Urban Resilience: Spatial Equity. Using spatial data science to model… | by Dea Bardhoshi | May, 2023

Using spatial data science to model populations + analysing educational equity in Tirana.

Photo by Gledisa Golikja on Unsplash


This is part 2 of the urban resilience project (part 1 here) focusing on demographic trends in Tirana! In the first part, we looked at power law distributions and built spatial markov models to understand population changes over time. In this second part, I wanted to delve a bit deeper into these predictions and look at what they mean for specific neighborhoods in Tirana. Let’s get started!

Last time, I used Tirana Open Data demographics information (data license: Creative Commons Attribution) to obtain this spatial Markov model matrix:

Spatial Markov Matrix Results (Image by Author)

Let’s take a look at what these results entail in the context of specific neighborhoods. As of 2021, the most populated areas of the city are Area 5, 2, 7, 4 and 11 followed closely by Kashar, a municipality outside of the bounds of Tirana proper with many new developments. Here is a quick visualization:

Kashar is an interesting example of periurban growth with companies like Coca-Cola, Vodafone, Top Channel and smaller businesses setting up shop there. In 2009, its population was just 20829 but as of 2021, it has almost tripled to 58664 people. These areas of very rapid growth are also some with the highest need for sustainable solutions: Kashar grows with about 11 new people a day and has a relatively young median age of 33 (source).

The other highest population areas have seen their own growth in the past 12 years:

Its interesting that these areas are neighboring each other: this enforces the intuition that the trends happening in places around a neighborhood likely influence the character of that neighborhood as well.

Some Examples

Let’s focus a bit on admin area #5. Its immediate neighbors are areas 7, 10 and 2 which have populations of 77124, 27637 and 83827 respectively. According to the spatial Markov results, given these neighbors, area #5 has a chance of about 90% of staying in the highest population bin. It also has a chance of about 5% of falling in the first and second bins.

Area #10 is another neighborhood in Tirana encompassing the city square, business district (Blloku/The Block) as well as some of the most bustling streets of Tirana. Its 2021 population is 27637 and its neighbors have populations of 77000–87000. Based on the Markov results, it would have around a 93% chance of staying in its current population bin.

When it comes to resilient development, cities should work towards providing high-quality resources to people living across all neighborhoods. The concept of a geographical availability of resources is also known as spatial equity: in a city working to provide all citizens access to similar opportunities, this means that people would have equal access to public spaces, a clean environment and institutions such as schools.

In this context, I want to explore the distribution of schools as a marker of spatial equity. Are all children throughout Tirana served with accessible, high-quality schools? Are there areas that are disadvantaged? What are some school trends and patterns? For this, I’ll be using data for Tirana’s middle and primary schools (together known as “9-vjecare”) (link, licensed with a Creative Commons Attribution license). Here is a visualization of school density in each of Tirana’s administrative areas:

School Density in each of Tirana’s Areas (image by author)

And here is the same visualization, only focusing on the 11 urban areas:

School density focused on 11 of Tirana’s urban areas (image by author)

At a glance, it seems that the areas with the highest density are in fact those outside of the 11 main admin areas. Namely, places like Shengjergj, Zall Bastar and Peze turn out to be the top 3. What does this mean for the kids who attend these schools? Is it necessarily easier for them to go to school safely or reliably?

Here is a street network visualization for walking from one of Kashar’s schools, “Sadik Stavileci”. The graph shows isochrones for how far you can travel from the school if walking in 5, 10 or 15 minutes (assuming a speed of 4.5 kilometers/hour).

Isochrones Map for Walking Distance from Kashar School (image by author)

As you can see, the distance kids can cover in a few minutes is probably not that great. This tool, however, is useful when planning out building projects so that a place is easily accessible by the people meant to use it. What is a reasonable time to walk to and from school? How do we improve services like transit or biking so that children are able to go to their schools safely? As a starting point on these, it would be interesting to calculate isochrones for all of Tirana’s schools and compare them to how many children would be within walking distance.

Sidebar: I made these graphs using OSMnx, a network analysis package that combines OpenStreetMaps data as well as network metrics. Here is the source notebook for doing this operation (isochrones).

Measuring Inequality: Spatial Autocorrelation

To measure inequalities in the spatial distribution, there’s a few other metrics we can use. Spatial Autocorrelation is one, and it consists of computing Moran’s I (which we did in for population counts in part 1). This is done to test the null hypothesis that schools in Tirana are distributed uniformly. The result from the test is 0.186 (p-value of 0.111).

PySAL also gives us two ways of visualizing autocorrelation: Moran’s plot and the distribution of Moran’s I under the null hypothesis:

Moran Plot + Empirical Distribution (image by author)

Moran’s plot shows the # of schools plotted agains a lagged # of schools (obtained by multiplying the number of schools and a spatial weights matrix). Qualitatively, we interpret the plot as showing positive spatial autocorrelation when the data points exhibit a high correlation. The distribution, on the other hand, is an empirical one: it is obtained by simulating a series of maps with randomly distributed schools counts and then calculating Moran’s I for each of them. (blue line: mean of distribution, red line: observed statistic in Tirana’s data)

📔 Conclusions + Notebook

This concludes part 2 of this project! Overall, I believe using spatial data science tools is something relatively unexplored, especially in the Albanian context, but definitely very useful. This project could be enriched with more fine-grained data (as in the schools example). Until then, here is the updated notebook.

Thanks for reading!

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