Some comments on modifiable areal units Transforming data from one to another geographical system

1. Some comments on modifiable areal units Transforming data from one to another geographical system Javier.gallego@jrc.it JRC – Ispra

2. Various problems linked with the change from one set of areal units to a different one How to aggregate data? Simple addition (easy in principle) Smoothing (making maps easy to interpret) How to disaggregate data? Other phenomena: e.g. what happens with correlations when data are aggregated? The modifiable areal unitproblem JRC – Ispra

3. Yi is known for geographic units Ai, i=1…I . We want Yk for subunits Bk So that Data disaggregation • Different situations: • Only the target variable Y for units Ai is known. • A covariable Z is known for units Bk, but limited information on the link between Y and Z. • A covariable Z is known for units Bk, and the link between Y and Z is rather well known . • Individual data with co-ordinates known (generally confidential) • Possibly with a covariable JRC – Ispra

4. First step: Ask yourself: Are you really sure that you do not have any additional information? If you are sure you have several options, but none of them is usually good: Attribution proportional to area Smoothing Good for map simplification May be used for disaggregation if the target variable tends to be geographically smooth. Disaggregation without additional information JRC – Ispra

5. Simple areal weighting: illustration Simulated example of administrative units and catchments • Aim: attributing to catchments values of a statistical magnitude known for administrative units • Method: attributing to each intersection an amount proportional to the area and reaggregating per catchment JRC – Ispra

6. Effect when the item is spatially concentrated The representation by administrative unit gives a poor picture, but reallocating to catchments worsens things JRC – Ispra

7. Item with homogeneous distribution in each administrative unit Reallocation gives a completely wrong picture. JRC – Ispra

8. Effect when the item is homogeneous per catchment Representation by administrative unit is quite bad, but reallocating to catchments does not improve things. JRC – Ispra

9. Examples of covariables: thematic maps (land cover, soil, DEM, etc.) Areal weighting with coefficients proportional to known Uj For subunit Bk Covariable Z known for sub-units with good information on the link Y-Zj. JRC – Ispra

10. Target variable: Y=use of fertilizers Co-variable Z: CORINE Land Cover We assume we have reliable data by NUTS 2 We need: Approx. input per ha of crop in the area Proportion of area of each crop in each CLC class (can be estimated from LUCAS) Example of disaggregation with good information from co-variables JRC – Ispra

11. Raw profiles of CLC classes from LUCAS (EU15 except Sweden) JRC – Ispra

12. CLC profiles with LUCAS need to be improved: Cleaning noise from co-location inaccuracy Adaptation to different geographical areas. Input per ha of a given crop is not homogeneous. Data per NUTS2 are not necessarily reliable Etc… But “perfect” is sometimes an enemy of “good” But things are not so easy…. JRC – Ispra

13. Disaggregation based on a model with parameters estimated using Y and Z Defining a mask EM algorithm Iterative estimation with several levels of aggregation Etc… Examples of covariables: thematic maps (land cover, soil, DEM, etc.) Covariable Z known for sub-units with little information on the link Y-Z. JRC – Ispra

14. Simple areal weighting combined with a mask The mask improves the mapping, but reaggregating in a different system degrades it again. JRC – Ispra

15. Target variable: population (available by commune) Co-variable: land cover map (CLC) Output: estimated population density map with the resolution of CLC. Example of disaggregation with an iterative algorithm JRC – Ispra

16. Disaggregating population density. Principle of the iterative algorithm Known levels To be estimated JRC – Ispra

17. Pretend that you only know data at the highest level (NUTS2) Disaggregate with your covariable (CLC) and an initial set of coefficients to commune level Measure disagreement with known commune data Get new coefficients that reduce the disagreement Repeat until the disagreement becomes stable Apply the estimated coefficients to the commune data. Iterative algorithm JRC – Ispra

18. Aggregating data to a different spatial system is easy in principle Posible impact on the variance If a covariable is known: Small area estimators (Bayesian technique), that uses: Sample units inside the small area Link between sample and co-variable everywhere Same spatial system desirable for co-variable and results. Individual data known (e.g. area frame survey) JRC – Ispra

19. It is always possible to disaggregate and produce a map. A different question is the quality of the disaggregation The key point is using pertinent covariables A number of algorithms can be used Assess how precise is the link between the co-variable and the target variable. General comments to disaggregation JRC – Ispra