AStA Advances in Statistical Analysis

, Volume 102, Issue 3, pp 455–478 | Cite as

Advances in estimation by the item sum technique using auxiliary information in complex surveys

  • María del Mar García Rueda
  • Pier Francesco PerriEmail author
  • Beatriz Rodríguez Cobo
Original Paper


To collect sensitive data, survey statisticians have designed many strategies to reduce nonresponse rates and social desirability response bias. In recent years, the item count technique has gained considerable popularity and credibility as an alternative mode of indirect questioning survey, and several variants of this technique have been proposed as new needs and challenges arise. The item sum technique (IST), which was introduced by Chaudhuri and Christofides (Indirect questioning in sample surveys, Springer-Verlag, Berlin, 2013) and Trappmann et al. (J Surv Stat Methodol 2:58–77, 2014), is one such variant, used to estimate the mean of a sensitive quantitative variable. In this approach, sampled units are asked to respond to a two-list of items containing a sensitive question related to the study variable and various innocuous, nonsensitive, questions. To the best of our knowledge, very few theoretical and applied papers have addressed the IST. In this article, therefore, we present certain methodological advances as a contribution to appraising the use of the IST in real-world surveys. In particular, we employ a generic sampling design to examine the problem of how to improve the estimates of the sensitive mean when auxiliary information on the population under study is available and is used at the design and estimation stages. A Horvitz–Thompson-type estimator and a calibration-type estimator are proposed and their efficiency is evaluated by means of an extensive simulation study. Using simulation experiments, we show that estimates obtained by the IST are nearly equivalent to those obtained using “true data” and that in general they outperform the estimates provided by a competitive randomized response method. Moreover, variance estimation may be considered satisfactory. These results open up new perspectives for academics, researchers and survey practitioners and could justify the use of the IST as a valid alternative to traditional direct questioning survey modes.


Auxiliary information Calibration estimator Domain estimator Item count technique Horvitz–Thompson estimator Randomized response Sensitive characteristic 

Mathematics Subject Classification

62D05 62P25 



This work is partially supported by Ministerio de Economía y Competitividad of Spain (Grant MTM2015-63609-R), Ministerio de Educación, Cultura y Deporte (Grant FPU, Spain) and by the project PRIN-SURWEY (Grant 2012F42NS8, Italy).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Statistics and Operational ResearchUniversity of GranadaGranadaSpain
  2. 2.Department of Economics, Statistics and FinanceUniversity of CalabriaArcavacata di RendeItaly

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