Latent Group Structure Research Articles

Grouped Heterogeneity in Linear Panel Data Models with Heterogeneous Error Variances

We develop a procedure to identify latent group structures in linear panel data models that exploits a grouping in the error variances of cross-sectional units. To accommodate such grouping, we introduce an objective function that avoids a singularity that arises in a pseudolikelihood approach. We provide theoretical and numerical evidence showing when allowing for variance groups improves classification. The developed procedure provides new evidence on the relation between firm-level research and development (R&D) investments and the business cycle. We find a well-defined group structure in the variances that ex-post can be related to firm size. Our estimates indicate stronger procyclical investment patterns at medium-size firms compared to large firms.

Public Debt and Economic Growth: A Panel Kink Regression Latent Group Structures Approach

This paper investigates the relationship between public debt and economic growth in the context of a panel kink regression with latent group structures. The proposed model allows us to explore the heterogeneous threshold effects of public debt on economic growth based on unknown group patterns. We propose a least squares estimator and demonstrate the consistency of estimating group structures. The finite sample performance of the proposed estimator is evaluated by simulations. Our findings reveal that the nonlinear relationship between public debt and economic growth is characterized by a heterogeneous threshold level, which varies among different groups, and highlight that the mixed results found in previous studies may stem from the assumption of a homogeneous threshold effect.

Latent Group Structure in Linear Panel Data Models with Endogenous Regressors

Latent Group Structure in Linear Panel Data Models with Endogenous Regressors

Identifying Latent Groups in Spatial Panel Data Using a Markov Random Field Constrained Product Partition Model

Understanding the heterogeneity over spatial locations is an important problem that has been widely studied in many applications such as economics and environmental science. In this paper, we focus on regression models for spatial panel data analysis, where repeated measurements are collected over time at various spatial locations. We propose a novel class of nonparametric priors that combines Markov random field (MRF) with the product partition model (PPM), and show that the resulting prior, called by MRF-PPM, is capable of identifying the latent group structure among the spatial locations while efficiently utilizing the spatial dependence information. We derive a closed-form conditional distribution for the proposed prior and introduce a new way to compute the marginal likelihood that renders efficient Bayesian inference. We further study the theoretical properties of the proposed MRF-PPM prior and show a clustering consistency result for the posterior distribution. We demonstrate the excellent empirical performance of our method via extensive simulation studies and applications to a US precipitation data and a California median household income data study.

Functional-Coefficient Quantile Regression for Panel Data with Latent Group Structure

This article considers estimating functional-coefficient models in panel quantile regression with individual effects, allowing the cross-sectional and temporal dependence for large panel observations. A latent group structure is imposed on the heterogeneous quantile regression models so that the number of nonparametric functional coefficients to be estimated can be reduced considerably. With the preliminary local linear quantile estimates of the subject-specific functional coefficients, a classic agglomerative clustering algorithm is used to estimate the unknown group structure and an easy-to-implement ratio criterion is proposed to determine the group number. The estimated group number and structure are shown to be consistent. Furthermore, a post-grouping local linear smoothing method is introduced to estimate the group-specific functional coefficients, and the relevant asymptotic normal distribution theory is derived with a normalization rate comparable to that in the literature. The developed methodologies and theory are verified through a simulation study and showcased with an application to house price data from U.K. local authority districts, which reveals different homogeneity structures at different quantile levels.

Simultaneous estimation and group identification for network vector autoregressive model with heterogeneous nodes

Individuals or companies in a large social or financial network often display rather heterogeneous behaviors for various reasons. In this work, we propose a network vector autoregressive model with a latent group structure to model heterogeneous dynamic patterns observed from network nodes, for which group-wise network effects and time-invariant fixed-effects can be naturally incorporated. In our framework, the model parameters and network node memberships can be simultaneously estimated by minimizing a least-squares type objective function. In particular, our theoretical investigation allows the number of latent groups G to be over-specified when achieving the estimation consistency of the model parameters and group memberships, which significantly improves the robustness of the proposed approach. When G is correctly specified, valid statistical inference can be made for model parameters based on the asymptotic normality of the estimators. A data-driven criterion is developed to consistently identify the true group number for practical use. Extensive simulation studies and two real data examples are used to demonstrate the effectiveness of the proposed methodology.

Model-based clustering using a new multivariate skew distribution

Quite often real data exhibit non-normal features, such as asymmetry and heavy tails, and present a latent group structure. In this paper, we first propose the multivariate skew shifted exponential normal distribution that can account for these non-normal characteristics. Then, we use this distribution in a finite mixture modeling framework. An EM algorithm is illustrated for maximum-likelihood parameter estimation. We provide a simulation study that compares the fitting performance of our model with those of several alternative models. The comparison is also conducted on a real dataset concerning the log returns of four cryptocurrencies.

A PANEL CLUSTERING APPROACH TO ANALYZING BUBBLE BEHAVIOR

AbstractThis study provides new mechanisms for identifying and estimating explosive bubbles in mixed‐root panel autoregressions with a latent group structure. A postclustering approach is employed that combines k‐means clustering with right‐tailed panel‐data testing. Uniform consistency of the k‐means algorithm is established. Pivotal null limit distributions of the tests are introduced. A new method is proposed to consistently estimate the number of groups. Monte Carlo simulations show that the proposed methods perform well in finite samples; and empirical applications of the proposed methods identify bubbles in the U.S. and Chinese housing markets and the U.S. stock market.

Identifying latent group structures in spatial dynamic panels

This paper considers the identification of latent group structures in spatial dynamic panels. We follow Lee and Yu (2010) and consider a rich spatial dynamic panel data (SDPD) model with two-way fixed effects. In addition, we also allow for latent panel structures where individuals can be classified into a few groups such that individuals within the same group share the common slope parameters and do not otherwise. Both the number of groups and the individuals’ group membership are unknown. To identify the latent group structures, we first adopt the GMM to obtain the preliminary unconstrained estimates of the slope coefficients. Then we apply the sequential binary segmentation algorithm (SBSA) of Wang and Su (2021) to these estimates and obtain the clusters. A BIC-type information criterion is proposed to choose the number of latent groups consistently. The asymptotic analysis shows that this method can identify the true group structure consistently, and the post-classification estimators enjoy the oracle property. Monte Carlo simulations demonstrate that our method has good finite sample performance. Finally, we apply our approach to the US housing market and identify two latent Metropolitan Statistical Areas groups.

Modeling panels of extremes

Extreme value applications commonly employ regression techniques to capture cross-sectional heterogeneity or time variation in the data. Estimation of the parameters of an extreme value regression model is notoriously challenging due to the small number of observations that are usually available in applications. When repeated extreme measurements are collected on the same individuals, that is, a panel of extremes is available, pooling the observations in groups can improve the statistical inference. We study three data sets related to risk assessment in finance, climate science, and hydrology. In all three cases the problem can be formulated as an extreme value panel regression model with a latent group structure and group-specific parameters. We propose a new algorithm that jointly assigns the individuals to the latent groups and estimates the parameters of the regression model inside each group. Our method efficiently recovers the underlying group structure without prior information, and for the three data sets it provides improved return level estimates and helps answer important domain-specific questions.

Estimation and identification of latent group structures in panel data

This paper provides a framework for joint estimation and identification of latent group structures in panel data models using a pairwise fusion penalized approach. The latent structure of the model allows individuals to be classified into different groups where the number of groups and the group membership are unknown. The individuals within a group have common slope parameters, while parameter heterogeneity is allowed across the groups. A penalized least squares (PLS) approach is introduced for models with exogenous regressors. When the model contains endogenous regressors, a penalized generalized method of moment (PGMM) is introduced. To implement the proposed approach, an alternating direction method of multipliers algorithm has been developed. The proposed method is further illustrated by simulation studies which demonstrate the finite sample performance of the method, and is applied in an empirical analysis.

Homogeneity and Sparsity Analysis for High-Dimensional Panel Data Models

In this article, we are interested in detecting latent group structures and significant covariates in a high-dimensional panel data model with both individual and time fixed effects. The slope coefficients of the model are assumed to be subject dependent, and there exist group structures where the slope coefficients are homogeneous within groups and heterogeneous between groups. We develop a penalized estimator for recovering the group structures and the sparsity patterns simultaneously. We propose a new algorithm to optimize the objective function. Furthermore, we propose a strategy to reduce the computational complexity by pruning the penalty terms in the objective function, which also improves the accuracy of group structure detection. The proposed estimator can recover the latent group structures and the sparsity patterns consistently in large samples. The finite sample performance of the proposed estimator is evaluated through Monte Carlo studies and illustrated with a real dataset.

A pairwise strategic network formation model with group heterogeneity: With an application to international travel

AbstractThis study considers a network formation model in which each dyad of agents strategically determines the link status. Our model allows the agents to have unobserved group heterogeneity in the propensity of link formation. For the model estimation, we propose a three-step maximum likelihood method, in which the latent group structure is estimated using the binary segmentation algorithm in the second step. As an empirical illustration, we focus on the network data of international visa-free travels. The results indicate the presence of significant strategic complementarity and a certain level of degree heterogeneity in the network formation behavior.

Dynamic clustering of multivariate panel data

We propose a dynamic clustering model for uncovering latent time-varying group structures in multivariate panel data. The model is dynamic in three ways. First, the cluster location and scale matrices are time-varying to track gradual changes in cluster characteristics over time. Second, all units can transition between clusters based on a Hidden Markov model (HMM). Finally, the HMM’s transition matrix can depend on lagged time-varying cluster distances as well as economic covariates. Monte Carlo experiments suggest that the units can be classified reliably in a variety of challenging settings. Incorporating dynamics in the cluster composition proves empirically important in a study of 299 European banks between 2008Q1 and 2018Q2. We find that approximately 3% of banks transition per quarter on average. Transition probabilities are in part explained by differences in bank profitability, suggesting that factors contributing to low profitability for some banks can lead to long-lasting changes in financial industry structure.

Detecting Unobserved Heterogeneity in Efficient Prices via Classifier-Lasso

This article proposes a new measure of efficient price as a weighted average of bid and ask prices, where the weights are constructed from the bid-ask long-run relationships in a panel error-correction model (ECM). To allow for heterogeneity in the long-run relationships, we consider a panel ECM with latent group structures so that all the stocks within a group share the same long-run relationship and do not otherwise. We extend the Classifier-Lasso method to the ECM to simultaneously identify the individual’s group membership and estimate the group-specific long-run relationship. We establish the uniform classification consistency and good asymptotic properties of the post-Lasso estimators under some regularity conditions. Empirically, we find that more than 30% of the Standard & Poor’s (S&P) 1500 stocks have estimated efficient prices significantly deviating from the midpoint—a conventional measure of efficient price. Such deviations explored from our data-driven method can provide dynamic information on the extent and direction of informed trading activities.

Incorporating Prior Knowledge of Latent Group Structure in Panel Data Models

Incorporating Prior Knowledge of Latent Group Structure in Panel Data Models

Massive data clustering by multi-scale psychological observations.

Clustering is the discovery of latent group structure in data and is a fundamental problem in artificial intelligence, and a vital procedure in data-driven scientific research over all disciplines. Yet, existing methods have various limitations, especially weak cognitive interpretability and poor computational scalability, when it comes to clustering massive datasets that are increasingly available in all domains. Here, by simulating the multi-scale cognitive observation process of humans, we design a scalable algorithm to detect clusters hierarchically hidden in massive datasets. The observation scale changes, following the Weber–Fechner law to capture the gradually emerging meaningful grouping structure. We validated our approach in real datasets with up to a billion records and 2000 dimensions, including taxi trajectories, single-cell gene expressions, face images, computer logs and audios. Our approach outperformed popular methods in usability, efficiency, effectiveness and robustness across different domains.

Multi-dimensional latent group structures with heterogeneous distributions

This paper aims to identify the multi-dimensional latent grouped heterogeneity of distributional effects. We consider a panel quantile regression model with additive cross-section and time fixed effects. The cross-section effects and quantile slope coefficients are both characterized by grouped patterns of heterogeneity, but each unit can belong to different groups for cross-section effects and slopes. We propose a composite-quantile approach to jointly estimate multi-dimensional group memberships, slope coefficients, and fixed effects. We show that using multiple quantiles improves clustering accuracy if memberships are quantile-invariant. We apply the methods to examine the relationship between managerial incentives and risk-taking behavior.

Latent group detection in functional partially linear regression models.

In this paper, we propose a functional partially linear regression model with latent group structures to accommodate the heterogeneous relationship between a scalar response and functional covariates. The proposed model is motivated by a salinity tolerance study of barley families, whose main objective is to detect salinity tolerant barley plants. Our model is flexible, allowing for heterogeneous functional coefficients while being efficient by pooling information within a group for estimation. We develop an algorithm in the spirit of the K-means clustering to identify latent groups of the subjects under study. We establish the consistency of the proposed estimator, derive the convergence rate and the asymptotic distribution, and develop inference procedures. We show by simulation studies that the proposed method has higher accuracy for recovering latent groups and for estimating the functional coefficients than existing methods. The analysis of the barley data shows that the proposed method can help identify groups of barley families with different salinity tolerantabilities.

Group structure detection for a high‐dimensional panel data model

This article investigates latent group structures in a high‐dimensional panel data model. It is assumed that subjects are classified into unobserved groups, where the fixed effects for each subject are the same within a group but heterogeneous across different groups. A penalized regression approach is proposed to identify latent group structures and significant covariates simultaneously. A new algorithm is proposed to optimize the objective function. When the sample size goes to infinity, it is shown that the proposed estimator recovers latent group structures and important covariates with probability approaching one. The finite sample performance of the proposed estimator is evaluated through Monte Carlo studies and illustrated using a real dataset.