“Alternative Distance Metrics for Enhanced Reliability of Spatial Regression Analysis of Health Data” Third International Workshop on "Geographical Analysis, Urban Modeling, Spatial Statistics"

1. Alternative Distance Metrics for Enhanced Reliability of Spatial Regression Analysis of Health Data Stefania Bertazzon & Scott Olson, 2008

2. Here, a spatial regression model is calibrated to increase its reliability by specifying a spatial weighting matrix that best captures neighbourhood connectivity, hence the spatial dependence in the observed variables. Introduction

3. The method we proposed to achieve this goal involves altering the method used for calculating the distance metrics inherent to the foundation of the spatial weighting matrix in spatial autoregressive models. This alternative approach can reflect overall spatial connectivity more accurately than the traditionally utilized distance metrics . Introduction

4. Locational foundation of spatial regression. Spatial Regression Y = X β + ρ WY + ε

5. Locational foundation of spatial regression. Spatial Regression Y = X β + ρ WY + ε

6. Locational foundation of spatial regression. Contiguity Matrix Y = X β + ρ Y + ε

7. Distance Metrics point ‘j’ Euclidean Distance: d ij = [(x i – x j ) 2 + (y i – y j ) 2 ] 1/2 Manhattan Distance d ij = | x i – x j | + | y i – y j | point ‘i’

8. Distance Metrics source: Jacobs, Allan. (1993). Great Streets . Cambridge, Mass.: MIT Press. Calgary, Canada The purpose is not to mimic the city road network but to select a distance metric that best represents neighbourhood connectivity, which is consequently defined by the interplay of road network and urban design. Combination of all historical street development patterns: Evolution of street patterns since 1900 showing gradual adaptation to the car. From: Southworth M. (1997). Streets and the Shaping of Towns and Cities . New York: McGraw-Hill.

9. Alternative Distance Metric point ‘j’ Euclidean distance: d ij = [(x i – x j ) 2 + (y i – y j ) 2 ] 1/2 Manhattan distance d ij = | x i – x j | + | y i – y j | Minkowski distance d ij = [(x i – x j ) p + (y i – y j ) p ] 1/p [ 1 1 ] 1/1 point ‘i’

10. Case Study Where: Y = number of catheterization cases; X 1 = number of 2 parent families with children at home***; X 2 = number of persons with a post-secondary, non-university degree**; X 3 = family median income**; X 4 = number of persons with grade 13 or lower education***. Negative relationship with Y Positive relationship with Y Y = β o + ρ WY + β 1 X 1 + β 2 X 2 + β 3 X 3 + β 4 X 4 + ε

11. Case Study Manhattan distance p=1 Euclidean distance p=2 Minkowski p=1.6 Study area: Calgary, Canada using data at the Census Tract scale

12. Findings

13. Findings

14. Findings

17. Thank You; Grazie