Methods of analysing change over time and space Ian Gregory (University of Portsmouth) & Paul Ell (Queens University, Belfast)

Advantages of temporal GIS data 1. Integration –Potentially any data with a spatial and a temporal reference can be integrated –Allows new data to be created 2. Analysis –Need to spot broad trends and places/times that show different patterns –Only limited techniques available: Multi-level modelling Geographically Weighted Regression (GWR) 3. Visualisation –Allows exploration of data and presentation of results In all cases we want to make best use of all of the available detail in the data (attribute, spatial and temporal)

Data integration: District-level net migration rates Net migration from the basic demographic equation NM t,t+n = (p t+n – p t ) - (B t,t+n - D t,t + n ) –Age and sex specific population, fertility and mortality data have been published decennially in Britain since the 1850s –Net migration for women aged 5 to 14 at the start of the decade can be calculated as: Females aged 15 to 24 at end of decade minus females aged 5 to 14 at start of decade minus number of deaths in the cohort through the decade –Problem: As net migration is the residual it is highly susceptible to error. In particular, the impact of any boundary changes will appear as migration. –Traditional studies: Most studies of net migration use county-level data to avoid boundary change issues Only use the census so are unable to sub-divide migrants by age/sex

Net migration through areal interpolation Standardise population and mortality data from many dates onto a single set of target units Integrate data from census and Registrar Generals Decennial Supplement Allows us to calculate net migration rates for males and females in ten-year cohorts from ages 5 to 14 to ages 55 to 64 (at start of decade).

Bristol Cheltenham Westbury Net migration rates among the 5 to 14 cohort Standardised time-series

Bristol Cheltenham Westbury Net migration rates among different cohorts in the 1920s Detailed attribute comparisons

Net migration: strengths and weaknesses Strengths: –From the census (comprehensive) –Can compute complete time-series from –Can be integrated with other aggregate information: Pop. density Employment Social class Proximity to coast/areas of natural beauty, etc. Weaknesses: –No information on flows –Low net mig. can be caused by high in and out mig. cancelling each other out –Ecological fallacy when analysing data

Other sources Pooley & Turnbull (1996) –Sample of 75,000 migrations by 16,000 people born created using genealogical societies. –Gives: Where each move was to and from (including grid references) When the move occurred Large amounts of attribute information on employment, family structure, etc. Strengths: –Detailed individual-level info Weaknesses: –Potentially biased sample –Doesnt include the young up to the present

Bringing them together –Both datasets are geo-referenced – can be integrated Allows: –Comparison of individual-level and ecological data (use of multi-level modelling) Tests whether ecological and individual level relationships are consistent Evaluates the accuracy of the sample Therefore: –Integrates different datasets –Makes full use of spatial, attribute and temporal information

Spatial analysis with GWR Global vs local analysis –Global analysis: Gives a single summary statistic or equation for whole study area Average relationship – implies spatial homogeneity –Local analysis: Allows parameters to vary over space Shows how relationships vary geographically Allows spatial heterogeneity

Geographically Weighted Regression Descriptive: Allows the relationship between the variables to vary over space by providing separate intercept and regression coefficients for every location on the map Test as to whether the model shows significant spatial variation Conventional regression: y i =a 0 +a 1 x 1i +a 2 x 2i +ε i GWR: y i =a 0 (u i,v i )+a 1 (u i,v i )x 1i +a 2 (u i,v i )x 2i +ε i –(u i,v i ) represents the coordinates of the ith point and a n (u i,v i ) is the impact of a n (u,v) at the ith point. This is implemented using a distance decay model

Example Global: LTLI i = UNEM i +31.1CROW i -3.5SPF i -22.5SC1 i -5.6DENS i Intercept UNEMDENS SC1

Mapping the R 2 i values Source: Fotheringham et al, 1998

Uses in spatio-temporal analysis –In C19 young women migrated as much as men but the spatial pattern differed significantly because of the different employment opportunities (main employers: domestic service, textiles) Conventional regression: –Mig proportional to DS and Text GWR: –Textiles attract women in Lancs/W. York –DS attracts women to wealthy areas eg West London, Cheltenham, Leamington Spa –Over time this pattern will become more complex and the differences between men and women will reduce