Spatial Misalignment

Transcription

1 Spatial Misalignment Let s use the terminology "points" (for point-level observations) and "blocks" (for areal-level summaries) Chapter 6: Spatial Misalignment p. 1/5

2 Spatial Misalignment Let s use the terminology "points" (for point-level observations) and "blocks" (for areal-level summaries) If a variable is observed at some points but inference is desired at other points, this is point-point misalignment: normally handled by kriging! Chapter 6: Spatial Misalignment p. 1/5

3 Spatial Misalignment Let s use the terminology "points" (for point-level observations) and "blocks" (for areal-level summaries) If a variable is observed at some points but inference is desired at other points, this is point-point misalignment: normally handled by kriging! What if the variable is observed at point level, but inference is desired at block levels? Leads to a block average and block kriging: Y (B) = 1 B B Y (s)ds 1 L Y (s l ), where the Monte Carlo approximation to the stochastic integral is based on random locations s l B, l = 1,...L. l Chapter 6: Spatial Misalignment p. 1/5

4 Block-Block Misalignment Population by census tract; residential structures by cell : Chapter 6: Spatial Misalignment p. 2/5

5 Block-Block vs. Block-Point Here a variable is observed at block level (say, census tracts) with inference desired at other blocks (say, the cells of the exposure windrose ) Chapter 6: Spatial Misalignment p. 3/5

6 Block-Block vs. Block-Point Here a variable is observed at block level (say, census tracts) with inference desired at other blocks (say, the cells of the exposure windrose ) In the geography literature, this is known as the modifiable areal unit problem (MAUP) Chapter 6: Spatial Misalignment p. 3/5

7 Block-Block vs. Block-Point Here a variable is observed at block level (say, census tracts) with inference desired at other blocks (say, the cells of the exposure windrose ) In the geography literature, this is known as the modifiable areal unit problem (MAUP) Hierarchical modeling offers a more sensible alternative to areal allocation (i.e., simply allocating counts proportional to the area of the subregions formed by the intersection of the two grids) Chapter 6: Spatial Misalignment p. 3/5

8 Block-Block vs. Block-Point Here a variable is observed at block level (say, census tracts) with inference desired at other blocks (say, the cells of the exposure windrose ) In the geography literature, this is known as the modifiable areal unit problem (MAUP) Hierarchical modeling offers a more sensible alternative to areal allocation (i.e., simply allocating counts proportional to the area of the subregions formed by the intersection of the two grids) Finally, what if the variable is observed at block level, but inference is sought at point level? Chapter 6: Spatial Misalignment p. 3/5

9 Block-Block vs. Block-Point Here a variable is observed at block level (say, census tracts) with inference desired at other blocks (say, the cells of the exposure windrose ) In the geography literature, this is known as the modifiable areal unit problem (MAUP) Hierarchical modeling offers a more sensible alternative to areal allocation (i.e., simply allocating counts proportional to the area of the subregions formed by the intersection of the two grids) Finally, what if the variable is observed at block level, but inference is sought at point level? Does this even make sense? Consider average rainfall over a block B vs. the number of disease cases in B Chapter 6: Spatial Misalignment p. 3/5

10 Bivariate misalignment Ozone measurements at fixed sites; counts of pediatric asthma cases by zip code in Atlanta, GA: Chapter 6: Spatial Misalignment p. 4/5

11 Bivariate misalignment issues When we have two spatially referenced variables, interest often lies in spatial regression. Chapter 6: Spatial Misalignment p. 5/5

12 Bivariate misalignment issues When we have two spatially referenced variables, interest often lies in spatial regression. But we cannot fit a regression if the two variables are misaligned: X at point level, Y at other points X at point level, Y at block level X at block level, Y at point level X at block level, Y at a different block level Chapter 6: Spatial Misalignment p. 5/5

13 Bivariate misalignment issues When we have two spatially referenced variables, interest often lies in spatial regression. But we cannot fit a regression if the two variables are misaligned: X at point level, Y at other points X at point level, Y at block level X at block level, Y at point level X at block level, Y at a different block level Solution: Bring the X s to the scale of the Y s, then fit the model (BCG, Sec 6.4) Chapter 6: Spatial Misalignment p. 5/5

14 Bivariate misalignment issues When we have two spatially referenced variables, interest often lies in spatial regression. But we cannot fit a regression if the two variables are misaligned: X at point level, Y at other points X at point level, Y at block level X at block level, Y at point level X at block level, Y at a different block level Solution: Bring the X s to the scale of the Y s, then fit the model (BCG, Sec 6.4) With more than two variables, bring all the variables to a common scale. Highest resolution is obviously preferred, but may be computationally infeasible! Chapter 6: Spatial Misalignment p. 5/5