JOINT RESEARCH CENTRE

1
Some comments on modifiable areal units
Transforming data from one to another
geographical system
Javier.gallego_at_jrc.it
2
The modifiable areal unit problem

• 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?

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Data disaggregation

• Yi is known for geographic units Ai, i1I .
• We want Yk for subunits Bk
• So that

• 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

4
Disaggregation without additional information

• 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.

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

6
Effect when the item is spatially concentrated
The representation by administrative unit gives a
poor picture, but reallocating to catchments
worsens things
7
Item with homogeneous distribution in each
administrative unit
Reallocation gives a completely wrong picture.
8
Effect when the item is homogeneous per catchment
Representation by administrative unit is quite
bad, but reallocating to catchments does not
improve things.
9
Covariable Z known for sub-units with good
information on the link Y-Zj.

• Examples of covariables thematic maps (land
  cover, soil, DEM, etc.)
• Areal weighting with coefficients proportional
  to known Uj
• For subunit Bk

10
Example of disaggregation with good information
from co-variables

• Target variable Yuse 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)

11
Raw profiles of CLC classes from LUCAS (EU15
except Sweden)
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But things are not so easy.

• 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

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Covariable Z known for sub-units with little
information on the link Y-Z.

• 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.)

14
Simple areal weighting combined with a mask
The mask improves the mapping, but reaggregating
in a different system degrades it again.
15
Example of disaggregation with an iterative
algorithm

• Target variable population (available by
  commune)
• Co-variable land cover map (CLC)
• Output estimated population density map with the
  resolution of CLC.

16
Disaggregating population density. Principle of
the iterative algorithm
Known levels
To be estimated
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Iterative algorithm

• 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.

18
Individual data known (e.g. area frame survey)

• 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.

19
General comments to disaggregation

• 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.