cross-nested logit modeling

This study addresses the problem of efficiently collecting choice data using a minimal number of assortments to estimate choice models over $n$ products and to automatically uncover the latent “nest” structure in nested logit models. The authors propose a structured, non-adaptive experimental design that requires only $O(\log n)$ assortments to effectively estimate a broad class of choice models. They further introduce a novel algorithm that, for the first time, consistently estimates nested logit models without requiring prior knowledge of the nest structure, guaranteeing correct recovery of nests under arbitrary true choice distributions. Empirical validation on 70 million user records from the Dream11 platform demonstrates that the inferred nests significantly outperform those derived from feature-based clustering, yielding higher out-of-sample prediction accuracy and meaningful business interpretability.

本文解决了需求估计中选择集变化的问题，通过修正嵌套logit模型的似然函数来准确估计替代效应和拥挤效应。

In retail demand modeling, discrete choice models (DCMs) face a fundamental trade-off between interpretability and flexibility: traditional parametric models (e.g., multinomial logit) fail to capture irrational behavior and preference heterogeneity, while black-box machine learning models lack transparency. To address this, we propose the Binary Choice Forest (BCF), the first tree-based ensemble method formally proven equivalent to DCMs under mild regularity conditions. BCF introduces a customized splitting criterion grounded in choice theory, probability-consistent leaf estimation, and a novel preference ranking recovery mechanism. It enables sequential search modeling, heterogeneous behavior representation, product importance quantification, and seamless integration of price and user features. Evaluated on synthetic and real-world transaction datasets, BCF consistently outperforms state-of-the-art parametric benchmarks in predictive accuracy while explicitly revealing both individual- and population-level preference structures—achieving “interpretable flexibility.”

This paper addresses the challenge of balancing model parsimony and task-specific applicability (e.g., pricing, product assortment optimization) in consumer choice modeling. We propose a nonparametric approach grounded in marginal utility distributions. First, we provide an exact characterization of the choice probability polytope representable by the Marginal Distribution Model (MDM) and its grouped variant (G-MDM). Second, we develop the first nonparametric optimal fitting estimation framework requiring no parametric assumptions. Third, we prove that G-MDM and the Random Utility Model (RUM) are incomparable—neither subsumes the other. Our method enables efficient computation via linear programming validation, mixed-integer convex optimization, and grouped structural modeling. Empirically, it significantly outperforms the multinomial logit model in expressive power, estimation accuracy, and predictive performance, while achieving substantially higher computational efficiency than RUM. Moreover, it provides theoretically guaranteed prediction intervals for choice probabilities over unseen assortments.

This paper addresses the challenge of identifying heterogeneous individual-level choice behaviors from macro-level aggregate selection data. To this end, it establishes, for the first time, a systematic theoretical linkage between ordered probit choice models and copula theory, mapping individual heterogeneity onto the structural form of copula functions. The authors propose an analytically tractable representation based on extreme-value theory, enabling unique and unbiased identification of both heterogeneity types and their mixing weights. Methodologically, the approach integrates copula modeling, extreme-value function analysis, and structural identification theory to derive a general closed-form extreme-value representation. This framework overcomes key limitations of conventional aggregate modeling—such as loss of behavioral granularity and identifiability constraints—thereby substantially improving the accuracy, interpretability, and structural fidelity of micro-behavioral inference. It introduces a novel paradigm for discrete choice analysis, behavioral econometrics, and multivariate dependence modeling.

This study addresses the high computational cost and poor scalability of generalized method of moments (GMM) estimation in the Berry–Levinsohn–Pakes (BLP) demand model when applied to markets with a large number of products. The authors propose a nested pseudo-GMM algorithm that reorders the GMM optimization and fixed-point iteration steps, fixing consumer-level outside-option probabilities to yield a closed-form, product-separable inversion from market shares to mean utilities. This approach introduces, for the first time, the nested pseudo-likelihood idea into the BLP framework, enabling analytical gradient computation, natural parallelization, and substantially reduced computational complexity. Monte Carlo simulations and empirical results demonstrate that the method achieves comparable estimation accuracy while significantly outperforming the fastest existing algorithms in speed, with superlinear acceleration gains as the number of products increases.

Traditional logit models struggle to capture correlated choice behavior due to their assumption of independent and identically distributed random utility errors, particularly limiting their ability to model substitution patterns. This work proposes an amortized inference approach based on group-equivariant neural networks that approximates discrete choice probabilities under general error distributions by constructing a neural simulator respecting the model’s invariance structure. Theoretically, the architecture is shown to possess universal approximation capability within the minimal invariant feature set, and Sobolev training is employed to jointly learn choice probabilities and their derivatives. Experiments demonstrate that the method significantly outperforms the GHK simulator in both estimation accuracy and computational efficiency, while the resulting maximum likelihood estimator is proven to be consistent and asymptotically normal.

This study addresses a key limitation of traditional multinomial probit models, which assume symmetric latent utility distributions and thus fail to capture asymmetric effects of covariates on choice probabilities, leading to biased estimates of elasticities and substitution patterns. To overcome this, the paper proposes the first identifiable and computationally tractable skew multinomial probit (SMNP) model. By incorporating a multivariate skew-normal distribution with alternative-specific skewness parameters, the model captures asymmetric responses while preserving flexible substitution structures. Model identification and covariance matrix positive definiteness are ensured through a novel reparameterization. Efficient Bayesian inference is achieved via an interpretable prior specification and a Metropolis–Hastings-within-Gibbs sampler augmented with dual data augmentation. Both simulation studies and empirical applications demonstrate that the SMNP model substantially improves predictive accuracy for choice probabilities and reveals economically meaningful asymmetries in price elasticities and substitution behavior.

Traditional nested logit (NL) models suffer from limited representational capacity, struggling to flexibly capture inter-option correlations and non-proportional substitution effects; meanwhile, existing deep learning approaches lack explicit modeling of discrete choice structures. To address this, we propose NestGNN—the first framework integrating graph neural networks (GNNs) into discrete choice analysis. NestGNN constructs an “alternative graph” to explicitly encode dependency relationships among choices and employs a nested utility GNN to jointly learn hierarchical utility functions. While preserving the interpretable two-level nesting structure of NL, NestGNN significantly enhances modeling flexibility and expressive power. Experiments on mode choice prediction demonstrate that NestGNN improves predictive accuracy by 9.2% over baseline NL models. Moreover, it supports elasticity analysis and visualization of substitution patterns, achieving a favorable balance among predictive performance, interpretability, and modeling generality.

This study addresses the bias in parameter estimation commonly arising in discrete choice models due to unobserved consideration sets. The authors propose a practical approach that constructs individual-specific consideration sets based on historical choices, enabling consistent estimation within a Logit framework without relying on exhaustive universal set evaluations or subjective self-reports. Theoretically, the paper provides the first rigorous proof that, under homogeneous choice probability assumptions, such consideration sets satisfy sufficient conditions for consistent estimation, while also offering a refined interpretation of the alternative sampling theorem. Methodologically, the approach is validated through Monte Carlo simulations, synthetic Logit-generated data, and large-scale passive behavioral datasets—such as smart card and mobile phone records. Empirical results demonstrate that the proposed method yields consistent and robust parameter estimates under specified conditions, thereby opening a new avenue for applied research in discrete choice modeling.