Bayesian adaptive lasso quantile regression with non-ignorable missing responses

Ranran Chen, Mai Dao, Keying Ye and Min Wang ()
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Ranran Chen: The University of Texas at San Antonio
Mai Dao: Wichita State University
Keying Ye: The University of Texas at San Antonio
Min Wang: The University of Texas at San Antonio

Computational Statistics, 2025, vol. 40, issue 3, No 19, 1643-1682

Abstract: Abstract In this paper, we develop a fully Bayesian adaptive lasso quantile regression model to analyze data with non-ignorable missing responses, which frequently occur in various fields of study. Specifically, we employ a logistic regression model to deal with missing data of non-ignorable mechanism. By using the asymmetric Laplace working likelihood for the data and specifying Laplace priors for the regression coefficients, our proposed method extends the Bayesian lasso framework by imposing specific penalization parameters on each regression coefficient, enhancing our estimation and variable selection capability. Furthermore, we embrace the normal-exponential mixture representation of the asymmetric Laplace distribution and the Student-t approximation of the logistic regression model to develop a simple and efficient Gibbs sampling algorithm for generating posterior samples and making statistical inferences. The finite-sample performance of the proposed algorithm is investigated through various simulation studies and a real-data example.

Keywords: Quantile regression; Bayesian adaptive lasso; Non-ignorable missing data; High-dimensional analysis (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00180-024-01546-6

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