From GEV to ResLogit: Spatially Correlated Discrete Choice Models for Pedestrian Movement Prediction

Rulla Al-Haideri; Bilal Farooq

physics.soc-phMar 1, 2026

From GEV to ResLogit: Spatially Correlated Discrete Choice Models for Pedestrian Movement Prediction

Authors: Rulla Al-Haideri, Bilal Farooq

Organizations: Laboratory of Innovations in Transportation (LiTrans), Toronto Metropolitan University, 350 Victoria Street, Toronto, Ontario, Canada

Abstract

High frequency pedestrian motion forecasting when interacting with autonomous vehicles (AVs) can be enhanced through the use of behavioural frameworks, such as discrete choice models, that can explicitly account for correlation among similar movement alternatives. We formulate the pedestrian next step choice as a spatial discrete choice defined by a grid of speed adjustment and heading change. Using naturalistic pedestrian-AV encounters from nuScenes and Argoverse 2 (1 sec decision interval), we estimate a multinomial logit baseline and four spatial generalized extreme value (GEV) specifications (SCL, GSCL, SCNL, and GSCNL). We then compare them to a residual neural network logit (ResLogit) model that learns cross alternative effects while retaining an interpretable linear utility component. Across the evaluated data, spatial GEV structures yield only marginal improvements over multinomial logit, whereas ResLogit achieves a substantially better fit and produces behaviourally coherent errors concentrated among neighbouring grid cells. The results suggest that in dense, high frequency spatial choice sets, learning based residual corrections can capture proximity induced correlation more effectively than analyst specified GEV nesting structures, while maintaining interpretability.

Figures & tables

Figure 1: Pedestrian spatial choice set grid.

	Argoverse 2	nuScenes
Total decision steps (raw)	1133	2170
Excluded steps (outside grid or final step)	270	340
Processed decision steps (valid 1–9)	863	1830
Choice 1	65	180
Choice 2	55	222
Choice 3	92	136

Table 1: Observed movement choice counts before and after filtering to the defined

3\times 3

grid.

Model	$I^{\text{dec}}$	$I^{\text{acc}}$	$I^{\text{turn}}$	FCRP	RCRP	$1/D$	ddist	ddir	$\alpha$	$\lambda$
ResLogit	✓	✓	✓	✓	✓	✓	✓	✓
MNL	✓	✓	✓	✓	✓	✓
SCL	✓	✓	✓	✓	✓	✓			✓	✓
GSCL	✓	✓	✓	✓	✓	✓			✓ a	✓
SCNL	✓	✓	✓	✓	✓	✓			✓	✓ b
GSCNL	✓	✓	✓	✓	✓	✓			✓ c	✓ b

Table 2: Model components included in each specification.

Symbol	Definition
$I^{\text{dec}}_{i}$	Indicator for deceleration alternatives (grid row: decelerate).
$I^{\text{acc}}_{i}$	Indicator for acceleration alternatives (grid row: accelerate).
$I^{\text{turn}}_{i}$	Indicator for turning alternatives (left or right cones).
$D_{t}$	AV–pedestrian distance at decision step $t$ (specified as $1/D_{t}$ ).
FCRP t	Front collision risk proximity at decision step $t$ (front intensity scaled by $1+\mathrm{CTTC}_{t}$ ).
RCRP t	Rear collision risk proximity at decision step $t$ (rear intensity scaled by $1+\mathrm{CTTC}_{t}$ ).

Table 3: Definitions of model variables and parameters.

Model	$k$	LL	Mean LL	AIC
MNL	6	-3,971.8760	-2.14696	7,955.75
SCL	7	-3,957.7975	-2.13935	7,929.60
GSCL	8	-3,953.9680	-2.13728	7,923.94
SCNL	8	-3,957.7050	-2.13930	7,931.41
GSCNL	9	-3,955.4295	-2.13807	7,928.86
ResLogit	8	-3,175.2334	-1.71634	6,366.46

Table 4: Model fit on the estimation sample (original train set,

N=1{,}850

Panel of Figure 2 — Figure 2: Confusion matrices for the spatial GEV models using maximum probability (MaxP) predictions.

	Original (cluster bootstrap)			Synthetic (IID bootstrap)
Variable	Coef.	S.E.	$p$	Coef.	S.E.	$p$
$\beta_{\text{dec}}$	1.091490	1.257677	0.386576	1.010338	0.028384	0.000000
$\beta_{\text{acc}}$	0.471755	0.862350	0.584988	0.453966	0.036242	0.000000
$\beta_{\text{turn}}$	0.266480	0.229563	0.247188	0.226830	0.016002	0.000000
$\beta_{\text{dist}}$	0.033585	0.206108	0.870735	0.018264	0.008713	0.037334
$\beta_{\text{front}}$	0.035592	0.327723	0.913633	0.038941	0.012480	0.002076

Table 6: ResLogit linear-utility coefficient estimates.

Panel of Figure 3 — Figure 3: ResLogit confusion matrices on original and synthetic data.

Panel of Figure 4 — Figure 4: Original versus synthetic distributions for ResLogit variables. The ddist and ddir plots are pooled across the nine alternatives.

Discrete Choice Modeling

Discrete choice modeling studies how people select among alternatives and how preferences can be estimated from observed choices.

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Unified Pedestrian Path Prediction Using Inverse Reinforcement Learning

Šimon Sukup, Ariyan Bighashdel, Pavol Jancura

Eindhoven University of Technology, Eindhoven, The Netherlands · Delft University of Technology, Delft, The Netherlands

Pedestrian Trajectory Prediction Trajectory Prediction Reinforcement Learning Spatiotemporal GNNs

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Pedestrian path prediction is crucial for enhancing the safety of autonomous vehicles and advanced driver-assistance systems. Previous studies explored different learning-task formulations for pedestrian path prediction and compared these formulations using shallow neural networks, but did not extend this analysis to more complex deep-learning models. This paper adapts the Spatial-Temporal Graph Attention Network (STGAT) to a unified pedestrian path prediction framework and introduces state and action definitions specific to STGAT. The resulting formulations support deterministic and stochastic policies, one-time and sequential decision-making, and reinforcement-learning algorithms including REINFORCE and proximal policy optimization. The proposed learning-task formulations improve prediction performance across the selected benchmark datasets compared with the standard supervised-learning formulation. These results demonstrate that reformulating the decision process and training objective can improve an advanced pedestrian trajectory prediction architecture and may provide a path toward improving other graph-based prediction models.

Abstract

Discrete Choice Modeling

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