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Original Articles

Randomized response estimation in multiple frame surveys

, &
Pages 189-206 | Received 05 Oct 2017, Accepted 07 May 2018, Published online: 31 May 2018
 

ABSTRACT

Large-scale surveys are increasingly delving into sensitive topics such as gambling, alcoholism, drug use, sexual behaviour and domestic violence. Sensitive, stigmatizing or even incriminating themes are difficult to investigate by using standard data-collection techniques since respondents are generally reluctant to release information concerning their personal sphere. Furthermore, such topics usually pertain elusive population (e.g. irregular immigrants and homeless, alcoholics, drug users, rape and sexual assault victims) which are difficult to sample since not adequately covered in a single sampling frame. On the other hand, researchers often utilize more than one data-collection mode (i.e. mixed-mode surveys) in order to increase response rates and/or improve coverage of the population of interest. Surveying sensitive and elusive populations and mixed-mode researches are strictly connected with multiple frame surveys which are becoming widely used to decrease bias due to undercoverage of the target population. In this work, we combine sensitive research and multiple frame surveys. In particular, we consider statistical techniques for handling sensitive data coming from multiple frame surveys using complex sampling designs. Our aim is to estimate the mean of a sensitive variable connected to undesirable behaviours when data are collected by using the randomized response theory. Some estimators are constructed and their properties theoretically investigated. Variance estimation is also discussed by means of the jackknife technique. Finally, a Monte Carlo simulation study is conducted to evaluate the performance of the proposed estimators and the accuracy of variance estimation.

2010 AMS SUBJECT CLASSIFICATIONS:

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This study was partially supported by Ministerio de Economía y Competitividad grant MTM2015-63609-R and FPU grant program, Spain and by Consejería de Empleo, Empresa y Comercio grant SEJ2954, Junta de Andalucía.

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