Unrelated question model with two decks of cards

Sedory, Stephen A.; Singh, Sarjinder; Olanipekun, Oluwaseun L.; Wark, Colin

doi:10.1111/stan.12202

Cited by 6 publications

(5 citation statements)

References 33 publications

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“…(2013), Sedory et al. (2020), and Su et al. (2021), we also consider the squared distance between the true proportions and the observed proportions as:

D = \frac{1}{2} \sum_{i = 0}^{1} \sum_{j = 0}^{1} {(θ_{i j} - {\overset{θ}{true}}_{i j})}^{2}

or equivalently

\begin{matrix} true \\ right \begin{matrix} D & = \frac{1}{2} {[θ_{11} - {\overset{θ}{true}}_{11}]}^{2} + \frac{1}{2} {[θ_{10} - {\overset{θ}{true}}_{10}]}^{2} + \frac{1}{2} {[θ_{01} - {\overset{θ}{true}}_{01}]}^{2} + \frac{1}{2} {[θ_{00} - {\overset{θ}{true}}_{00}]}^{2} \\ = \frac{1}{2} {[P π_{A B} + false(1 - P false) π_{y_{1} y_{2}} - {\overset{θ}{true}}_{11}]}^{2} \\ + \frac{1}{2} {[P false(π_{A} - π_{A B} false) + false(1 - P false) false(π_{y_{1}} - π_{y_{1} y_{2}} false) - {\overset{θ}{true}}_{10}]}^{2} \\ + \frac{1}{2} [P false(π_{B} - π_{A B} false) + false(1 - P false) false(π_{y_{2}} - π_{y_{1} y_{2} ...} \end{matrix} \end{matrix}

…”

Section: Unbiased Estimator Of Proportions and Variancementioning

confidence: 99%

“…For estimating the unknown population proportions 𝜋 𝐴𝐵 , 𝜋 𝐴 , and 𝜋 𝐵 , let θ11 = , and θ00 = 𝑛 00 𝑛 be the observed proportions of "(Yes, Yes)," "(Yes, No)," "(No, Yes)," and "(No, No)" responses. Following Odumade and Singh (2009), Singh andSedory (2011, 2012), Lee et al (2013), Sedory et al (2020), andSu et al (2021), we also consider the squared distance between the true proportions and the observed proportions as: 11) or equivalently…”

Section: Unbiased Estimator Of Proportions and Variancementioning

confidence: 99%

“…Relevant literature on this topic can be had from Fox (2015) and Singh (2020), and a very recent problem of estimating the proportion of a single sensitive variable by making use of unrelated question can also be had from Sedory et al. (2020) and Su et al. (2021).…”

Section: Introductionmentioning

confidence: 99%

“…In other words, a judicious choice of an unrelated question 𝑌 in a population could lead to a more efficient estimator of the population proportion. Relevant literature on this topic can be had from Fox (2015) and Singh (2020), and a very recent problem of estimating the proportion of a single sensitive variable by making use of unrelated question can also be had from Sedory et al (2020) and Su et al (2021).…”

Section: Introductionmentioning

confidence: 99%

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Two sensitive characteristics and their overlap with two questions per card

Sedory

Singh

2021

Biometrical J

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“…(2013), Sedory et al. (2020), and Su et al. (2021), we also consider the squared distance between the true proportions and the observed proportions as:

D = \frac{1}{2} \sum_{i = 0}^{1} \sum_{j = 0}^{1} {(θ_{i j} - {\overset{θ}{true}}_{i j})}^{2}

or equivalently

\begin{matrix} true \\ right \begin{matrix} D & = \frac{1}{2} {[θ_{11} - {\overset{θ}{true}}_{11}]}^{2} + \frac{1}{2} {[θ_{10} - {\overset{θ}{true}}_{10}]}^{2} + \frac{1}{2} {[θ_{01} - {\overset{θ}{true}}_{01}]}^{2} + \frac{1}{2} {[θ_{00} - {\overset{θ}{true}}_{00}]}^{2} \\ = \frac{1}{2} {[P π_{A B} + false(1 - P false) π_{y_{1} y_{2}} - {\overset{θ}{true}}_{11}]}^{2} \\ + \frac{1}{2} {[P false(π_{A} - π_{A B} false) + false(1 - P false) false(π_{y_{1}} - π_{y_{1} y_{2}} false) - {\overset{θ}{true}}_{10}]}^{2} \\ + \frac{1}{2} [P false(π_{B} - π_{A B} false) + false(1 - P false) false(π_{y_{2}} - π_{y_{1} y_{2} ...} \end{matrix} \end{matrix}

…”

Section: Unbiased Estimator Of Proportions and Variancementioning

confidence: 99%

Section: Unbiased Estimator Of Proportions and Variancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Two sensitive characteristics and their overlap with two questions per card

Sedory

Singh

2021

Biometrical J

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“…Since the pioneer work of (Warner, 1965 ), many extensions and developments have been proposed by various authors. These concern, first, improvements of the Warner design with respect to the statistical efficiency and/or the respondent’s cooperation by modifying the structure, for example, see (Boruch, 1971 ; Greenberg, Abul-Ela, Simmons, & Horvitz, 1969 ; Kuk, 1990 ; Cruyff, Böckenholt, & van der Heijden, 2016 ; Ulrich, Schröter, Striegel, & Simon, 2012 ; Gupta, Tuck, Gill, & Crowe, 2013 ; Lee, Sedory, & Singh, 2013 ; Su, Sedory, & Singh, 2017 ; Sayed & Mazloum, 2020 ; Sedory, Singh, Olanipekun, & Wark, 2020 ; Reiber, Schnuerch, & Ulrich, 2022 ; Zapata, Sedory, & Singh, 2022 ). Second, they concern the improvement of the analysis of RR data by relating the sensitive question measured with RR, with covariates and taking into account the possibility for noncompliance to the instructions of RR design (Scheers & Dayton, 1988 ; Clark & Desharnais, 1998 ; Böckenholt & van der Heijden, 2007 ; Cruyff, van den Hout, van der Heijden, & Böckenholt, 2007 ; Böckenholt, Barlas, & van der Heijden, 2009 ; Moshagen, Musch, & Erdfelder, 2012 ; Hoffmann & Musch, 2016 ; Reiber, Pope, & Ulrich, 2020 ; Hoffmann, Meisters, & Musch, 2020 ; Wolter & Diekmann, 2021 ; Meisters, Hoffmann, & Musch, 2022b ).…”

Section: Introductionmentioning

confidence: 99%

The analysis of randomized response “ever” and “last year” questions: A non-saturated Multinomial model

2023

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Randomized response (RR) is a well-known interview technique designed to eliminate evasive response bias that arises from asking sensitive questions. The most frequently asked questions in RR are either whether respondents were “ever” carriers of the sensitive characteristic, or whether they were carriers in a recent period, for instance, “last year”. The present paper proposes a design in which both questions are asked, and derives a multinomial model for the joint analysis of these two questions. Compared to the separate analyses with the binomial model, the model makes a useful distinction between last year and former carriers of the sensitive characteristic, it is more efficient in estimating the prevalence of last year carriers, and it has a degree of freedom that allows for a goodness-of-fit test. Furthermore, it is easily extended to a multinomial logistic regression model to investigate the effects of covariates on the prevalence estimates. These benefits are illustrated in two studies on the use of anabolic androgenic steroids in the Netherlands, one using Kuk and one using both the Kuk and forced response. A salient result of our analyses is that the multinomial model provided ample evidence of response biases in the forced response condition.

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