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

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.

[1]  Forrest W. Crawford,et al.  Combining List Experiment and Direct Question Estimates of Sensitive Behavior Prevalence. , 2013, Journal of survey statistics and methodology.

[2]  Walter T. Federer,et al.  Block Total Response as an Alternative to the Randomized Response Method in Surveys , 1979 .

[3]  Martin Korndörfer,et al.  Measuring and explaining tax evasion: Improving self-reports using the crosswise model , 2014 .

[4]  P. Kott,et al.  Developing Calibration Weights and Standard-Error Estimates for a Survey of Drug-Related Emergency-Department Visits , 2014 .

[5]  J. Strickler,et al.  Measuring Induced Abortion in Mexico , 2004 .

[6]  Raghunath Arnab,et al.  Randomized response techniques: An application to the Botswana AIDS impact survey , 2010 .

[7]  Estimating a Finite Population Proportion Bearing a Sensitive Attribute from a Single Probability Sample by Item Count Technique , 2016 .

[8]  Wendy Visscher,et al.  The Item Count Technique as a Method of Indirect Questioning: A Review of Its Development and a Case Study Application , 2011 .

[9]  K. Dietz,et al.  Doping in fitness sports: estimated number of unreported cases and individual probability of doping. , 2006, Addiction.

[10]  Kenneth F. Greene,et al.  Using the Predicted Responses from List Experiments as Explanatory Variables in Regression Models , 2015, Political Analysis.

[11]  Sarjinder Singh,et al.  A generalized approach to randomised response for quantitative variables , 2015 .

[12]  Arijit Chaudhuri,et al.  Randomized Response and Indirect Questioning Techniques in Surveys , 2010 .

[13]  Kosuke Imai,et al.  Statistical Analysis of List Experiments , 2012, Political Analysis.

[14]  Stephen G. Sutton,et al.  Understanding recreational fishers' compliance with no-take zones in the Great Barrier Reef Marine Park , 2013 .

[15]  Lakhbir S. Hayre,et al.  Scrambled randomized response methods for obtaining sensitive quantitative data , 1983 .

[16]  Giancarlo Diana,et al.  Estimating a sensitive proportion through randomized response procedures based on auxiliary information , 2009 .

[17]  K. Imai,et al.  Comparing and Combining List and Endorsement Experiments: Evidence from Afghanistan , 2014 .

[18]  Purnima Shaw.  Estimating a finite population mean of a sensitive quantitative variable from a single probability sample by the Item Count Technique , 2015, Model. Assist. Stat. Appl..

[19]  J. Shabbir,et al.  An alternative item sum technique for improved estimators of population mean in sensitive surveys , 2017 .

[20]  Rolf Ulrich,et al.  Randomized response estimates for doping and illicit drug use in elite athletes. , 2010, Drug and alcohol dependence.

[21]  Adam Glynn.  What Can We Learn with Statistical Truth Serum?Design and Analysis of the List Experiment , 2013 .

[22]  C. Särndal,et al.  Calibration Estimators in Survey Sampling , 1992 .

[23]  Sixten Lundström,et al.  Estimation in Surveys with Nonresponse: Särndal/Estimation in Surveys with Nonresponse , 2005 .

[24]  P. Perri,et al.  Estimating Induced Abortion and Foreign Irregular Presence Using the Randomized Response Crossed Model , 2016 .

[25]  Eric M. Larson,et al.  An Innovative Technique for Asking Sensitive Questions: the Three-Card Method , 2002 .

[26]  Ben Jann,et al.  Asking Sensitive Questions Using the Crosswise Model An Experimental Survey Measuring Plagiarism , 2012 .

[27]  G. Tian,et al.  Incomplete Categorical Data Design: Non-Randomized Response Techniques for Sensitive Questions in Surveys , 2013 .

[28]  Miller Jd.  The nominative technique: a new method of estimating heroin prevalence. , 1985 .

[29]  Paul E. Tracy,et al.  Randomized Response: A Method for Sensitive Surveys , 1986 .

[30]  Michael S. Goodstadt,et al.  The Randomized Response Technique: A Test on Drug Use , 1975 .

[31]  Peter G. M. van der Heijden,et al.  Meta-Analysis of Randomized Response Research , 2005 .

[32]  Ben Jann,et al.  Item Sum: A New Technique for Asking Quantitative Sensitive Questions , 2014 .

[33]  I. Olkin,et al.  Sampling theory of surveys, with applications , 1955 .

[34]  Zawar Hussain,et al.  An Alternative Item Count Technique in Sensitive Surveys , 2012 .

[35]  S. Jacobson,et al.  Estimating Illegal Resource Use at a Ugandan Park with the Randomized Response Technique , 2007 .

[36]  Ben Jann,et al.  Estimating the Prevalence of Illicit Drug Use Among Students Using the Crosswise Model , 2014, Substance use & misuse.

[37]  P. V. Sukhatme,et al.  Sampling Theory of Surveys with Applications. , 1957 .

[38]  Giancarlo Diana,et al.  New scrambled response models for estimating the mean of a sensitive quantitative character , 2010 .

[39]  Ted Chang,et al.  Using Calibration Weighting to Adjust for Nonignorable Unit Nonresponse , 2010 .

[40]  Jochen Musch,et al.  A randomized‐response investigation of the education effect in attitudes towards foreigners , 2009 .

[41]  Arijit Chaudhuri,et al.  Item Count Technique in estimating the proportion of people with a sensitive feature , 2007 .

[42]  The randomized response technique as a tool for estimating non-compliance rates in fisheries: a case study of illegal red abalone (Haliotis rufescens) fishing in Northern California , 2009, Environmental Conservation.

[43]  Peter G M van der Heijden,et al.  Prevalence of use of performance enhancing drugs by fitness centre members. , 2013, Drug testing and analysis.

[44]  Peter G. M. van der Heijden,et al.  A validation of a computer‐assisted randomized response survey to estimate the prevalence of fraud in social security , 2006 .

[45]  Benzion Boukai,et al.  A note on randomized response models for quantitative data , 2004 .

[46]  Jon A. Krosnick,et al.  Social desirability bias in voter turnout reports Tests using the item count technique , 2010 .

[47]  Kosuke Imai,et al.  Multivariate Regression Analysis for the Item Count Technique , 2011 .

[48]  Jon A. Krosnick,et al.  Measuring Voter Turnout By Using The Randomized Response Technique , 2010 .

[49]  D. Horvitz,et al.  A Generalization of Sampling Without Replacement from a Finite Universe , 1952 .

[50]  Milani Y. Chaloupka,et al.  Application of the randomized response technique to marine park management: an assessment of permit compliance , 1985 .

[51]  Tasos C. Christofides.  A new version of the item count technique , 2015, Model. Assist. Stat. Appl..

[52]  Ivar Krumpal,et al.  Estimating the prevalence of xenophobia and anti-Semitism in Germany: A comparison of randomized response and direct questioning. , 2012, Social science research.

[53]  Arijit Chaudhuri,et al.  Indirect Questioning in Sample Surveys , 2013 .

[54]  J. Hox,et al.  A Comparison of Randomized Response, Computer-Assisted Self-Interview, and Face-to-Face Direct Questioning , 2000 .

[55]  P. Kline,et al.  Use of Random Response to Estimate Angler Noncompliance with Fishing Regulations , 1995 .

[56]  Rolf Ulrich,et al.  Randomized Response Estimates for the 12‐Month Prevalence of Cognitive‐Enhancing Drug Use in University Students , 2013, Pharmacotherapy.

[57]  S L Warner,et al.  Randomized response: a survey technique for eliminating evasive answer bias. , 1965, Journal of the American Statistical Association.

[58]  Jodie Houston,et al.  A Survey of Tax Evasion Using the Randomized Response Technique , 2001, Contemporary Issues in Taxation Research.

[59]  Joe Kerkvliet.  ESTIMATING A LOGIT MODEL WITH RANDOMIZED DATA: THE CASE OF COCAINE USE , 1994 .

[60]  T. Nepusz,et al.  A potential inflating effect in estimation models: Cautionary evidence from comparing performance enhancing drug and herbal hormonal supplement use estimates , 2013 .

[61]  M. Rueda,et al.  An improved class of estimators in RR surveys , 2018 .

[62]  Giancarlo Diana,et al.  A calibration-based approach to sensitive data: a simulation study , 2012 .

[63]  A. Chaudhuri,et al.  Randomized Response: Theory and Techniques , 1987 .

[64]  E. Oliveras,et al.  Examples of methods to address underreporting of induced abortion: Preceding Birth Technique and Randomized Response Technique. , 2010 .

[65]  Giancarlo Diana,et al.  A class of estimators for quantitative sensitive data , 2011 .

[66]  C. Ellertson,et al.  The Measure of Induced Abortion Levels in Mexico Using Random Response Technique , 2006 .

[67]  Giancarlo Diana,et al.  Scrambled Response Models Based on Auxiliary Variables , 2013 .

[68]  M. Gavin,et al.  Quantifying illegal hunting: a novel application of the quantitative randomised response technique. , 2015 .