Unlocking Spatial Autocorrelation: A Step-by-Step Guide to Calculation of Local Geary using ESDA & Pysal

Are you tired of dealing with confusing spatial patterns in your data? Do you want to uncover hidden relationships between your variables and understand how they vary across space? Look no further! In this comprehensive guide, we’ll dive into the world of spatial autocorrelation and explore the calculation of Local Geary using ESDA (Exploratory Spatial Data Analysis) and Pysal (Python Spatial Analysis Library).

What is Spatial Autocorrelation?

Spatial autocorrelation refers to the phenomenon where nearby values of a variable tend to be similar. This can occur due to various factors, such as geographic proximity, environmental factors, or social networks. Understanding spatial autocorrelation is crucial in fields like geography, epidemiology, urban planning, and economics, where spatial patterns can have a significant impact on decision-making.

Types of Spatial Autocorrelation

There are two main types of spatial autocorrelation:

• Positive Autocorrelation: Nearby values are similar, resulting in clustering or hotspots.
• Negative Autocorrelation: Nearby values are dissimilar, resulting in scattered patterns.

What is Local Geary?

Local Geary is a measure of spatial autocorrelation that calculates the similarity between a value and its neighbors. It’s a local version of the Global Geary index, which measures autocorrelation across the entire dataset. Local Geary is useful for identifying areas with high concentrations of similar values or anomalies.

Why Use ESDA and Pysal?

ESDA and Pysal are powerful tools for spatial analysis in Python. ESDA provides a range of functions for Exploratory Spatial Data Analysis, while Pysal offers a comprehensive library for spatial analysis and modeling. By combining these tools, we can efficiently calculate Local Geary and gain insights into our data.

Calculating Local Geary using ESDA and Pysal

Now that we’ve covered the basics, let’s dive into the step-by-step process for calculating Local Geary using ESDA and Pysal.

Step 1: Import Necessary Libraries

import esda
import pysal
import numpy as np
import pandas as pd
import geopandas as gpd
import matplotlib.pyplot as plt

Step 2: Load and Prepare Data

Load your dataset into a Pandas dataframe or GeoPandas GeoDataFrame. For this example, we’ll use a sample dataset of average temperatures across different cities.

df = pd.read_csv('temperatures.csv')
gdf = gpd.GeoDataFrame(df, geometry=gpd.points_from_xy(df.longitude, df.latitude))

Step 3: Calculate Spatial Weights

Calculate spatial weights using the `pysal.lib.weights` module. We’ll use a simple contiguity weights matrix, where each city is connected to its immediate neighbors.

w = pysal.lib.weights.Queen.from_dataframe(gdf)
w.transform = 'r'

Step 4: Calculate Local Geary

Use the `esda.geary` module to calculate Local Geary for each city. We’ll pass in the temperature values and spatial weights.

local_geary = esda.geary.Local_Geary(gdf['temperature'], w)

Step 5: Visualize Results

Visualize the Local Geary values using a choropleth map. We’ll use Matplotlib for this example.

fig, ax = plt.subplots(figsize=(10, 10))
gdf.plot(column='local_geary', cmap='viridis', ax=ax)
plt.show()

Interpreting Local Geary Values

The Local Geary values range from -1 to 1, indicating the level of spatial autocorrelation:

• Negative values: Indicate negative autocorrelation, where nearby values are dissimilar.
• Zero values: Indicate no autocorrelation, where nearby values are unrelated.
• Positive values: Indicate positive autocorrelation, where nearby values are similar.

Example Output

Let’s take a look at the calculated Local Geary values for our sample dataset:

City	Temperature (°C)	Local Geary
New York	10.2	0.73
Los Angeles	18.5	0.42
Chicago	7.1	-0.25
Houston	22.1	0.91

Conclusion

In this article, we’ve covered the calculation of Local Geary using ESDA and Pysal. By following these steps, you can unlock the power of spatial autocorrelation analysis and gain valuable insights into your data. Remember to interpret the Local Geary values in the context of your research question and data characteristics.

Next Steps

Want to take your spatial analysis skills to the next level? Explore other ESDA and Pysal functions, such as:

• Calculating Moran’s I and Getis-Ord Gi*
• Conducting spatial regression analysis
• Visualizing spatial patterns using clustering and network analysis

Stay tuned for more tutorials and guides on spatial analysis in Python!

Note: This article is for educational purposes only and is not intended to be used as a professional or academic resource.

Frequently Asked Question

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