Geostatistical Analysis in ArcMap and Geoda

Exploring Spatial Patterns in Your Data

• Geostatistical Analysis tools in ArcMap are used to examine data.
• Descriptive statistics using ArcMap and Geoda are used to analyze data.
• Geostatistical Analysis tools can be used for further analysis.

Why Explore Your Data?

• Exploring your data allows a better selection of an appropriate tool for analysis.
• Skipping data exploration can lead to incorrect conclusions and decisions.

Geoda vs. ArcMap

• Geoda is free, open-source, and simple software for statistical analysis.
• ArcMap is proprietary GIS software for statistical analysis alongside other analyses.
• ArcMap allows for multiple data layers to be viewed simultaneously, while Geoda displays only one layer at a time.
• Some tools are available in both ArcMap and Geoda, while some are only available in one or the other.

Explore The Location Of Your Data

• Explore the size of the study area.
• Explore the mean and median of the data.
• Explore the direction data is oriented.
• Explore where data clusters are relative to the rest of the data.

Mean Center

• The Mean Center is the geographic center of a set of features.
• It's calculated using the average x and y values of the centroids (midpoints) of input polygons.

Median Center

• This is robust to outliers.
• The algorithm finds the point that minimizes travel distance to all other features.
• The location is refined until it minimizes Euclidean distances to all features.

Direction Distribution (Standard Deviational Ellipse)

• Summarizes spatial characteristics of features (central tendency, dispersion, directional trends).
• The ellipse shows if features are elongated and the orientation.
• A one standard deviation ellipse covers approximately 68% of the features.
• Two standard deviations cover approximately 95% of the features.
• Three standard deviations cover approximately 99% of the features.

Explore The Values Of Your Data

Normal Distribution

• Some analysis tools assume a normal distribution, with mean and median values being similar and data being symmetrical.

Data Frequency Using Histograms

• Histograms visually represent data frequency in classes.

Data Distribution Using a QQ Plot

• A normal QQ plot analyzes the relationship of the data to a normal distribution line. The dissimilar patterns in the plot show it's not normally distributed.

Box Plot

• Displays the median and interquartile range (IQR) of data (25% to 75% ).
• It shows a multiple-of-interquartile-range(Hinge) values.

Maps (for examining data values and frequencies)

• Quantile maps visually represent data and frequencies; each category has an equal number of observations.
• Natural breaks maps categorizes data to reduce variation within groups while maximizing variation between groups.
• Equal interval maps categorizes data with equal range values

Maps (for finding outliers)

• Percentile maps group ranked data into categories, with the lowest and highest 1% being potential outliers.
• Box maps divide data into four categories plus two outlier categories, detecting outliers with greater certainty than percentile maps.
• Standard deviation maps show data within three standard deviations above and below the mean; this is sensitive to outliers.

Semivariogram Cloud

• Shows spatial autocorrelation by plotting points; closer points with greater variations in values may indicate outliers.

Voronoi Map

• Cluster Voronoi maps show spatial outliers in data; simple Voronoi maps pinpoint data points that are many class breaks away from surrounding polygons. Data points far away from the surrounding polygons may be outliers

Histogram

• Data in extreme last bars of histogram that are far from adjacent values may be outliers.

Normal QQ Plot

• Values at the tails of a normal QQ plot could be outliers, especially if the values don't align with the reference line.

Boxplot

• Points outside the horizontal lines (hinges) are possible outliers.

Explore Spatial Relationships In Your Data

Spatial Autocorrelation

• Objects closer together are more related than those farther apart.
• Semivariogram graphs or clouds, Moran's I, and Getis-Ord G statistics are used to explore this.

Semivariogram

• Height (sill) is variation in data values.
• Range is the distance between points where the semivariogram flattens out.
• A horizontal line on a semivariogram indicates no spatial autocorrelation.

Variation in Your Data

• Many spatial statistics assume data is stationary, where relationships depend on distance instead of exact location.
• Voronoi maps (Simple, Mean, Mode, Cluster, Entropy) can discover how data varies and relate points to their surrounding points.

A Simple Voronoi Map

• Illustrates data value at each location and illustrates data variation across locations with classification.

Types of Voronoi Maps

• Simple: assigns a polygon based on the value recorded at the sample point.
• Mean: assigns the average value of the sample point and its neighbors.
• Mode: assigns the most frequent occurring value to a polygon.
• Cluster: assign data points in a similar color or category differently if the patterns are different from its neighbors
• Entropy: assigns values based on the relationships between surrounding sample points

Explore Trends in Your Data

Trend Analysis

• The trend analysis tool in ArcMap visually compares trend lines to patterns in data.
• Data locations in the map along X and Y axes. The values create the height, or Z-axis, of the points in the data points.
• Trends are analyzed by measuring the direction and order of the fitted trendline.
  • The fitted trendline can be a mathematical function (polynomial).

Selecting an Analysis Technique

Geostatistical Interpolation

• Creates surfaces using relationships between data locations and their values; this predicts values based on your existing data.
  • Assumes data is not clustered, normally distributed, stationary (no local variation), autocorrelated, and no local trends.

Global Deterministic Interpolation

• Uses existing values at each location using entire dataset to create surfaces
  • Assumes that outliers have been removed, and assume overall global trends in the data.

Local Deterministic Interpolation

• Uses subsets/neighborhoods within the dataset to create surface components
  • Assumes that the data is normally distributed.

Inverse Distance Weighted (IDW) Interpolation

• A type of local deterministic interpolation.
  • Assumes that the data is not clustered, and autocorrelated.

Other Spatial Statistical Tests

• Getis-Ord G and Global Moran's I: are tests that assess spatial autocorrelation (overall clustering and dispersion of values)
• Hot Spot Analysis (Getis-Ord Gi*) and Anselin's local Moran's I: determine specific clusters of high or low values.
• Regression: evaluates relationship between two or more feature attributes (e.g., location, crime rates, race, income, housing values).

This quiz explores the tools and techniques for geostatistical analysis using ArcMap and Geoda. It emphasizes the importance of data exploration and compares the capabilities of both software programs. Test your knowledge on how to effectively analyze spatial patterns in your data.