Variational Bayesian Inference for Quantile Regression Models with Nonignorable Missing Data
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 malfuncti...
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| Format: | Article |
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MDPI AG
2023-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/18/3926 |
| _version_ | 1797578981216616448 |
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| author | Xiaoning Li Mulati Tuerde Xijian Hu |
| author_facet | Xiaoning Li Mulati Tuerde Xijian Hu |
| author_sort | Xiaoning Li |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T22:30:22Z |
| format | Article |
| id | doaj.art-cb8e75b40ebe45c6aaa3a4fb0d484f04 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T22:30:22Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-cb8e75b40ebe45c6aaa3a4fb0d484f042023-11-19T11:49:30ZengMDPI AGMathematics2227-73902023-09-011118392610.3390/math11183926Variational Bayesian Inference for Quantile Regression Models with Nonignorable Missing DataXiaoning Li0Mulati Tuerde1Xijian Hu2College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaQuantile 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.https://www.mdpi.com/2227-7390/11/18/3926lasso regularizationnonignorable missing dataquantile regressionvariational Bayesian inference |
| spellingShingle | Xiaoning Li Mulati Tuerde Xijian Hu Variational Bayesian Inference for Quantile Regression Models with Nonignorable Missing Data Mathematics lasso regularization nonignorable missing data quantile regression variational Bayesian inference |
| title | Variational Bayesian Inference for Quantile Regression Models with Nonignorable Missing Data |
| title_full | Variational Bayesian Inference for Quantile Regression Models with Nonignorable Missing Data |
| title_fullStr | Variational Bayesian Inference for Quantile Regression Models with Nonignorable Missing Data |
| title_full_unstemmed | Variational Bayesian Inference for Quantile Regression Models with Nonignorable Missing Data |
| title_short | Variational Bayesian Inference for Quantile Regression Models with Nonignorable Missing Data |
| title_sort | variational bayesian inference for quantile regression models with nonignorable missing data |
| topic | lasso regularization nonignorable missing data quantile regression variational Bayesian inference |
| url | https://www.mdpi.com/2227-7390/11/18/3926 |
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