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

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), relativel...

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Bibliographic Details
Published in:Advances in statistical analysis : AStA : a journal of the German Statistical Society 2020-06, Vol.104 (2), p.261-283
Main Authors: Biswas, Jayabrata, Ghosh, Pulak, Das, Kiranmoy
Format: Article
Language:English
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
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Summary: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.
ISSN:1863-8171
1863-818X
DOI:10.1007/s10182-020-00362-9