Heterogeneous Variable Selection in Nonlinear Panel Data Models: A Semi-Parametric Bayesian Approach

Abstract

In this paper, we develop a general method for heterogeneous variable selection in Bayesian nonlinear panel data models. Heterogeneous variable selection refers to the possibility that subsets of units are unaffected by certain variables. It may be present in applications as diverse as health treatments, consumer choice-making, macroeconomics, and operations research. Our method additionally allows for other forms of cross-sectional heterogeneity. We consider a two-group approach for the model's unitspecific parameters: each unit-specific parameter is either equal to zero (heterogeneous variable selection) or comes from a Dirichlet process (DP) mixture of multivariate normals (other cross-sectional heterogeneity). We develop our approach for general nonlinear panel data models, encompassing multinomial logit and probit models, poisson and negative binomial count models, exponential models, among many others. For inference, we develop an efficient Bayesian MCMC sampler. In a Monte Carlo study, we find that our approach is able to capture heterogeneous variable selection whereas a "standard" DP mixture is not. In an empirical application, we find that accounting for heterogeneous variable selection and non-normality of the continuous heterogeneity leads to an improved in-sample and out-of-sample performance and interesting insights. These findings illustrate the usefulness of our approach.

Bayesian and Classical Semi-parametric Estimation of the Balanced Longitudinal Data Model

“…Burhan and Hamoud (2018) compared the estimate of the transfer function using the non-parametric method, represented by two methods: positional linear regression, the cubic bootstrap method, and the semi-parametric method, represented by a single-indicator semi-parametric model with the proposed cubic bootstrap, and the study proved that the proposed estimator is the best among the studied estimators. Castelein et al (2020) developed a general method for selecting heterogeneous variables in non-linear Longitudinal data models such as polynomial logarithms models based on the Bayesian semi-parametric method and Dirichlet process mixture (DPM) and they reached an improvement in performance in the process of selecting variables heterogeneous.…”