Variational Bayesian Quantile Regression with Non-Ignorable Missing Response Data
For non-ignorable missing response variables, the mechanism of whether the response variable is missing can be modeled through logistic regression. In Bayesian computation, the lack of a conjugate prior for the logistic function poses a significant challenge. Introducing a new Pólya-Gamma variable a...
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MDPI AG
2025-05-01
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| Online Access: | https://www.mdpi.com/2075-1680/14/6/408 |
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| author | Juanjuan Zhang Weixian Wang Maozai Tian |
| author_facet | Juanjuan Zhang Weixian Wang Maozai Tian |
| author_sort | Juanjuan Zhang |
| collection | DOAJ |
| description | For non-ignorable missing response variables, the mechanism of whether the response variable is missing can be modeled through logistic regression. In Bayesian computation, the lack of a conjugate prior for the logistic function poses a significant challenge. Introducing a new Pólya-Gamma variable and employing lower-bound approximation are two common methods for parameter inference in conjugate Bayesian logistic regression. It can be observed that these two methods yield essentially the same variational posterior in the calculation of the variational Bayesian posterior. This paper applies a popular Bayesian spike-and-slab LASSO prior for variable selection in quantile regression with non-ignorable missing response variables, which demonstrates good performance in both simulations and practical applications. |
| format | Article |
| id | doaj-art-f0437beca3ba47bfbb928efa4b30cd1c |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
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| series | Axioms |
| spelling | doaj-art-f0437beca3ba47bfbb928efa4b30cd1c2025-08-20T03:27:11ZengMDPI AGAxioms2075-16802025-05-0114640810.3390/axioms14060408Variational Bayesian Quantile Regression with Non-Ignorable Missing Response DataJuanjuan Zhang0Weixian Wang1Maozai Tian2School of Digital Economy and Trade, Guangzhou Huashang College, Guangzhou 511300, ChinaSchool of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, ChinaSchool of Statistics and Data Science, Xinjiang University of Finance and Economics, Urumqi 830012, ChinaFor non-ignorable missing response variables, the mechanism of whether the response variable is missing can be modeled through logistic regression. In Bayesian computation, the lack of a conjugate prior for the logistic function poses a significant challenge. Introducing a new Pólya-Gamma variable and employing lower-bound approximation are two common methods for parameter inference in conjugate Bayesian logistic regression. It can be observed that these two methods yield essentially the same variational posterior in the calculation of the variational Bayesian posterior. This paper applies a popular Bayesian spike-and-slab LASSO prior for variable selection in quantile regression with non-ignorable missing response variables, which demonstrates good performance in both simulations and practical applications.https://www.mdpi.com/2075-1680/14/6/408non-ignorable missingnessBayesian quantile regressionlogistic regression |
| spellingShingle | Juanjuan Zhang Weixian Wang Maozai Tian Variational Bayesian Quantile Regression with Non-Ignorable Missing Response Data Axioms non-ignorable missingness Bayesian quantile regression logistic regression |
| title | Variational Bayesian Quantile Regression with Non-Ignorable Missing Response Data |
| title_full | Variational Bayesian Quantile Regression with Non-Ignorable Missing Response Data |
| title_fullStr | Variational Bayesian Quantile Regression with Non-Ignorable Missing Response Data |
| title_full_unstemmed | Variational Bayesian Quantile Regression with Non-Ignorable Missing Response Data |
| title_short | Variational Bayesian Quantile Regression with Non-Ignorable Missing Response Data |
| title_sort | variational bayesian quantile regression with non ignorable missing response data |
| topic | non-ignorable missingness Bayesian quantile regression logistic regression |
| url | https://www.mdpi.com/2075-1680/14/6/408 |
| work_keys_str_mv | AT juanjuanzhang variationalbayesianquantileregressionwithnonignorablemissingresponsedata AT weixianwang variationalbayesianquantileregressionwithnonignorablemissingresponsedata AT maozaitian variationalbayesianquantileregressionwithnonignorablemissingresponsedata |