The extended crosswise model adjusted for random answering
The extended crosswise model adjusted for random answering
The Extended Crosswise Model is a popular randomized response design that employs a sensitive and innocuous statement, and asks respondents if one of these statements is true, or if none or both are true. Although the model has a degree of freedom, it is unable to detect random answering. In this article, we propose a new method to detect and correct for random answering. This method makes use of a non-sensitive control statement and a quasi-randomized innocuous statement to which both answers are known, which allows for the detection of and correction for random answering. A simulation study shows that this method yields unbiased estimates of the prevalence of sensitive attribute. For four surveys among elite athletes, we present prevalence estimates of doping use that are corrected for random answering.
Sayed, Khadiga H.A.
9f0ba98e-f5a6-41c1-8e29-9ef779803ff9
Cruyff, Maarten J.L.F.
87113ca0-c784-493a-b96e-5ad4a9e16465
Petróczi, Andrea
8511a554-694d-45bc-9248-1ec7fcd63e34
Van Der Heijden, Peter G.M.
85157917-3b33-4683-81be-713f987fd612
Sayed, Khadiga H.A.
9f0ba98e-f5a6-41c1-8e29-9ef779803ff9
Cruyff, Maarten J.L.F.
87113ca0-c784-493a-b96e-5ad4a9e16465
Petróczi, Andrea
8511a554-694d-45bc-9248-1ec7fcd63e34
Van Der Heijden, Peter G.M.
85157917-3b33-4683-81be-713f987fd612
Sayed, Khadiga H.A., Cruyff, Maarten J.L.F., Petróczi, Andrea and Van Der Heijden, Peter G.M.
(2026)
The extended crosswise model adjusted for random answering.
Journal of Survey Statistics and Methodology, [smag004].
(doi:10.1093/jssam/smag004).
Abstract
The Extended Crosswise Model is a popular randomized response design that employs a sensitive and innocuous statement, and asks respondents if one of these statements is true, or if none or both are true. Although the model has a degree of freedom, it is unable to detect random answering. In this article, we propose a new method to detect and correct for random answering. This method makes use of a non-sensitive control statement and a quasi-randomized innocuous statement to which both answers are known, which allows for the detection of and correction for random answering. A simulation study shows that this method yields unbiased estimates of the prevalence of sensitive attribute. For four surveys among elite athletes, we present prevalence estimates of doping use that are corrected for random answering.
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Accepted/In Press date: 22 January 2026
e-pub ahead of print date: 27 March 2026
Identifiers
Local EPrints ID: 510826
URI: http://eprints.soton.ac.uk/id/eprint/510826
ISSN: 2325-0984
PURE UUID: 77145aa0-9fd9-4060-be27-2bd6899c7cae
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Date deposited: 22 Apr 2026 16:51
Last modified: 23 Apr 2026 01:51
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Author:
Khadiga H.A. Sayed
Author:
Maarten J.L.F. Cruyff
Author:
Andrea Petróczi
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