1. GIS and Spatial Statistics: Methods and Applications in Public Health
Institute of Behavioral Science, Computing and Research Services, and the Social Sciences Data Lab
University of Colorado at Boulder - March 11, 2008
GIS and Spatial Statistics: Methods and Applications in Public Health
Marcia Castro
Assistant Professor of Demography
Harvard School of Public Health

2. Spatial Statistics First Law of Geography (Tobler 1979)
“Everything is related to everything else, but near things are more related than distant things.”

3. Types of research questions
Spatial determinants of transmission
Spatial associations of risk factors with disease and interaction with temporal processes
Origins of diseases and outbreaks
Spatial and temporal distribution of disease and risk factors
Planning of surveillance program and targeting control activities
Improved allocation of limited resources

4. Types of spatial data Points Area
Events – crimes, accidents, flu cases
Sample from a surface – air quality monitors, house sales
Objects – county centroids
Area
Aggregates of events – accidents per census tract
Summary measures – density, mean house value

5. Spatial Pattern Analysis
Some attributes
Testing of Hypothesis
Hypothesis generation
Pattern evolution
Pattern prediction
Clustering
Test spatial regression assumptions
Cannot unequivocally determine cause and effect
Cannot assign meaning to spatial relationships

6. Problems / Challenges Modifiable areal unit problem (MAUP)
Scale effect – spatial data analysis at different scales may produce different results
Zoning effect – regrouping zones at a given scale may produce different results
Optimal neighborhood size
Alternative zoning schemes

7. Problems / Challenges Spatial dependence Spatial heterogeneity
Tobler’s law
Spatial heterogeneity
Uneven distributions at the global scale
Boundary problems
Missing data
Confidentiality
Collection, analysis, publication, data sharing
Disclosure risk
Methods do mask data

8. Spatial Autocorrelation
Null hypothesis:
Spatial randomness
Values observed at one location do not depend on values observed at neighboring locations
Observed spatial pattern of values is equally likely as any other spatial pattern
The location of values may be altered without affecting the information content of the data
Regular
Random
Aggregated

9. Spatial autocorrelation
Formal test of match between locational similarity and value similarity
Locational similarity defined by spatial weights
Binary or Standardized
Types of neighborhoods:
Contiguity (common boundary)
Distance (distance band, K-nearest neighbors)
General weights (social distance, distance decay)

10. Spatial autocorrelation
Test for the presence of spatial autocorrelation
Global
Local
LISA – Local Indicators of Spatial Autocorrelation

11. Local spatial autocorrelation – LISA
Moran’s Ii, Geary’s ci, Ki
Test CSR – positive and negative autocorrelation
positive - similar values (either high or low) are spatially clustered
negative - neighboring values are dissimilar

12. Local spatial autocorrelation – LISA
Gi (d)
Does not consider the value of location i itself
Used for spread or diffusion studies
Useful for focal clustering
e.g. cholera infection around a specific water source
Gi*(d)
Takes the value of location i into account
Most appropriate for the identification of clusters
High and low values
Choice of d is not straightforward

13. Local Statistics (21)  (10)  (9)  (12)  (6)  (22)  (19)  (17) 
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14. Local Statistics (21)  (10)  (9)  (12)  (22)  (19)  (17)  (3) 
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15. Local Statistics Multiple and dependent tests
Two sources of spatial dependence
Geometric
Between the values of nearby locations

16. Proportion of rejected hypotheses that are erroneously rejected
Local Statistics
Multiple comparison correction
Conservative – Bonferroni, Sidak
Probability that a true null hypothesis is incorrectly rejected - Type I error
False Discovery Rate
Proportion of null hypotheses incorrectly rejected among all those that were rejected
Q = V / (V + S)
Proportion of rejected hypotheses that are erroneously rejected
FDR defined as the mean of Q:

17. FDR & Local Statistics

18. Methods Geostatistics
Semivariogram & Kriging
Weight the surrounding measured values to derive a prediction for each location
Weights are obtained from the semivariogram

19. Semivariogram

20. Creating the empirical semivariogram
values

21. Directional Influence (Anisotropy)

22. Fitting a model to the empirical semivariogram
Empirical values
Fitted model

23. Kriging
BLUE
Different models
e.g. Cokriging
Prediction error

24. Methods Multivariate analysis
The presence of spatial autocorrelation violates the independence assumption of standard linear regression models
Checking residuals – Moran’s I
Geographically weighted regression
Local estimates of regression parameters
Spatial weights – distance-decay kernel functions
Not parsimonious

25. Methods Multivariate analysis Spatially filtered regression
Spatial econometrics
Spatial lag model (real contagion)
Value of the dependent variable in one area is influenced by the values of that variable in the surrounding neighborhood;
A weighted average of the dependent value for the neighborhood location is introduced as an additional covariate.
Spatial error model (false contagion model)
Omitted covariates;
Autoregressive error term is included.

26. Spatial Analysis & Policy Making
“…although basic science is directed at the discovery of general principles, the ultimate value of such knowledge, apart from simple curiosity, lies in our ability to apply it to local conditions and, thus, determine specific outcomes. Although such science may itself be placeless, the application of scientific knowledge in policy inevitably requires explicit attention to spatial variation, particularly when the basis of policy is local.”
(Goodchild, Anselin, Appelbaum and Harthorn 2000: 142)