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arxiv: 2410.12618 · v1 · submitted 2024-10-16 · 📊 stat.AP

Spatio-Temporal Analysis of Public Transportation Undercrowding: Leveraging APC Data for a Comprehensive Evaluation of Usage Rates

Arianna Burzacchi , Valeria Maria Urbano , Marika Arena , Giovanni Azzone , Piercesare Secchi , Simone Vantini This is my paper

Pith reviewed 2026-05-23 19:10 UTC · model grok-4.3

classification 📊 stat.AP
keywords public transportationundercrowdingAPC dataGLMMGMERFoccupancy rateMilanspatio-temporal analysis
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The pith

APC data combined with mixed models identifies undercrowded segments and rides on Milan public transport routes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a methodology that processes large-scale Automatic People Counting data through Generalized Linear Mixed Effects Models and Generalized Mixed-Effect Random Forests to estimate the probability of undercrowding. It examines this probability first at the level of individual route segments and then across entire rides on a radial surface line in Milan. A sympathetic reader would care because the approach supplies a repeatable way to locate mismatches between supplied capacity and observed demand using existing sensor streams rather than new surveys. The analysis traces both spatial patterns across stops and how undercrowding evolves over the course of a full journey.

Core claim

The study proposes and applies a methodology based on Automatic People Counting data processed through Generalized Linear Mixed Effects Models and Generalized Mixed-Effect Random Forests to analyze the probability of undercrowding at the segment level and the ride level on a radial surface transport route in Milan, identifying factors that influence undercrowding.

What carries the argument

Generalized Linear Mixed Effects Model and Generalized Mixed-Effect Random Forest fitted to an undercrowding indicator derived from APC passenger counts, used to model probability at both segment and ride levels.

If this is right

  • Segments can be ranked by their modeled probability of undercrowding.
  • Covariates such as time of day and location are shown to affect the probability of undercrowding at the segment level.
  • The same models extend the analysis to the full ride, revealing the temporal distribution of undercrowding across the journey.
  • The occupancy-rate indicator directly compares observed demand against vehicle capacity on each segment.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Transit planners could prioritize schedule or vehicle-size adjustments on the segments the models flag as most undercrowded.
  • The same APC-plus-mixed-model pipeline could be rerun on other routes or cities that already collect comparable passenger-count data.
  • Adding ride-level predictions to segment-level ones gives operators a way to assess whether undercrowding on one part of a trip affects the whole journey.

Load-bearing premise

The APC sensors record passenger numbers and occupancy without systematic measurement error, missing counts, or route-specific calibration issues that would distort the undercrowding indicator.

What would settle it

A side-by-side manual passenger count on the same Milan route segments and time periods that produces occupancy rates differing substantially from the APC-derived rates would undermine the undercrowding classifications.

Figures

Figures reproduced from arXiv: 2410.12618 by Arianna Burzacchi, Giovanni Azzone, Marika Arena, Piercesare Secchi, Simone Vantini, Valeria Maria Urbano.

Figure 1
Figure 1. Figure 1: Distribution of the number of rides between weeks (a) and day types (b). [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Compared to the original dataset of raw APC measurements, the elaborated version [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: 10-Fold CV MSE for different degrees of time slot [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: ROC curve evaluated on the test set for both Model 5 (in red) and Model 6 (in black). [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Random effects The estimated random effects of the GLMM are depicted in [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Marginal effect of Time slot and Day type on the probability of undercrowding. x axis: [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Marginal effect of Week and Day type on the probability of undercrowding. x axis: Week; [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Number of fully undercrowded rides at level [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Fully undercrowded aggregated rides by time slot, day type, and month. Limit value for [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
read the original abstract

The analysis of the transportation usage rate provides opportunities for evaluating the efficacy of the transportation service offered by proposing an indicator that integrates actual demand and capacity. This study aims to develop a methodology for analyzing the occupancy rate from large-scale datasets to identify gaps between supply and demand in public transportation. Leveraging the spatio-temporal granularity of data from Automatic People Counting (APC) and relying on the Generalized Linear Mixed Effects Model and the Generalized Mixed-Effect Random Forest, in this study we propose a methodology for analyzing factors determining undercrowding. The results of the model are examined at both the segment and ride levels. Initially, the analysis focuses on identifying segments more likely associated with undercrowding, understanding factors influencing the probability of undercrowding, and exploring their relationships. Subsequently, the analysis extends to the temporal distribution of undercrowding, encompassing its impact on the entire journey. The proposed methodology is applied to analyze APC data, provided by the company responsible for public transport management in Milan, on a radial route of the surface transportation network.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper develops a methodology to analyze undercrowding in public transport by defining an occupancy-based indicator from Automatic Passenger Counting (APC) data on a Milan radial route. It applies Generalized Linear Mixed Effects Models (GLMM) and Generalized Mixed-Effect Random Forests (GMERF) to identify segments and ride-level factors associated with undercrowding probability, then extends the analysis to temporal patterns across entire journeys.

Significance. If APC counts prove accurate and the models are validated with appropriate metrics, the work could offer a data-driven framework for detecting supply-demand gaps in transit networks, with potential applications in service planning. The hierarchical modeling approach suits the spatio-temporal structure of ride and segment data.

major comments (2)
  1. [Abstract/Methods] Abstract and Methods: The manuscript provides no description of APC sensor calibration, handling of missing scans, route-specific bias correction, or validation against manual counts. This is load-bearing because the binary undercrowding indicator is derived directly from APC occupancy values; any systematic error would propagate to all segment probabilities and temporal analyses.
  2. [Results] Results: No equations, model specifications, goodness-of-fit metrics (e.g., AUC, R², or deviance), error bars, or cross-validation details are referenced for the GLMM and GMERF fits, preventing assessment of whether the identified factors are statistically supported or merely descriptive.
minor comments (2)
  1. [Introduction] Notation for the undercrowding threshold and occupancy rate should be defined explicitly with a formula early in the text.
  2. [Methods] Clarify the distinction between segment-level and ride-level random effects in the GMERF specification.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive feedback and the recommendation for major revision. Below we respond point-by-point to the major comments, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract/Methods] Abstract and Methods: The manuscript provides no description of APC sensor calibration, handling of missing scans, route-specific bias correction, or validation against manual counts. This is load-bearing because the binary undercrowding indicator is derived directly from APC occupancy values; any systematic error would propagate to all segment probabilities and temporal analyses.

    Authors: We agree that explicit documentation of APC data quality is essential. The manuscript will be revised to add a dedicated subsection in Methods describing the computation of the occupancy indicator from raw APC counts, our handling of missing scans, and any route-level adjustments performed. We will also discuss known limitations of APC data. However, detailed sensor calibration protocols and results from manual-count validation campaigns are proprietary to the data provider (the Milan public transport operator) and are not available to the authors; we will state this limitation clearly. revision: partial

  2. Referee: [Results] Results: No equations, model specifications, goodness-of-fit metrics (e.g., AUC, R², or deviance), error bars, or cross-validation details are referenced for the GLMM and GMERF fits, preventing assessment of whether the identified factors are statistically supported or merely descriptive.

    Authors: We accept this criticism. The revised Results section will include the explicit model equations for both the GLMM and GMERF, tables of estimated coefficients with standard errors, goodness-of-fit statistics (AUC, deviance, and pseudo-R² where applicable), and a description of the cross-validation strategy used to assess predictive performance. These additions will allow readers to evaluate the statistical support for the reported associations. revision: yes

standing simulated objections not resolved
  • Proprietary details on APC sensor calibration and independent manual-count validation, which are not accessible to the authors.

Circularity Check

0 steps flagged

No circularity; modeling applies standard GLMM/GMERF to external APC-derived indicators

full rationale

The paper applies GLMM and GMERF to undercrowding indicators computed directly from APC passenger counts supplied by the Milan operator. No equations, predictions, or uniqueness claims reduce outputs to fitted parameters or self-citations by construction. The derivation chain processes observed spatio-temporal data through off-the-shelf mixed-effects models; the central results (segment probabilities and ride-level factors) are statistical outputs of those models on external inputs, not tautological re-expressions of the inputs themselves.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that APC counts are reliable proxies for occupancy and that standard mixed-effects modeling assumptions hold for this transportation context; no new entities are postulated.

free parameters (1)
  • GLMM and GMERF hyperparameters and random effect variances
    Fitted to the APC dataset to capture segment- and ride-level variation; values not reported in abstract.
axioms (2)
  • domain assumption APC sensor data provides unbiased measurements of passenger counts and vehicle capacity
    Invoked when defining the undercrowding indicator from raw counts; no calibration or error model is mentioned in the abstract.
  • standard math Standard assumptions of generalized linear mixed models (linearity on link scale, correct random effect distribution) hold for the occupancy data
    Required for the GLMM component to produce valid probability estimates.

pith-pipeline@v0.9.0 · 5733 in / 1465 out tokens · 25417 ms · 2026-05-23T19:10:20.850470+00:00 · methodology

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