A semi-parametric quantile regression approach to zero-inflated and incomplete longitudinal outcomes

• Published in: Advances in statistical analysis : AStA : a journal of the German Statistical Society Vol. 104; no. 2; pp. 261 - 283
• Main Authors: Biswas, Jayabrata, Ghosh, Pulak, Das, Kiranmoy
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2020; Springer Nature B.V
• Subjects: Computer simulation; Econometrics; Economics; Finance; Forecasting techniques; Insurance; Management; Markov chains; Mathematics and Statistics; Missing data; Modelling; Normal distribution; Original Paper; Parameter estimation; Probability Theory and Stochastic Processes; Quantiles; Regression analysis; Regression models; Retirement; Statistics; Statistics for Business; Zero-inflated longitudinal data; Health insurance; Missing data; Probit model; Varying coefficients models; Joint quantile models
• ISSN: 1863-8171; 1863-818X
• DOI: 10.1007/s10182-020-00362-9

Quantile regression models are typically used for modeling non-Gaussian outcomes, and such models allow quantile-specific inference. While there exists a vast literature on conditional quantile regression (where the model parameters are estimated precisely for one prefixed quantile level), relatively less work has been reported on joint quantile regression. The challenge in joint quantile regression is to avoid quantile crossing while estimating multiple quantiles simultaneously. In this article, we propose a semi-parametric approach of handling non-Gaussian zero-inflated and incomplete longitudinal outcomes. We use a two-part model for handling the excess zeros, and propose a dynamic joint quantile regression model for the nonzero outcomes. A multinomial probit model is used for modeling the missingness. We develop a Bayesian joint estimation method where the model parameters are estimated through Markov Chain Monte Carlo. The unknown distribution of the outcome can be constructed based on the estimated quantiles. We analyze data from the health and retirement study and model the out-of-pocket medical expenditure through the proposed joint quantile regression method. Simulation studies are performed to assess the practical usefulness and efficiency of the proposed approach compared to the existing methods.