Prediction of a Sensitive Feature under Indirect Questioning via Warner’s Randomized Response Technique and Latent Class Model
We investigate the association of a sensitive characteristic or latent variable with observed binary random variables by the randomized response (RR) technique of Warner in his publication (Warner, S.L. <i>J. Am. Stat. Assoc.</i><b>1965</b>, <i>60</i>, 63–69) and...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/2/345 |
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| author | Shen-Ming Lee Phuoc-Loc Tran Truong-Nhat Le Chin-Shang Li |
| author_facet | Shen-Ming Lee Phuoc-Loc Tran Truong-Nhat Le Chin-Shang Li |
| author_sort | Shen-Ming Lee |
| collection | DOAJ |
| description | We investigate the association of a sensitive characteristic or latent variable with observed binary random variables by the randomized response (RR) technique of Warner in his publication (Warner, S.L. <i>J. Am. Stat. Assoc.</i><b>1965</b>, <i>60</i>, 63–69) and a latent class model. First, an expectation-maximization (EM) algorithm is provided to easily estimate the parameters of the null and alternative/full models for the association between a sensitive characteristic and an observed categorical random variable under the RR design of Warner’s paper above. The likelihood ratio test (LRT) is utilized to identify observed categorical random variables that are significantly related to the sensitive trait. Another EM algorithm is then presented to estimate the parameters of a latent class model constructed through the sensitive attribute and the observed binary random variables that are obtained from dichotomizing observed categorical random variables selected from the above LRT. Finally, two classification criteria are conducted to predict an individual in the sensitive or non-sensitive group. The practicality of the proposed methodology is illustrated with an actual data set from a survey study of the sexuality of first-year students, except international students, at Feng Chia University in Taiwan in 2016. |
| first_indexed | 2024-03-09T11:46:28Z |
| format | Article |
| id | doaj.art-62fcd90b26684919a0565486910c609e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T11:46:28Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-62fcd90b26684919a0565486910c609e2023-11-30T23:20:54ZengMDPI AGMathematics2227-73902023-01-0111234510.3390/math11020345Prediction of a Sensitive Feature under Indirect Questioning via Warner’s Randomized Response Technique and Latent Class ModelShen-Ming Lee0Phuoc-Loc Tran1Truong-Nhat Le2Chin-Shang Li3Department of Statistics, Feng Chia University, Taichung 40724, TaiwanDepartment of Mathematics, College of Natural Science, Can Tho University, Can Tho, VietnamFaculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, VietnamSchool of Nursing, The State University of New York, University at Buffalo, Buffalo, NY 14214, USAWe investigate the association of a sensitive characteristic or latent variable with observed binary random variables by the randomized response (RR) technique of Warner in his publication (Warner, S.L. <i>J. Am. Stat. Assoc.</i><b>1965</b>, <i>60</i>, 63–69) and a latent class model. First, an expectation-maximization (EM) algorithm is provided to easily estimate the parameters of the null and alternative/full models for the association between a sensitive characteristic and an observed categorical random variable under the RR design of Warner’s paper above. The likelihood ratio test (LRT) is utilized to identify observed categorical random variables that are significantly related to the sensitive trait. Another EM algorithm is then presented to estimate the parameters of a latent class model constructed through the sensitive attribute and the observed binary random variables that are obtained from dichotomizing observed categorical random variables selected from the above LRT. Finally, two classification criteria are conducted to predict an individual in the sensitive or non-sensitive group. The practicality of the proposed methodology is illustrated with an actual data set from a survey study of the sexuality of first-year students, except international students, at Feng Chia University in Taiwan in 2016.https://www.mdpi.com/2227-7390/11/2/345bootstrapexpectation-maximization (EM) algorithmlatent classlikelihood ratio testmaximum likelihoodrandomized response |
| spellingShingle | Shen-Ming Lee Phuoc-Loc Tran Truong-Nhat Le Chin-Shang Li Prediction of a Sensitive Feature under Indirect Questioning via Warner’s Randomized Response Technique and Latent Class Model Mathematics bootstrap expectation-maximization (EM) algorithm latent class likelihood ratio test maximum likelihood randomized response |
| title | Prediction of a Sensitive Feature under Indirect Questioning via Warner’s Randomized Response Technique and Latent Class Model |
| title_full | Prediction of a Sensitive Feature under Indirect Questioning via Warner’s Randomized Response Technique and Latent Class Model |
| title_fullStr | Prediction of a Sensitive Feature under Indirect Questioning via Warner’s Randomized Response Technique and Latent Class Model |
| title_full_unstemmed | Prediction of a Sensitive Feature under Indirect Questioning via Warner’s Randomized Response Technique and Latent Class Model |
| title_short | Prediction of a Sensitive Feature under Indirect Questioning via Warner’s Randomized Response Technique and Latent Class Model |
| title_sort | prediction of a sensitive feature under indirect questioning via warner s randomized response technique and latent class model |
| topic | bootstrap expectation-maximization (EM) algorithm latent class likelihood ratio test maximum likelihood randomized response |
| url | https://www.mdpi.com/2227-7390/11/2/345 |
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