Bias reduction in the logistic model parameters with the LogF(1,1) penalty under MAR assumption
In this paper, we present a novel validated penalization method for bias reduction to estimate parameters for the logistic model when data are missing at random (MAR). Specific focus was given to address the data missingness problem among categorical model covariates. We penalize a logit log-likelih...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2022-11-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2022.1052752/full |
| _version_ | 1797987492374249472 |
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| author | Muna Al-Shaaibi Muna Al-Shaaibi Ronald Wesonga Ronald Wesonga |
| author_facet | Muna Al-Shaaibi Muna Al-Shaaibi Ronald Wesonga Ronald Wesonga |
| author_sort | Muna Al-Shaaibi |
| collection | DOAJ |
| description | In this paper, we present a novel validated penalization method for bias reduction to estimate parameters for the logistic model when data are missing at random (MAR). Specific focus was given to address the data missingness problem among categorical model covariates. We penalize a logit log-likelihood with a novel prior distribution based on the family of the LogF(m,m) generalized distribution. The principle of expectation-maximization with weights was employed with the Louis' method to derive an information matrix, while a closed form for the exact bias was derived following the Cox and Snell's equation. A combination of simulation studies and real life data were used to validate the proposed method. Findings from the validation studies show that our model's standard errors are consistently lower than those derived from other bias reduction methods for the missing at random data mechanism. Consequently, we conclude that in most cases, our method's performance in parameter estimation is superior to the other classical methods for bias reduction when data are MAR. |
| first_indexed | 2024-04-11T07:48:11Z |
| format | Article |
| id | doaj.art-4fd6167d8aac4d50940b98882b3ec7d4 |
| institution | Directory Open Access Journal |
| issn | 2297-4687 |
| language | English |
| last_indexed | 2024-04-11T07:48:11Z |
| publishDate | 2022-11-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj.art-4fd6167d8aac4d50940b98882b3ec7d42022-12-22T04:36:10ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872022-11-01810.3389/fams.2022.10527521052752Bias reduction in the logistic model parameters with the LogF(1,1) penalty under MAR assumptionMuna Al-Shaaibi0Muna Al-Shaaibi1Ronald Wesonga2Ronald Wesonga3Department of Statistics, Sultan Qaboos University, Muscat, OmanData Science Analytics Lab, Department of Statistics, Sultan Qaboos University, Muscat, OmanDepartment of Statistics, Sultan Qaboos University, Muscat, OmanData Science Analytics Lab, Department of Statistics, Sultan Qaboos University, Muscat, OmanIn this paper, we present a novel validated penalization method for bias reduction to estimate parameters for the logistic model when data are missing at random (MAR). Specific focus was given to address the data missingness problem among categorical model covariates. We penalize a logit log-likelihood with a novel prior distribution based on the family of the LogF(m,m) generalized distribution. The principle of expectation-maximization with weights was employed with the Louis' method to derive an information matrix, while a closed form for the exact bias was derived following the Cox and Snell's equation. A combination of simulation studies and real life data were used to validate the proposed method. Findings from the validation studies show that our model's standard errors are consistently lower than those derived from other bias reduction methods for the missing at random data mechanism. Consequently, we conclude that in most cases, our method's performance in parameter estimation is superior to the other classical methods for bias reduction when data are MAR.https://www.frontiersin.org/articles/10.3389/fams.2022.1052752/fullpenalizationparameter estimationbias reductionMARLogF(1,1) penalty |
| spellingShingle | Muna Al-Shaaibi Muna Al-Shaaibi Ronald Wesonga Ronald Wesonga Bias reduction in the logistic model parameters with the LogF(1,1) penalty under MAR assumption Frontiers in Applied Mathematics and Statistics penalization parameter estimation bias reduction MAR LogF(1,1) penalty |
| title | Bias reduction in the logistic model parameters with the LogF(1,1) penalty under MAR assumption |
| title_full | Bias reduction in the logistic model parameters with the LogF(1,1) penalty under MAR assumption |
| title_fullStr | Bias reduction in the logistic model parameters with the LogF(1,1) penalty under MAR assumption |
| title_full_unstemmed | Bias reduction in the logistic model parameters with the LogF(1,1) penalty under MAR assumption |
| title_short | Bias reduction in the logistic model parameters with the LogF(1,1) penalty under MAR assumption |
| title_sort | bias reduction in the logistic model parameters with the logf 1 1 penalty under mar assumption |
| topic | penalization parameter estimation bias reduction MAR LogF(1,1) penalty |
| url | https://www.frontiersin.org/articles/10.3389/fams.2022.1052752/full |
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