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The Randomized Response Technique (Warner,  Journal of the American Statistical Association ,  60 , 63-69, 1965) has been developed to control for socially desirable responses in surveys on sensitive attributes. The Crosswise Model (CWM; Yu et al.,  Metrika, 67 , 251-263, 2008) and its extension, the Extended Crosswise Model (ECWM; Heck et al.,  Behavior Research Methods, 50,  1895-1905, 2018), are advancements of the Randomized Response Technique that have provided promising results in terms of improved validity of the obtained prevalence estimates compared to estimates based on conventional direct questions. However, recent studies have raised the question as to whether these promising results might have been primarily driven by a methodological artifact in terms of random responses rather than a successful control of socially desirable responding. The current study was designed to disentangle the influence of successful control of socially desirable responding and random answer behavior on the validity of (E)CWM estimates. To this end, we orthogonally manipulated the direction of social desirability (undesirable vs. desirable) and the prevalence (high vs. low) of sensitive attributes. Our results generally support the notion that the ECWM successfully controls social desirability bias and is inconsistent with the alternative account that ECWM estimates are distorted by a substantial influence of random responding. The results do not rule out a small proportion of random answers, especially when socially undesirable attributes with high prevalence are studied, or when high randomization probabilities are applied. Our results however do rule out that random responding is a major factor that can account for the findings attesting to the improved validity of (E)CWM as compared with DQ estimates.

More than random responding: Empirical evidence for the validity of the (Extended) Crosswise Model