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

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

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

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

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

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

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

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

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)

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

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

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

Local Statistics (21)  (10)  (9)  (12)  (6)  (22)  (19)  (17)  (3)  (7)  (20)  (16)  (18)  (13)  (11)  (5)  (4)  (24)  (15)  (8)  (14)  (23)  (2)  (1) 

Local Statistics (21)  (10)  (9)  (12)  (22)  (19)  (17)  (3)  (7)  (20)  (16)  (18)  (13)  (11)  (5)  (4)  (24)  (15)  (8)  (14)  (23)  (2)  (1)  (6) 

Local Statistics Multiple and dependent tests Two sources of spatial dependence Geometric Between the values of nearby locations

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:

FDR & Local Statistics

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

Semivariogram

Creating the empirical semivariogram values

Directional Influence (Anisotropy)

Fitting a model to the empirical semivariogram Empirical values Fitted model

Kriging BLUE Different models e.g. Cokriging Prediction error

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

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.

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)