Spatial Analysis Techniques

• Spatial analysis techniques are descriptions and formulas to analyse spatial data

Overview of Techniques Covered

• Overlay Analysis
• Buffer Analysis
• Hotspot Analysis
• Spatial Interpolation
• Network Analysis
• Geostatistical Modeling
• Spatial Autocorrelation
• Cluster Analysis

Overlay Analysis

• Combines multiple layers of data to identify data relationships and interactions
• It involves superimposing spatial datasets to create a new dataset highlighting interactions
• Common applications for overlay analysis are urban planning, environmental management, and resource allocation
• It uses Boolean operations (AND, OR, NOT) on raster or vector data

Buffer Analysis

• Creates zones around specific geographic features
• Generates buffer zones at a specified distance around points, lines, or polygons
• Common applications include environmental studies, urban planning, and public health, such as determining areas within a certain distance from a road or river

Mathematical Formula:

• d = √(x2 - x1)² + (y2 – y1)²

Hotspot Analysis

• Identifies areas with statistically significant clusters of high (hotspots) or low (cold spots) values
• Detects regions where data points are unusually concentrated, determining whether clustering is significant or due to random chance
• Common applications include crime mapping, disease outbreak detection, environmental monitoring, and market analysis

Mathematical Formula (Getis-Ord G*i):

• Variable explanations are provided to understand the formula.
• G* tests for high or low value clusters.
• High positive G*i values: Clustering of high attribute values ("hot spot").
• High negative values: Clustering of low attribute values (a "cold spot").
• Values near zero: No significant local clustering.

Spatial Interpolation

• Estimates unknown values at specific locations based on known values from surrounding areas.
• Spatial distribution is used to predict values in unmeasured regions.
• Methods include Inverse Distance Weighting (IDW), Kriging, and Spline interpolation.
• Applications in environmental science, meteorology, agriculture, and geology such as predicting rainfall or soil properties.

Mathematical Formula (IDW):

• Z(x) = (∑^n_(i=1) Zi/di) / (∑^n_(i=1) 1/di)
• where dᵢ is the distance to known points and Zᵢ the known value, p is the power parameter.

Network Analysis

• Studies relationships and interactions within networks
• Analyzes how nodes (points) and edges (lines) connect, assessing the flow of resources, information, or traffic
• Common applications are transportation planning, logistics, utility management, and telecommunications such as identifying bottlenecks or optimizing routes

Mathematical Formula (Dijkstra's Algorithm):

• D(v) = min(D(u) + w(u, v))
• D(v) is the shortest distance to vertex v; u is a neighboring vertex; and w(u, v) is the weight of the edge.
• Dijkstra's Algorithm is applied to find the lowest fuel cost route in a road network with five intersections

Geostatistical Modeling

• Uses statistical methods to analyze and predict spatial patterns and distributions
• Models spatial variability and performs predictive analysis based on the spatial correlation of known data points
• Techniques: Kriging, variogram analysis, and spatial regression
• Applications: Geology, environmental science, agriculture, and epidemiology, such as mapping mineral deposits or pollution levels

Mathematical Formula (Kriging):

• Z(x) = ∑^n_(i=1) λᵢZ(xᵢ)
• where λᵢ are the weights assigned to the known values Z(xᵢ)

Spatial Autocorrelation

• Measures the degree to which similar values occur near each other in space
• Quantifies the similarity (or dissimilarity) of an attribute among neighboring locations
• Positive Autocorrelation: Similar values cluster together
• Negative Autocorrelation: Dissimilar values are adjacent
• Applications: Geography, ecology, epidemiology, and urban planning

Mathematical Formula (Moran's I):

• I = (n * ∑ᵢ∑ⱼ wᵢⱼ(Yᵢ – Y)(Yⱼ – Y)) / (∑ᵢ∑ⱼ wᵢⱼ * ∑ᵢ(Yᵢ – Y)²)
• Where I is Moran’s I.
• Moran's I is a global measure evaluating spatial autocorrelation across a dataset.
• Expected Moran's I and variance create the basis for hypothesis testing.
• Moran’s Scatterplot and Local Moran’s I give localized insights into spatial patterns.

Hypothesis Testing for Autocorrelation:

• State the hypotheses: H₀ is I = E[I] indicating no spatial autocorrelation; H₁: I ≠ E[I] indicating spatial autocorrelation.
• Select significance level: Typically α = 0.05.
• Calculate the test statistic: z = (I - E[I]) / √Var[I].
• Determine the p-value comparing the computed z-value against the standard normal distribution.
• Decision: If the p-value is less than α, indicate significant spatial autocorrelation.

Univariate ESDA Techniques

• Choropleth Maps: visualize distribution by shading areas
• Frequency Distributions and Histograms: display distribution of data highlighting how often each value appears to help spotting anomalies
• Measures of Center, Spread, and Shape: summarize key data aspects like central tendency, variability and shape providing an overview of data properties
• Percentiles and Quartiles: divide data into equal parts determining distribution and extreme values, used to compare datasets and highlight outliers
• Outlier Detection: crucial for data cleaning
• Boxplots: show data distribution effectively comparing multiple distributions given quartiles for highlighting the median, interquartile range, and potential outliers
• Normal QQ Plot: assesses whether dataset follows a normal distribution providing observed values against expected normal values

Bivariate ESDA Techniques

• Scatterplots and Bubble Maps: analyze the relationship between two variables
• Bivariate Choropleth Maps: allows for the simultaneous display of two variables helpful to spatial patterns
• Bivariate Correlation Analysis: quantifies the degree of association between two variables using the most common correlation coefficients
• Bivariate Moran's I / LISA: spatial statistics measuring across-correlation between two variables across geographic areas
• Cross-Variogram Analysis: assesses spatial covariance widely studying co dependencies

Point Pattern Analysis

• It is an approach to analyzing geographic distributions and point patterns
• Centrography focuses on centrality, location, and dispersion.
• Point Pattern Analysis involves understanding the processes of point patterns

Centrography

• Is a set of descriptive statistical techniques summarizing the spatial characteristics of point patterns
• It focuses on centrality, location, and dispersion within a spatial distribution.
• Central Tendency: Measures the central point of a distribution.
• Dispersion and Orientation: Analyzes the spread and direction of points.
• Shape Analysis: Examines the overall shape formed by the points.

Standard Distance

• Measures the average distance of points from the mean center

Standard Deviational Ellipse (SDE)

• Summarizes spatial distribution by dispersion and orientation of the point pattern
• Major Axis: direction of maximum dispersion
• Minor Axis: direction of minimum dispersion
• Common techniques are measured depending on accessibility and dispersion

Spatial Process describes

• A mechanism generating a spatial pattern, shows points or events distributed in space.
• Influenced by environmental conditions, human activities, and random chance.
• Dispersed Pattern: Events scattered nearly uniformly
• Random Spatial Pattern: No clusters or dispersion identified
• Clustered Spatial Pattern: Clusters evident in parts of the region

Complete Spatial Randomness (CSR) Definition

• Spatial pattern where events occur independently and uniformly across a study area

Common characteristics

• Each location has an equal probability of hosting an event
• The occurrence of one event does not influence the occurrence of another

First-Order Effects

• Variations in point density due to underlying factors

Second-Order Effects

• Interactions between points; presence influences likelihood.

Point Pattern Analyses Methods divide in 2 main streams

• Distance-based methods: Analyze distances among events for interactions.
• Density-based methods: Examine intensity of event occurrence for variations.

Common Distance techniques

• Nearest Neighbor Method
• G and F distance functions
• Ripley's K function

Density Methods

• Quadrat Count Methods: Study area is divided and events counted
• Kernel Density Estimation (KDE): Provides continuous, local estimate

Average Nearest Neighbour Analysis

• It Assesses whether a point pattern is random, dispersed, or clustered by the observed mean distance
• The mean distance depends on Complete Spatial Randomness (CSR)

Ripley's K Function

• Identifies clustering or dispersion using a distance function
• It also compares the count of points and range versus what is expected under CSR

Kernel Density Estimation (KDE)

• Creates smooth maps; the concentration of points in an area.
• This estimates the probability density function of point distribution.