A Ratio Estimator for the Mean Using a Mixture Optional Enhance Trust (MOET) Randomized Response Model
When researchers conduct surveys seeking sensitive, socially stigmatized information, respondents, on average, modify their answers to represent themselves favorably. To overcome this issue, researchers may use Randomized Response Technique (RRT) models. Recently, Parker et al. proposed a model that...
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MDPI AG
2024-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/22/3617 |
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| author | Sat Gupta Michael Parker Sadia Khalil |
| author_facet | Sat Gupta Michael Parker Sadia Khalil |
| author_sort | Sat Gupta |
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| description | When researchers conduct surveys seeking sensitive, socially stigmatized information, respondents, on average, modify their answers to represent themselves favorably. To overcome this issue, researchers may use Randomized Response Technique (RRT) models. Recently, Parker et al. proposed a model that incorporates some of the most critical recent quantitative RRT advancements—mixture, optionality, and enhanced trust—into a single model, which they called a Mixture Optional Enhanced (MOET) model. We now improve upon the MOET model by incorporating auxiliary information into the analysis. Positively correlated auxiliary information can improve the mean response estimation through use of a ratio estimator. In this study, we propose just such an estimator for the MOET model. Further, we investigate the conditions under which the ratio estimator outperforms the basic MOET estimator proposed by Parker et al. in 2024. We also consider the possibility that the collection of auxiliary information may compromise privacy; and we study the impact of privacy reduction on the overall model performance as assessed by the unified measure (UM) proposed by Gupta et al. in 2018. |
| format | Article |
| id | doaj-art-f308a966221a4cb8a36acafbdfa48fe1 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-f308a966221a4cb8a36acafbdfa48fe12024-11-26T18:12:03ZengMDPI AGMathematics2227-73902024-11-011222361710.3390/math12223617A Ratio Estimator for the Mean Using a Mixture Optional Enhance Trust (MOET) Randomized Response ModelSat Gupta0Michael Parker1Sadia Khalil2Department of Mathematics and Statistics, UNC Greensboro, Greensboro, NC 27413, USADepartment of Mathematics and Statistics, UNC Greensboro, Greensboro, NC 27413, USADepartment of Statistics, Lahore College for Women University, Lahore 54000, PakistanWhen researchers conduct surveys seeking sensitive, socially stigmatized information, respondents, on average, modify their answers to represent themselves favorably. To overcome this issue, researchers may use Randomized Response Technique (RRT) models. Recently, Parker et al. proposed a model that incorporates some of the most critical recent quantitative RRT advancements—mixture, optionality, and enhanced trust—into a single model, which they called a Mixture Optional Enhanced (MOET) model. We now improve upon the MOET model by incorporating auxiliary information into the analysis. Positively correlated auxiliary information can improve the mean response estimation through use of a ratio estimator. In this study, we propose just such an estimator for the MOET model. Further, we investigate the conditions under which the ratio estimator outperforms the basic MOET estimator proposed by Parker et al. in 2024. We also consider the possibility that the collection of auxiliary information may compromise privacy; and we study the impact of privacy reduction on the overall model performance as assessed by the unified measure (UM) proposed by Gupta et al. in 2018.https://www.mdpi.com/2227-7390/12/22/3617Randomized Response Technique (RRT)respondent privacysocial desirability bias (SDB)unified measure (UM)ratio estimatorauxiliary variable |
| spellingShingle | Sat Gupta Michael Parker Sadia Khalil A Ratio Estimator for the Mean Using a Mixture Optional Enhance Trust (MOET) Randomized Response Model Mathematics Randomized Response Technique (RRT) respondent privacy social desirability bias (SDB) unified measure (UM) ratio estimator auxiliary variable |
| title | A Ratio Estimator for the Mean Using a Mixture Optional Enhance Trust (MOET) Randomized Response Model |
| title_full | A Ratio Estimator for the Mean Using a Mixture Optional Enhance Trust (MOET) Randomized Response Model |
| title_fullStr | A Ratio Estimator for the Mean Using a Mixture Optional Enhance Trust (MOET) Randomized Response Model |
| title_full_unstemmed | A Ratio Estimator for the Mean Using a Mixture Optional Enhance Trust (MOET) Randomized Response Model |
| title_short | A Ratio Estimator for the Mean Using a Mixture Optional Enhance Trust (MOET) Randomized Response Model |
| title_sort | ratio estimator for the mean using a mixture optional enhance trust moet randomized response model |
| topic | Randomized Response Technique (RRT) respondent privacy social desirability bias (SDB) unified measure (UM) ratio estimator auxiliary variable |
| url | https://www.mdpi.com/2227-7390/12/22/3617 |
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