A semiparametric model for cluster data

TL;DR

This paper introduces a semiparametric model for cluster data that captures varying factor impacts across clusters, allowing for nonlinear interactions and accounting for within-cluster correlation, with proven asymptotic properties.

Contribution

It presents a novel semiparametric approach for analyzing cluster data with varying effects, nonlinear interactions, and correlation structures, along with estimation and hypothesis testing methods.

Findings

Effective estimation of functional coefficients and correlation structures.

Simulation studies confirm the method's finite sample performance.

Application to Bangladesh data reveals new insights.

Abstract

In the analysis of cluster data, the regression coefficients are frequently assumed to be the same across all clusters. This hampers the ability to study the varying impacts of factors on each cluster. In this paper, a semiparametric model is introduced to account for varying impacts of factors over clusters by using cluster-level covariates. It achieves the parsimony of parametrization and allows the explorations of nonlinear interactions. The random effect in the semiparametric model also accounts for within-cluster correlation. Local, linear-based estimation procedure is proposed for estimating functional coefficients, residual variance and within-cluster correlation matrix. The asymptotic properties of the proposed estimators are established, and the method for constructing simultaneous confidence bands are proposed and studied. In addition, relevant hypothesis testing problems are addressed. Simulation studies are carried out to demonstrate the methodological power of the proposed methods in the finite sample. The proposed model and methods are used to analyse the second birth interval in Bangladesh, leading to some interesting findings.