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Social Interactions Models with Latent Structures

Zhongjian Lin, Zhentao Shi, Yapeng Zheng

TL;DR

This paper develops a latent-structure framework for binary choice models with social interactions across groups, allowing group-specific slopes while maintaining within-group homogeneity by identifying latent clusters. It combines Nested Pseudo Likelihood (NPL) with Classifier-Lasso (C-Lasso) to detect cluster memberships and estimate cluster-specific parameters, and uses a parametric bootstrap to debias incidental-parameter bias in FE-rich panel settings. The authors establish consistency, asymptotic normality, and classification-consistency, and propose an information criterion to consistently select the number of latent clusters. Monte Carlo evidence demonstrates strong finite-sample performance and highlights the value of correcting for heterogeneity, while an Add Health application reveals a significant peer effect in one cluster and negligible effects in the other, emphasizing the importance of latent structure in inference. Overall, the approach advances the estimation and inference of heterogeneous social interactions and provides practical tools for uncovering latent group structures in networked data.

Abstract

This paper studies estimation and inference of heterogeneous peer effects featuring group fixed effects and slope heterogeneity under latent structure. We adapt the Classifier-Lasso algorithm to consistently discover latent structures and determine the number of clusters. To solve the incidental parameter problem in the binary choice model with social interactions, we propose a parametric bootstrap method to debias and establish its asymptotic validity. Monte Carlo simulations confirm strong finite sample performance of our methods. In an application to students' risky behaviors, the algorithm detects two latent clusters and finds that peer effects are significant within one of the clusters, demonstrating the practical applicability in uncovering heterogeneous social interactions.

Social Interactions Models with Latent Structures

TL;DR

This paper develops a latent-structure framework for binary choice models with social interactions across groups, allowing group-specific slopes while maintaining within-group homogeneity by identifying latent clusters. It combines Nested Pseudo Likelihood (NPL) with Classifier-Lasso (C-Lasso) to detect cluster memberships and estimate cluster-specific parameters, and uses a parametric bootstrap to debias incidental-parameter bias in FE-rich panel settings. The authors establish consistency, asymptotic normality, and classification-consistency, and propose an information criterion to consistently select the number of latent clusters. Monte Carlo evidence demonstrates strong finite-sample performance and highlights the value of correcting for heterogeneity, while an Add Health application reveals a significant peer effect in one cluster and negligible effects in the other, emphasizing the importance of latent structure in inference. Overall, the approach advances the estimation and inference of heterogeneous social interactions and provides practical tools for uncovering latent group structures in networked data.

Abstract

This paper studies estimation and inference of heterogeneous peer effects featuring group fixed effects and slope heterogeneity under latent structure. We adapt the Classifier-Lasso algorithm to consistently discover latent structures and determine the number of clusters. To solve the incidental parameter problem in the binary choice model with social interactions, we propose a parametric bootstrap method to debias and establish its asymptotic validity. Monte Carlo simulations confirm strong finite sample performance of our methods. In an application to students' risky behaviors, the algorithm detects two latent clusters and finds that peer effects are significant within one of the clusters, demonstrating the practical applicability in uncovering heterogeneous social interactions.
Paper Structure (24 sections, 6 theorems, 52 equations, 1 figure, 5 tables)

This paper contains 24 sections, 6 theorems, 52 equations, 1 figure, 5 tables.

Table of Contents

  1. Introduction
  2. Related literature
  3. Social Interactions Models
  4. Nested Pseudo Likelihood Algorithm: Common Slope Parameter
  5. Classification and Estimation with Latent Structures
  6. Adjusted Algorithm
  7. Large Sample Theory
  8. First-step NPL Estimator
  9. Inference for Model with Homogeneous Slopes
  10. Classification Consistency
  11. Information Criterion
  12. Monte Carlo Evidence
  13. Heterogeneous Peer Effects in Risky Behavior
  14. Add Health Dataset
  15. Empirical Results
  16. ...and 9 more sections

Key Result

Proposition 1

Suppose Assumption npl and Assumption assu:invertibility_assumption1 in Appendix appendix:first-NPL hold.To study the global consistency of $\widetilde{P}_g$ over $g\in[G]$, Assumption assu:invertibility_assumption1 is needed to guarantee the invertibility of the Jacobian matrices with respect to th

Figures (1)

  • Figure 1: Diagram of classification and estimation procedure. It displays an example of the adjusted algorithm with four groups classified into two clusters.

Theorems & Definitions (6)

  • Proposition 1
  • Theorem 1
  • Theorem 2
  • Proposition 2
  • Lemma A.1
  • Lemma A.2