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Correcting socioeconomic bias in mobile phone mobility estimates using multilevel regression and poststratification

This paper proposes using multilevel regression and poststratification (MRP) to correct socioeconomic sampling biases in mobile phone call detail records, demonstrating that this method significantly improves the accuracy of mobility estimates like the radius of gyration by aligning carrier data with census demographics.

Original authors: Leo Ferres, Laetitia Gauvin

Published 2026-04-20

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Leo Ferres, Laetitia Gauvin

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Problem: The "VIP Lounge" of Data

Imagine you want to understand how people move around a giant city. You decide to look at a list of phone calls made by people who use one specific mobile phone company (let's call them "Company X").

You might think, "Great! I have data on millions of people. This must represent the whole city."

But here's the catch: Company X isn't a random sample of the city. It's more like a VIP lounge or a specific club.

In this specific case (Santiago, Chile), the company's users are mostly middle-income people.
The very rich (who might have different travel habits) and the very poor (who might use prepaid phones or different carriers) are barely there.

If you just take the average of everyone in that VIP lounge, you get a distorted picture of the whole city. It's like trying to guess the average height of all humans in the world by only measuring professional basketball players. You'd think everyone is 7 feet tall!

The Solution: The "Smart Re-Weighting" System

The authors of this paper wanted to fix this distortion. They used a statistical technique called Multilevel Regression and Poststratification (MRP).

To understand MRP, imagine you are a chef trying to make a soup that tastes exactly like the "City Soup" (the real population), but you only have a bucket of ingredients from the "VIP Lounge" (the biased phone data).

The Recipe (The Model): First, the chef tastes the VIP ingredients to see how they behave. They notice: "Oh, the middle-income ingredients make the soup spicy, while the rich ingredients make it salty." They build a recipe (a mathematical model) that predicts how different types of people move, based on their income, gender, and where they live.
The Census Map (The Target): The chef also has a perfect map of the whole city (the Census). This map says, "In the whole city, 30% are rich, 40% are middle-income, and 30% are poor."
The Re-Weighting (Poststratification): Now, the chef doesn't just dump the VIP bucket into the pot. Instead, they use the recipe to simulate what the rich and poor people would have done if they were in the bucket. Then, they mix these simulated ingredients into the pot in the exact proportions found on the Census map.

The Result: You get a bowl of soup that tastes like the real city, even though you started with a biased bucket of ingredients.

What Did They Find?

When they applied this "Smart Re-Weighting" to the phone data, the results changed dramatically:

The "Naive" Mistake: If you just looked at the raw phone data, you'd think the average person travels about 24 kilometers a day.
The "Corrected" Truth: After fixing the bias, the average person actually travels only 20 kilometers.
The Surprise: The raw data made it look like the richest people traveled the most. But once they fixed the math, it turned out that middle-income people actually travel the furthest. The rich people in the data were just an unrepresentative group that happened to live far from the city center, skewing the numbers.

The "Geography-Only" Shortcut

The paper also asked: What if we don't know the income of the phone users? Can we still fix the bias?

They found that yes, we can, to a certain extent.

The Analogy: Imagine you don't know who is rich or poor in the VIP lounge, but you know where they live. Since rich people tend to live in one part of town and poor people in another, you can use geography as a proxy.
If a neighborhood is known to be wealthy, you assume the phone users there are wealthy. If it's a working-class neighborhood, you assume they are working-class.
This "Geography-Only" method didn't fix the problem perfectly (it missed some of the extreme details), but it still corrected the biggest errors. It's like using a blurry map instead of a high-definition one; it's not perfect, but it's much better than guessing.

Why Does This Matter?

City planners, doctors, and governments use phone data to make big decisions:

Where to build a new bus line?
How to stop a virus from spreading?
Where to build a new hospital?

If they use the "naive" (biased) data, they might build a bus line for a group that doesn't actually exist in the numbers, or miss the areas where the virus is spreading fastest.

The Bottom Line:
This paper teaches us that data is not always truth. Just because you have a lot of data doesn't mean it represents everyone. By using a clever statistical "re-weighting" trick (MRP), we can take a biased snapshot of the world and turn it into a clear, accurate picture of reality. It's the difference between looking at a funhouse mirror and looking through a clean window.

1. Problem Statement

Mobile phone Call Detail Records (CDR) are a primary data source for studying human mobility, urban planning, and epidemic modeling. However, CDR data from a single mobile operator suffers from systematic representativeness bias.

The Bias: The user base of a specific carrier is not a random sample of the total population. In high-penetration markets like Chile (where mobile ownership is near-universal), the bias stems from carrier preference, contract types, and usage patterns rather than phone ownership itself.
The Consequence: This leads to skewed demographic distributions in the data. For example, in the Santiago Metropolitan Region, the study found that the highest-income group (ABC1) was severely underrepresented (14.4% of CDR users vs. 31.1% of the census population), while middle-income groups were overrepresented.
Impact on Metrics: Because mobility patterns (specifically the Radius of Gyration, or ROG) correlate with socioeconomic status (SES), this demographic skew distorts aggregate mobility estimates. Naive averages from CDR data do not reflect the true population mobility.

2. Methodology: Multilevel Regression and Poststratification (MRP)

The authors propose applying Multilevel Regression and Poststratification (MRP), a statistical framework traditionally used in political science for small-area estimation, to correct CDR-based mobility metrics.

A. Data Sources

CDR Data: Anonymized voice-call records from Telefónica Chile (Movistar) covering May–July 2016 (~118,400 user-month-weekday observations).
Census Data: 2017 Chilean Census for population counts and demographics.
Socioeconomic Data:
- Individual Level: GSE (Socioeconomic Group) labels provided by the carrier based on salary data.
- Population Level: ISMT (Territorial Sociomaterial Index) derived from the 2017 census to establish the true population distribution of GSE across geographic units.

B. Model Specification

The authors fit a Bayesian multilevel model to predict the mean log-transformed Radius of Gyration ( $\log(ROG)$ ).

Unit of Analysis: Cells defined by the unique combination of Distrito (census district), GSE, Gender, Month, and Weekday/Weekend.
Equation:
$y_{ijkmt} = \mu + \beta^{GSE}_j + \beta^{gender}_k + \beta^{GSE \times gender}_{jk} + \beta^{weekday}_t + \beta^{month}_m + \alpha_{comuna} + \epsilon_{ijkmt}$
- Fixed Effects: Main effects for GSE, gender, and their interaction; temporal controls for month and weekday.
- Random Effects: A random intercept ( $\alpha_{comuna}$ ) for the 47 comunas (administrative divisions) to capture unobserved geographic heterogeneity.
- Weighting: Observations are weighted by the number of users in each cell to account for precision.

C. Poststratification

After fitting the model, predictions are aggregated to the population level using census weights:

Frame Construction: The population is divided into cells based on Distrito $\times$ GSE $\times$ Gender.
Weighting: Weights ( $N_j$ ) are calculated as the product of the census population count in the district and the conditional probabilities of GSE and gender within that district.
Aggregation: The final estimate is a weighted average of the model's posterior predictions, effectively reweighting the biased sample to match the true population demographics.

D. Geography-Only Variant

The authors also tested a reduced model that excludes individual SES labels (which are often unavailable). This model relies solely on geographic random effects (comuna) and poststratifies based on the geographic distribution of SES. This serves as a practical alternative when individual-level SES data is missing, provided SES is spatially clustered.

3. Key Contributions

Quantification of Bias: The study provides empirical evidence that CDR data from a major Chilean carrier is significantly biased against high-income groups and overrepresents middle-income groups, leading to distorted mobility metrics.
Methodological Innovation: It is the first application of MRP to correct mobility estimates derived from non-representative CDR data, moving beyond simple rescaling methods.
Practical Framework: The authors demonstrate that MRP can be applied even when individual SES data is missing, using a "geography-only" variant that leverages spatial clustering of socioeconomic groups.
Open Source Tool: The authors released mobmrp, an open-source Python library to facilitate the adoption of this pipeline for other researchers.

4. Key Results

Correction Magnitude: The MRP-corrected average Radius of Gyration for the entire population is 20.23 km, which is 16.6% lower than the naive CDR average of 24.24 km.
Reversal of Rankings:
- Naive Data: Suggested ABC1 (highest income) had the highest mobility (27.4 km).
- Corrected Data: Revealed that C2 (middle income) actually has the highest mobility (21.9 km), while ABC1 drops to 20.2 km.
- Reasoning: The naive bias occurred because high-income areas are geographically distant from the city center, inflating raw ROG. Once the model controlled for geography (comuna), the true within-area mobility gradient favored middle-income groups.
Geography-Only Performance: The geography-only model reduced the estimate to 19.40 km. While it corrected the aggregate bias in the right direction, it failed to accurately capture the extreme deficit of the lowest-income group (GSE E), highlighting the necessity of individual SES data for granular corrections.
Model Diagnostics: The full model showed excellent convergence (Gelman-Rubin $\hat{R} \le 1.01$ ) and the inclusion of the comuna random intercept was found to be essential for model fit.

5. Significance and Implications

Policy Rigor: Uncorrected CDR data can lead to misleading conclusions in urban planning, transportation, and public health (e.g., epidemic modeling). This study demonstrates that treating carrier samples as random population samples is scientifically unsound.
Equity: The correction reveals that mobility patterns differ significantly across demographic groups. Ignoring these biases may result in policies that favor the overrepresented groups in the data.
Generalizability: The MRP framework is applicable to any setting where non-representative passive data exists, provided census or survey data is available to define the target population distribution.
Limitations: The study notes that the correction conflates demographic reweighting with the statistical back-transformation from log-scale. Additionally, the aggressive filtering of users (requiring daily calls) may introduce its own selection bias, and the data reflects a specific temporal snapshot (2016) where voice calls were declining.

In conclusion, the paper establishes MRP as a principled, robust method for transforming biased mobile phone data into accurate, population-representative mobility estimates, significantly improving the reliability of data-driven decision-making.