Here we go again: a reply to ’what’s 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). ‘England’s multiethnic educational system? a classification of secondary schools’. Environment and Planning A 37:45 – 62 Johnston, R., Burgess, S., Wilson, D., Harris, R. (2006). ‘School and Residential Ethnic Segregation: An Analysis of Variation across England’s 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

26. 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 3:1 – 32