1. IS415 Geospatial Analytics for Business Intelligence
Lesson 10: Geospatial Data Analysis
Part 1: Lattice Analysis

2. What will you learn from this lesson
The differences between GIS analysis and geospatial data analysis
Challenges face in analysing geospatial data
The basic concepts of point patterns and point patterns analysis techniques

3. Core Competencies Capable to setup a Geospatial Web Server
Capable to design and implement web map services that are conformed to OCG WMS standard
Capable to design and implement web feature services that are conformed to OCG WFS standard

4. Tobler’s First law of Geography
Everything is related to everything else, but near things are more related than distant things
Structure of Spatial Dependence
Distance decay
Closeness = Similarity
Source: and

5. Question?

6. Defining Spatial Weight Matrices
Adjacency criterion:
if location j is adjacent to i,
wij = 
if location j is not adjacent to i.
Distance criterion:
if location j is within distance d from i,
wij (d) = 
otherwise.
A general spatial distance weight matrices:
wij (d) = dij-ab

7. Spatial Weight Matrix: Contiguity Weight

8. Identifying Global Pattern of Spatial Distribution
Moran I:
Geary C:
Moran I (Z value) is
positive: observations tend to be similar;
negative: observations tend to be dissimilar;
approximately zero: observations are arranged randomly over space.
Geary C:
large C value (>>1): observations tend to be dissimilar;
small C value (<<1) indicates that they tend to be similar.

9. Identifying Local Patterns of Spatial Distribution
Local Moran:
significant and negative if location i is
associated with relatively low values in
surrounding locations;
significant and positive if location i is
associated with relatively high values of
the surrounding locations.
Local Geary:
significant and small Local Geary (t<0)
suggests a positive spatial association
(similarity);
significant and large Local Geary (t>0)
suggests a negative spatial association
(dissimilarity).

10. Modifiable Areal Unit Problem (MAUP)
Aggregation Problem
Special case of ecological fallacy
Spatial heterogeneity
A million spatial allocarrelation coefficients
Zonation Problem
Both in size and spatial arrangement

11. Why do relationships vary spatially?
Sampling variation
Nuisance variation, not real spatial non-stationarity
Relationships intrinsically different across space
Real spatial non-stationarity
Model misspecification
Can significant local variations be removed?

12. Some definitions
Spatial non-stationarity: the same stimulus provokes a different response in different parts of the study region
Global models: statements about processes which are assumed to be stationary and as such are location independent
Local models: spatial decompositions of global models, the results of local models are location dependent – a characteristic we usually anticipate from geographic (spatial) data

13. Regression
Regression establishes relationship among a dependent variable and a set of independent variable(s)
A typical linear regression model looks like:
yi=0 + 1x1i+ 2x2i+……+ nxni+i
With yi the dependent variable, xji (j from 1 to n) the set of independent variables, and i the residual, all at location i
When applied to spatial data, as can be seen, it assumes a stationary spatial process
The same stimulus provokes the same response in all parts of the study region
Highly untenable for spatial process

14. Geographically weighted regression
Local statistical technique to analyze spatial variations in relationships
Spatial non-stationarity is assumed and will be tested
Based on the “First Law of Geography”: everything is related with everything else, but closer things are more related

15. GWR Addresses the non-stationarity directly
Allows the relationships to vary over space, i.e., s do not need to be everywhere the same
This is the essence of GWR, in the linear form:
yi=i0 + i1x1i+ i2x2i+……+ inxni+i
Instead of remaining the same everywhere, s now vary in terms of locations (i)

16. A Hedonic House Pricing Model
Housing hedonic model in Milwaukee
Data: MPROP 2004 – samples used
Dependent variable: the assessed value (price)
Independent variables: air conditioner, floor size, fire place, house age, number of bathrooms, soil and Impervious surface (remote sensing acquired)

17. The global model

18. The global model
62% of the dependent variable’s variation is explained
All determinants are statistically significant
Floor size is the largest positive determinant; house age is the largest negative determinant
Deteriorated environment condition (large portion of soil&impervious surface) has significant negative impact

19. GWR run: summary
Number of nearest neighbors for calibration: 176 (adaptive scheme)
AIC: (global: )
GWR performs better than global model

20. GWR run: non-stationarity check
F statistic
Numerator DF
Denominator DF*
Pr (> F)
Floor Size
2.51
325.76
0.00
House Age
1.40
192.81 1
001.69
Fireplace
1.46
80.62
0.01
Air Conditioner
1.23
429.17
Number of Bathrooms
2.49
262.39
Soil&Imp. Surface
1.42
375.71
Tests are based on variance of coefficients, all independent variables vary significantly over space

22. General conclusions
Except for floor size, the established relationship between house values and the predictors are not necessarily significant everywhere in the City
Same amount of change in these attributes (ceteris paribus) will bring larger amount of change in house values for houses locate near the Lake than those farther away

23. General conclusions
In the northwest and central eastern part of the City, house ages and house values hold opposite relationship as the global model suggests
This is where the original immigrants built their house, and historical values weight more than house age’s negative impact on house values

24. Calibration of GWR Local weighted least squares
Weights are attached with locations
Based on the “First Law of Geography”: everything is related with everything else, but closer things are more related than remote ones

25. Weighting schemes Determines weights
Most schemes tend to be Gaussian or Gaussian-like reflecting the type of dependency found in most spatial processes
It can be either Fixed or Adaptive
Both schemes based on Gaussian or Gaussian-like functions are implemented in GWR3.0 and R

26. Fixed weighting scheme
Bandwidth
Weighting function

27. Problems of fixed schemes
Might produce large estimate variances where data are sparse, while mask subtle local variations where data are dense
In extreme condition, fixed schemes might not be able to calibrate in local areas where data are too sparse to satisfy the calibration requirements (observations must be more than parameters)

28. Adaptive weighting schemes
Weighting function
Bandwidth

29. Adaptive weighting schemes
Adaptive schemes adjust itself according to the density of data
Shorter bandwidths where data are dense and longer where sparse
Finding nearest neighbors are one of the often used approaches

30. Calibration
Surprisingly, the results of GWR appear to be relatively insensitive to the choice of weighting functions as long as it is a continuous distance-based function (Gaussian or Gaussian-like functions)
Whichever weighting function is used, however the result will be sensitive to the bandwidth(s)

31. Calibration
An optimal bandwidth (or nearest neighbors) satisfies either
Least cross-validation (CV) score
CV score: the difference between observed value and the GWR calibrated value using the bandwidth or nearest neighbors
Least Akaike Information Criterion (AIC)
An information criterion, considers the added complexity of GWR models