Lecture 8: Introduction to Spatial Statistics

Spatial Statistics

Location-based technique that involves methods for analyzing spatial distributions, patterns, processes and relationships

Central Feature

Identifies the most centrally located feature. Point that is the shortest distance to all other points in the dataset

Mean Center

Identifies the geographic center/center of concentration for a set of features

Median Center

Identifies the location that minimizes the overall Euclidean distance to the features in a dataset

Linear Directional Mean

Identifies the mean direction and orientation of the lines

Standard Distance

Measures the degree of concentration/dispersion of the features around the geometric mean center

Directional Distribution

To summarize the spatial characteristics of the geographical features: central tendency, dispersion, and directional trends

Descriptive statistics

similar to traditional statistics (computing mean, std dev, etc); single, summary measures of a spatial distribution

Spatial pattern analysis

Checking hotspots/cold spots (clustering/dispersion), outliers

Identifying and measuring spatial relationships

use of regression/spatial regression methods to examine relationships and identifying factors significant to/promoting the spatial pattern

Geostatistics

predictive modeling, interpolation methods using sample points; ideal for analyzing and predicting the values associated with nearly any kind of spatially continuous phenomena

Global statistics

identify and measure the pattern of the entire study area

Local statistics

identify variation across the study area, focusing on individual features and relationships to nearby features (for specific areas of clustering)

Global Moran’s I

Measures whether the pattern of feature values if clustered, dispersed or random

Local Moran’s I

Measures the strength of patterns for each specific feature. Compares the value of each feature in a pair to the mean value for all features in the study area.

Spatial Regression

• calculates a separate regression for each polygon and its neighbors

• maps the parameters from the model, such as the regression coefficient (b) and/or its significance value

Geostatistics

to optimize spatial sampling, selection of spatial resolution for image data and selection of support size for ground data

extent of similarity (Inverse Distance Weighted) or the degree of smoothing (Radial Basis Functions)

Deterministic techniques create surfaces from measured points based on either these two

Geostatistical

quantify the spatial autocorrelation among measured points and account for the spatial configuration of the sample points around the prediction location

Kriging

a geostatistical method used for spatial interpolation, estimating values at unsampled locations based on known values at nearby locations