Semi-Parametric Models for Longitudinal Data Analysis

Liu Yang^1, and Xu-Feng Niu²

¹Liberty Mutual Insurance, Boston, Massachusetts, USA

²Department of Statistics, Florida State University, Florida, USA

Cite this paper:
Liu Yang and Xu-Feng Niu. Semi-Parametric Models for Longitudinal Data Analysis. Journal of Finance and Economics. 2021; 9(3):93-105. doi: 10.12691/jfe-9-3-1

Abstract

Longitudinal studies are widely used in various fields, such as public health, clinic trials and financial data analysis. A major challenge for longitudinal studies is the repeated measurements from each subject, which cause time dependent correlations within subjects. Generalized Estimating Equations (GEE) can deal with correlated outcomes for longitudinal data through marginal effect. Our proposed model will be based on GEE, with a semi-parametric approach, to provide a flexible structure for regression models: coefficients for parametric covariates will be estimated and nuisance covariates will be fitted in kernel smoothers for the non-parametric part. The profile kernel estimator and the seemingly unrelated kernel estimator (SUR) will be used to obtain consistent and efficient semi-parametric estimators. We provide simulation results for estimating semi-parametric models with one or multiple non-parametric terms. Financial market data is a major component of data analysis; thus, we focus on the financial market in the application part. Credit card loan data will be used with the payment information for each customer across six months to investigate whether gender, income, age, or other factors will influence payment status significantly. Furthermore, we propose model comparisons to evaluate whether different models should be fitted for different subgroups of consumers, such as male and female.

Keywords:
longitudinal study generalized estimating equations (GEE) semi-parametric model profile-kernel estimator the seemingly unrelated kernel estimator (SUR)

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