Point Pattern Analysis of Theft from Motor Vehicles in Toronto
Embedded Files
Ryan Grammer
GIST 602B
Problem Statement
Theft from parked cars is all to common in big cities, including Toronto. In this analysis, we will take a look at reported theft from car locations in Toronto for the year of 2023. By analyzing the locations where the most theft occurs, we can work with Law Enforcement to help curb crime. The null hypothesis is that the theft from motor vehicle locations are randomly distributed across the entire study area. Are we able to find a pattern in the locations that theft takes place to find that certain areas are more likely to have cars broken into?
Theft from parked cars is all to common in big cities, including Toronto. In this analysis, we will take a look at reported theft from car locations in Toronto for the year of 2023. By analyzing the locations where the most theft occurs, we can work with Law Enforcement to help curb crime. The null hypothesis is that the theft from motor vehicle locations are randomly distributed across the entire study area. Are we able to find a pattern in the locations that theft takes place to find that certain areas are more likely to have cars broken into?
Data
The study area of this analysis is the city of Toronto. It is the capital city of the Ontario province in Canada and is also the most populous city in Canada. Toronto covers 244 square miles, approximately 27 miles long and 12 miles wide at its farthest ends. As of 2022, the city had a population a little north of 3 million people, while the greater Toronto area had an estimated 6.5 million.
The study area of this analysis is the city of Toronto. It is the capital city of the Ontario province in Canada and is also the most populous city in Canada. Toronto covers 244 square miles, approximately 27 miles long and 12 miles wide at its farthest ends. As of 2022, the city had a population a little north of 3 million people, while the greater Toronto area had an estimated 6.5 million.
This data comes from the Toronto Police Service, the city's police force. The dataset contains all Theft from Motor Vehicle occurrences by reported date and related offenses since 2014, although we will be specifically looking at the offenses that occurred in 2023.
This data comes from the Toronto Police Service, the city's police force. The dataset contains all Theft from Motor Vehicle occurrences by reported date and related offenses since 2014, although we will be specifically looking at the offenses that occurred in 2023.
Map of the study area
Metadata table
Methods
The projection that I used for this data is NAD 1983 UTM Zone 17N. I came to the conclusion that this projection is best as it was recommended by Esri Canada. This projected coordinate system works well to minimize distortion in large scale maps, such as the Toronto area. Since Toronto is relatively small, it works out that the city's limits fall in the middle of Zone 17N, limiting distortion.
The projection that I used for this data is NAD 1983 UTM Zone 17N. I came to the conclusion that this projection is best as it was recommended by Esri Canada. This projected coordinate system works well to minimize distortion in large scale maps, such as the Toronto area. Since Toronto is relatively small, it works out that the city's limits fall in the middle of Zone 17N, limiting distortion.
There are 8,687 points in the dataset for the year 2023. Each point indicates a location where a theft from a motor vehicle occurred. From the description of the dataset, "the location of crime occurrences have been deliberately offset to the nearest road intersection node to protect the privacy of parties involved in the occurrence".
There are 8,687 points in the dataset for the year 2023. Each point indicates a location where a theft from a motor vehicle occurred. From the description of the dataset, "the location of crime occurrences have been deliberately offset to the nearest road intersection node to protect the privacy of parties involved in the occurrence".
The extent of the analysis is the city of Toronto. From the description of the dataset, we find that all theft occurred within the city limits. Instead of using the Feature to Polygon geoprocessing tool in ArcGIS Pro, I was able to find a dataset that includes the boundary of the city.
The extent of the analysis is the city of Toronto. From the description of the dataset, we find that all theft occurred within the city limits. Instead of using the Feature to Polygon geoprocessing tool in ArcGIS Pro, I was able to find a dataset that includes the boundary of the city.
The Quadrat Count method is a point pattern analysis that divides the study area into a grid of equal sized areas (quadrats), then counts the number of features in each quadrat. First, we add a weight field to the dataset, giving each feature a weight of 1 using the Calculate Field geoprocessing tool. We then use the Create Fishnet tool to create the quadrats, which are sized in a 10x10 grid. Finally, we use the Summarize Within tool to get a sum of points in each quadrat.
The Quadrat Count method is a point pattern analysis that divides the study area into a grid of equal sized areas (quadrats), then counts the number of features in each quadrat. First, we add a weight field to the dataset, giving each feature a weight of 1 using the Calculate Field geoprocessing tool. We then use the Create Fishnet tool to create the quadrats, which are sized in a 10x10 grid. Finally, we use the Summarize Within tool to get a sum of points in each quadrat.
Add Field Geoprocessing Tool (ArcGIS Pro)
Calculate Field Geoprocessing Tool (ArcGIS Pro)
Create Fishnet Geoprocessing Tool (ArcGIS Pro)
Summarize Within Geoprocessing Tool (ArcGIS Pro)
Frequency Geoprocessing Tool (ArcGIS Pro)
The Average Nearest Neighbor method analyzes the distance between each point and the closest point to that point (the nearest neighbor), then takes the average of all the distances from those calculated. A ratio is then calculated by dividing the calculated average distance by the expected average distance based on a random distribution. If the ratio is less than 1, the features are considered to be clustered, while a ratio greater than 1 considers the points to be dispersed. A ratio of exactly 1 is a random distribution of points.
The Average Nearest Neighbor method analyzes the distance between each point and the closest point to that point (the nearest neighbor), then takes the average of all the distances from those calculated. A ratio is then calculated by dividing the calculated average distance by the expected average distance based on a random distribution. If the ratio is less than 1, the features are considered to be clustered, while a ratio greater than 1 considers the points to be dispersed. A ratio of exactly 1 is a random distribution of points.
Average Nearest Neighbor Geoprocessing Tool (ArcGIS Pro)
The Ripley K method analyzes the point pattern by using a distance increment. By calculating the number of neighbors that a feature has as the distance grows, we can compare the number to the average number of neighbors that all the features have. If the number of neighbors at a specific distance is higher than the average (expected) number of neighbors, the distribution is considered to be clustered. Similarly, if the number of neighbors at a specific distance is higher than the average (expected) number of neighbors, the distribution is considered to be dispersed. The Ripley K method creates a line graph, where we can see how the distance affects the clustering of points as it grows.
The Ripley K method analyzes the point pattern by using a distance increment. By calculating the number of neighbors that a feature has as the distance grows, we can compare the number to the average number of neighbors that all the features have. If the number of neighbors at a specific distance is higher than the average (expected) number of neighbors, the distribution is considered to be clustered. Similarly, if the number of neighbors at a specific distance is higher than the average (expected) number of neighbors, the distribution is considered to be dispersed. The Ripley K method creates a line graph, where we can see how the distance affects the clustering of points as it grows.
Ripley's K Function Geoprocessing Tool (ArcGIS Pro)
I used a 50 x 50 grid for the Quadrat Count analysis. This means there were 2500 quadrats covering the entire study area. Since the study area is oriented diagonally due to the way the city limits are, 1079 quadrats cover areas that are in the study area. This is plenty of quadrats to cover the area of the city (632 square kilometers). Each quadrat covers around 3/5th's of a square kilometer of the study area, making the quadrats around 750 meters x 750 meters. For the Ripley's K Function analysis, I used a 50 meter distance increment to take into account the large area that the study area covers. This distance increment, along with the beginning distance at 0, and 10 distance bands, can be used to accurately analyze the data set. The largest distance calculated was less than one-third of a mile (500 meters).
I used a 50 x 50 grid for the Quadrat Count analysis. This means there were 2500 quadrats covering the entire study area. Since the study area is oriented diagonally due to the way the city limits are, 1079 quadrats cover areas that are in the study area. This is plenty of quadrats to cover the area of the city (632 square kilometers). Each quadrat covers around 3/5th's of a square kilometer of the study area, making the quadrats around 750 meters x 750 meters. For the Ripley's K Function analysis, I used a 50 meter distance increment to take into account the large area that the study area covers. This distance increment, along with the beginning distance at 0, and 10 distance bands, can be used to accurately analyze the data set. The largest distance calculated was less than one-third of a mile (500 meters).
Results
Quadrat Count Method
Quadrat Count Method
Variance Mean Ratio Table
From the Quadrat Count Method, we see that the variance is 57.95, and the Variance Mean Ratio (VMR) is 16.68. The analysis concludes that the dataset is clustered since the VMR is greater than 1.
From the Quadrat Count Method, we see that the variance is 57.95, and the Variance Mean Ratio (VMR) is 16.68. The analysis concludes that the dataset is clustered since the VMR is greater than 1.
Average Nearest Neighbor Method
Average Nearest Neighbor Method
HTML Report for Average Nearest Neighbor
The Average Nearest Neighbor analysis method shows us a z-score of -104.41 and p-value of 0. We can conclude that the distribution tends to be clustered, as the z-score is negative and the p-value is 0.
The Average Nearest Neighbor analysis method shows us a z-score of -104.41 and p-value of 0. We can conclude that the distribution tends to be clustered, as the z-score is negative and the p-value is 0.
Ripley's K Method
Ripley's K Method
Ripley's K Function Line Graph
The Ripley's K Function line graph shows that the observed spatial pattern is clustered throughout the distances. We see that the Observed K values are way above the high confidence envelope, and that they remain above the high confidence envelope as the distance increases.
The Ripley's K Function line graph shows that the observed spatial pattern is clustered throughout the distances. We see that the Observed K values are way above the high confidence envelope, and that they remain above the high confidence envelope as the distance increases.
Conclusion
Based on the three different analyses conducted, we can conclude that the dataset follows a clustered spatial distribution. The Quadrat Count method showed us that the Variance Mean Ratio (VMR) was 16.68, which is greater than 1. Our conclusion is supported by this analysis method as a VMR greater 1 is considered to be clustered. The Average Nearest Neighbor analysis method shows us a z-score of -104.41 and p-value of 0. We can conclude that the distribution tends to be clustered, as a negative z-score is considered to be clustered and a p-value of 0 is conclusive that this could not have been a random distribution.
Based on the three different analyses conducted, we can conclude that the dataset follows a clustered spatial distribution. The Quadrat Count method showed us that the Variance Mean Ratio (VMR) was 16.68, which is greater than 1. Our conclusion is supported by this analysis method as a VMR greater 1 is considered to be clustered. The Average Nearest Neighbor analysis method shows us a z-score of -104.41 and p-value of 0. We can conclude that the distribution tends to be clustered, as a negative z-score is considered to be clustered and a p-value of 0 is conclusive that this could not have been a random distribution.
The Ripley's K Function line graph shows that the observed spatial pattern is clustered throughout the distances. Any line that is above the high confidence envelope is considered to be clustered. We see that the Observed K values are way above the high confidence envelope, and that they remain above the high confidence envelope as the distance increases, so we can confidently conclude that this analysis shows the dataset has a clustered spatial pattern. The three methodologies used in this analysis all agree with one another, as they all conclude that the dataset is clustered.
The Ripley's K Function line graph shows that the observed spatial pattern is clustered throughout the distances. Any line that is above the high confidence envelope is considered to be clustered. We see that the Observed K values are way above the high confidence envelope, and that they remain above the high confidence envelope as the distance increases, so we can confidently conclude that this analysis shows the dataset has a clustered spatial pattern. The three methodologies used in this analysis all agree with one another, as they all conclude that the dataset is clustered.
There are some limitations that affect the outcome of the analysis. First, "the location of crime occurrences have been deliberately offset to the nearest road intersection node to protect the privacy of parties involved in the occurrence". This means that the points in the dataset are not as distributed as they could have been, as the points are gathered at the closest intersection from where the theft took place. This means that some areas have multiple points stacked on top of each other, where if we had the original dataset, we would see more variability in how the data is distributed. The second limitation is that there are many areas in Toronto that do not have roads and instead are a "cold spot", or an area where no points are located. The main areas where this occurs include the Toronto Zoo and the Downsville Airport, both located within the study area. There are many other areas as well such as parks and universities, which by themselves do not contribute much, but collectively can be a limitation because of the amount of area they cover.
There are some limitations that affect the outcome of the analysis. First, "the location of crime occurrences have been deliberately offset to the nearest road intersection node to protect the privacy of parties involved in the occurrence". This means that the points in the dataset are not as distributed as they could have been, as the points are gathered at the closest intersection from where the theft took place. This means that some areas have multiple points stacked on top of each other, where if we had the original dataset, we would see more variability in how the data is distributed. The second limitation is that there are many areas in Toronto that do not have roads and instead are a "cold spot", or an area where no points are located. The main areas where this occurs include the Toronto Zoo and the Downsville Airport, both located within the study area. There are many other areas as well such as parks and universities, which by themselves do not contribute much, but collectively can be a limitation because of the amount of area they cover.
To conclude, we can reject the Null Hypothesis that the theft from motor vehicle locations are randomly distributed across the entire study area. We found that the spatial distribution of the data is clustered, meaning there are certain areas that are more likely to have cars broken into.
To conclude, we can reject the Null Hypothesis that the theft from motor vehicle locations are randomly distributed across the entire study area. We found that the spatial distribution of the data is clustered, meaning there are certain areas that are more likely to have cars broken into.
References
ArcGIS Pro Geoprocessing Tool Help
ArcGIS Pro Geoprocessing Tool Help
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