Variational Bayesian Inference for Quantile Regression Models with Nonignorable Missing Data

Xiaoning Li, Mulati Tuerde () and Xijian Hu
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Xiaoning Li: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
Mulati Tuerde: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
Xijian Hu: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China

Mathematics, 2023, vol. 11, issue 18, 1-31

Abstract: Quantile regression models are remarkable structures for conducting regression analyses when the data are subject to missingness. Missing values occur because of various factors like missing completely at random, missing at random, or missing not at random. All these may result from system malfunction during data collection or human error during data preprocessing. Nevertheless, it is important to deal with missing values before analyzing data since ignoring or omitting missing values may result in biased or misinformed analysis. This paper studies quantile regressions from a Bayesian perspective. By proposing a hierarchical model framework, we develop an alternative approach based on deterministic variational Bayes approximations. Logistic and probit models are adopted to specify propensity scores for missing manifests and covariates, respectively. Bayesian variable selection method is proposed to recognize significant covariates. Several simulation studies and real examples illustrate the advantages of the proposed methodology and offer some possible future research directions.

Keywords: lasso regularization; nonignorable missing data; quantile regression; variational Bayesian inference (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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