Advertisement

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 Perri
  • Beatriz Rodríguez Cobo
Original Paper
  • 175 Downloads

Abstract

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.

Keywords

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

Mathematics Subject Classification

62D05 62P25 

Notes

Acknowledgements

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).

References

  1. Arcos, A., Rueda, M.M., Singh, S.: Generalized approach to randomized response for quantitative variables. Qual. Quant. 49, 1239–1256 (2015)CrossRefGoogle Scholar
  2. Arias, A., Sutton, S.G.: Understanding recreational fishers compliance with no-take zones in the Great Barrier Reef Marine Park. Ecol. Soc. (2013).  https://doi.org/10.5751/ES-05872-180418 Google Scholar
  3. Arnab, R., Singh, S.: Randomized response techniques: an application to the Botswana AIDS impact survey. J. Stat. Plan. Inference 140, 941–953 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  4. Aronow, P.M., Coppock, A., Crawford, F.W., Green, D.P.: Combining list experiment and direct question estimates of sensitive behavior prevalence. J. Surv. Stat. Methodol. 3, 43–66 (2015)CrossRefGoogle Scholar
  5. Bar-Lev, S.K., Bobovitch, E., Boukai, B.: A note on randomized response models for quantitative data. Metrika 60, 255–260 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  6. Blair, G., Imai, K.: List: statistical methods for the item count technique and list experiment. http://CRAN.Rproject.org/package=list (2010)
  7. Blair, G., Imai, K.: Statistical analysis of list experiments. Polit. Anal. 20, 47–77 (2012)CrossRefGoogle Scholar
  8. Blair, G., Imai, K., Lyall, J.: Comparing and combining list and endorsement experiments: evidence from Afghanistan. Am. J. Polit. Sci. 58, 1043–1063 (2014)CrossRefGoogle Scholar
  9. Blank, S.G., Gavin, M.C.: 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. Environ. Conserv. 36, 112–119 (2009)CrossRefGoogle Scholar
  10. Chaloupka, M.Y.: Application of the randomized response technique to marine park management: an assessment of permit compliance. Environ. Manag. 9, 393–398 (1985)CrossRefGoogle Scholar
  11. Chaudhuri, A.: Randomized Response and Indirect Questioning Techniques in Surveys. Chapman & Hall, Boca Raton (2011)zbMATHGoogle Scholar
  12. Chaudhuri, A., Christofides, T.C.: Item count technique in estimating the proportion of people with a sensitive feature. J. Stat. Plan. Inference 137, 589–593 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  13. Chaudhuri, A., Christofides, T.C.: Indirect Questioning in Sample Surveys. Springer-Verlag, Berlin (2013)CrossRefzbMATHGoogle Scholar
  14. Chaudhuri, A., Mukerjee, R.: Randomized Response: Theory and Techniques. Marcel Dekker Inc, New York (1988)zbMATHGoogle Scholar
  15. Conteh, A., Gavin, M.C., Solomon, J.: Quantifying illegal hunting: a novel application of the randomised response technique. Biol. Conserv. 189, 16–23 (2015)CrossRefGoogle Scholar
  16. Christofides, T.C.: A new version of the item count technique. Model Assist. Stat. Appl. 10, 289–297 (2015)Google Scholar
  17. Deville, J.C., Särndal, C.E.: Calibration estimators in survey sampling. J. Am. Stat. Assoc. 87, 376–382 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  18. Diana, G., Perri, P.F.: Estimating a sensitive proportion through randomized response procedures based on auxiliary information. Stat. Pap. 50, 661–672 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  19. Diana, G., Perri, P.F.: New scrambled response models for estimating the mean of a sensitive quantitative character. J. Appl. Stat. 37, 1875–1890 (2010)MathSciNetCrossRefGoogle Scholar
  20. Diana, G., Perri, P.F.: A class of estimators for quantitative sensitive data. Stat. Pap. 52, 633–650 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  21. Diana, G., Perri, P.F.: A calibration-based approach to sensitive data: a simulation study. J. Appl. Stat. 39, 53–65 (2012)MathSciNetCrossRefGoogle Scholar
  22. Dietz, P., Striegel, H., Franke, A.G., Lieb, K., Simon, P., Ulrich, R.: Randomized response estimates for the 12-month prevalence of cognitive-enhancing drug use in university students. Pharmacotherapy 33, 44–50 (2013)CrossRefGoogle Scholar
  23. Droitcour, J.A., Caspar, R.A., Hubbard, M.L., Parsley, T.L., Visseher, W., Ezzati, T.M.: The item count technique as a method of indirect questioning: a review of its development and a case study application. In: Biemer, P.P., Groves, R.M., Lyburg, L.E., Mathiowetz, N., Sudmar, S. (eds.) Measurement Error in Surveys, pp. 187–209. Wiley, New York (1991)Google Scholar
  24. Droitcour, J.A., Larson, E.M.: An innovative technique for asking sensitive questions: the three-card method. Bull. Soc. Methodol. 75, 5–23 (2002)CrossRefGoogle Scholar
  25. Eichhorn, B.H., Hayre, L.S.: Scrambled randomized response methods for obtaining sensitive quantitative data. J. Stat. Plan. Inference 7, 306–316 (1983)CrossRefGoogle Scholar
  26. Fox, J.A., Tracy, P.E.: Randomized Response: A Method for Sensitive Survey. Sage Publication Inc, Newbury Park (1986)CrossRefGoogle Scholar
  27. Glynn, A.N.: What can we learn with statistical truth serum? Design and analysis of the list experiment. Pub. Opin. Q. 77, 159–172 (2013)CrossRefGoogle Scholar
  28. Goodstadt, M.S., Gruson, V.: The randomized response technique: a test on drug use. J. Am. Stat. Assoc. 70, 814–818 (1975)CrossRefGoogle Scholar
  29. Holbrook, A.L., Krosnick, J.A.: Measuring voter turnout by using the randomized response technique: evidence calling into question the method’s validity. Pub. Opin. Q. 74, 328–343 (2010a)CrossRefGoogle Scholar
  30. Holbrook, A.L., Krosnick, J.A.: Social desirability bias in voter turnout reports: tests using the item count technique. Pub. Opin. Q. 74, 37–67 (2010b)CrossRefGoogle Scholar
  31. Horvitz, D.G., Thompson, D.J.: A generalization of sampling without replacement from a finite universe. J. Am. Stat. Assoc. 47, 663–685 (1952)MathSciNetCrossRefzbMATHGoogle Scholar
  32. Houston, J., Tran, A.: A survey of tax evasion using the randomized response technique. Adv. Tax. 13, 69–94 (2001)CrossRefGoogle Scholar
  33. Hussain, Z., Shah, E.A., Shabbir, J.: An alternative item count technique in sensitive surveys. Revista Colombiana de Estadistica 35, 39–54 (2012)MathSciNetzbMATHGoogle Scholar
  34. Hussain, Z., Shabbir, N., Shabbir J.: An alternative item sum technique for improved estimators of population mean in sensitive surveys. Hacet. J. Math. Stat., First published online 46, 907–934 (2017)Google Scholar
  35. Imai, K.: Multivariate regression analysis for the item count technique. J. Am. Stat. Assoc. 106, 407–416 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  36. Imai, K., Park, B., Greene, K.F.: Using the predicted responses from list experiments as explanatory variables in regression models. Polit. Anal. 23, 180–196 (2015)CrossRefGoogle Scholar
  37. James, R.A., Nepusz, T., Naughton, D.P., Petróczi, A.: A potential inflating effect in estimation models: cautionary evidence from comparing performance enhancing drug and herbal hormonal supplement use estimates. Psychol. Sports Exerc. 14, 84–96 (2013)CrossRefGoogle Scholar
  38. Jann, B., Jerke, J., Krumpal, I.: Asking sensitive questions using the crosswise model: an experimental survey measuring plagiarism. Pub. Opin. Q. 76, 32–49 (2012)CrossRefGoogle Scholar
  39. Kerkvliet, J.: Estimating a logit model with randomized data: the case of cocaine use. Aust. J. Stat. 36, 9–20 (1994)CrossRefGoogle Scholar
  40. Korndörfer, M., Krumpal, I., Schmukle, S.C.: Measuring and explain tax evasion: improving self-reports using the crosswise model. J. Econ. Psychol. 45, 18–32 (2014)CrossRefGoogle Scholar
  41. Kott, P.S.: Developing calibration weights and standard-error estimates for a survey of drug-related emergency-department visits. J. Off. Stat. 30, 521–532 (2014)CrossRefGoogle Scholar
  42. Kott, P.S., Chang, T.: Using calibration weighting to adjust for nonignorable unit nonresponse. J. Am. Stat. Assoc. 105, 1265–1275 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  43. Krumpal, I.: Estimating the prevalence of xenophobia and anti-semitism in Germany: a comparison of the randomized response technique and direct questioning. Soc. Sci. Res. 41, 1387–1403 (2012)CrossRefGoogle Scholar
  44. Lara, D., Strickler, J., Olavarrieta, C.D., García, S.G., Ellertson, C.: Measuring induced abortion in Mexico: a comparison of four methodologies. Soc. Methods Res. 32, 529–558 (2004)MathSciNetCrossRefGoogle Scholar
  45. Lara, D., García, S.G., Ellertson, C., Camlin, C., Suaréz, J.: The measure of induced abortion in Mexico using random response technique. Soc. Methods Res. 35, 279–301 (2006)MathSciNetCrossRefGoogle Scholar
  46. Lensvelt-Mulders, G.J.L.M., Hox, J.J., van der Heijden, P.G.M., Mass, C.J.M.: Meta-analysis of randomized response research: thirty-five years of validation. Soc. Methods Res. 33, 319–348 (2005)MathSciNetCrossRefGoogle Scholar
  47. Lensvelt-Mulders, G.J.L.M., van der Heijden, P.G.M., Laudy, O., van Gils, G.: A validation of a computer-assisted randomized response survey to estimate the prevalence of fraud in social security. J. R. Stat. Soc. A 169, 305–318 (2006)MathSciNetCrossRefGoogle Scholar
  48. Miller, J.D.: A New Survey Technique for Studying Deviant Behavior. Ph.D. Thesis, The George Washington University (1984)Google Scholar
  49. Miller, J.D.: The nominative technique: a new method of estimating heroin prevalence. NIDA Res. Monogr. 57, 104–124 (1985)Google Scholar
  50. Oliveras, E., Letamo, G.: Examples of methods to address underreporting of induced abortion: preceding birth technique and randomized response technique. In: Singh, S., Remez, L., Tartaglione, A. (eds.) Methodologies for Estimating Abortion Incidence and Abortion-Related Morbidity: A Review, pp. 63–69. Guttmacher Institute, International Union for the Scientific Study of Population, New York, Paris (2010)Google Scholar
  51. Ostapczuk, M., Musch, J., Mashagen, M.: A randomized-response investigation of the education effect in attitudes towards foreigners. Eur. J. Soc. Psychol. 39, 920–931 (2009)CrossRefGoogle Scholar
  52. Perri, P.F., Diana, G.: Scrambled response models based on auxiliary variables. In: Torelli, N., Pesarin, F., Bar-Hen, A. (eds.) Advances in Theoretical and Applied Statistics, pp. 281–291. Spriger-Verlag, Berlin (2013)CrossRefGoogle Scholar
  53. Perri, P.F., Pelle, E., Stranges, M.: Estimating induced abortion and foreign irregular presence using the randomized response crossed model. Soc. Indic. Res. 129, 601–618 (2016)CrossRefGoogle Scholar
  54. Raghavarao, D., Federer, W.F.: Block total response as an alternative to the randomized response method in survey. J. R. Stat. Soc. B 41, 40–45 (1979)MathSciNetzbMATHGoogle Scholar
  55. Rueda, M., Cobo, B., Arcos, A.: An improved class of estimators in RR surveys. Math. Methods Appl. Sci. (2017).  https://doi.org/10.1002/mma.4256 zbMATHGoogle Scholar
  56. Särndal, C.E.: The calibration approach in survey theory and practice. Surv Methodol. 33, 99–119 (2007)Google Scholar
  57. Särndal, C.E., Lundström, S.: Estimation in Survey with Nonresponse. Wiley, New York (2005)CrossRefzbMATHGoogle Scholar
  58. Schill, D.J., Kline, P.A.: Use of random response to estimate angler noncompliance with fishing regulations. North Am. J. Fish. Manag. 15, 721–731 (1995)CrossRefGoogle Scholar
  59. Shamsipour, M., Yunesian, M., Fotouhi, A., Jann, B., Rahimi-Movaghar, A., Asghari, F., Akhlaghi, A.A.: Estimating the prevalence of illicit drug use among students using the crosswise model. Subst. Use Misuse 49, 1303–1310 (2014)CrossRefGoogle Scholar
  60. Shaw, P.: Estimating a finite population mean of a sensitive quantitative variable from a single probability sample by the Item Count Technique. Model Assist. Stat. Appl. 10, 411–419 (2015)Google Scholar
  61. Shaw, P.: Estimating a finite population proportion bearing a sensitive attribute from a single probability sample by Item Count Technique. In: Chaudhuri, A., Christofides, T.C., Rao, C.R. (eds.) Handbook of Statistics Vol. 34: Data Gathering, Analysis and Protection of Privacy Through Randomized Response Techniques: Qualitative and Quantitative Human Traits, pp. 387–404. Elsevier, Amsterdam (2016)Google Scholar
  62. Simon, P., Striegel, H., Aust, F., Dietz, K., Ulrich, R.: Doping in fitness sports: estimated number of unreported cases and individual probability of doping. Addiction 101, 1640–1644 (2006)CrossRefGoogle Scholar
  63. Solomon, J., Jacobson, S.K., Wald, K.D., Gavin, M.: Estimating illegal resources use at the Ugandan park with the randomized response technique. Hum. Dimens. Wildlife 12, 75–88 (2007)CrossRefGoogle Scholar
  64. Striegel, H., Ulrich, R., Simon, P.: Randomized response estimates for doping and illicit drug use in elite athletes. Drug Alcohol Depend. 106, 230–232 (2010)CrossRefGoogle Scholar
  65. Stubbe, J.H., Chorus, A.M.J., Frank, L.E., de Hon, O., van der Heijden, P.G.M.: Prevalence of use of performance enhancing drugs by fitness center members. Drug Test. Anal. 6, 434–438 (2013)Google Scholar
  66. Sukhatme, P.V., Sukhatme, B.V., Sukhatme, S., Asok, C.: Sampling Theory of Surveys with Applications. Iowa State University Press, Ames (1984)zbMATHGoogle Scholar
  67. Tian, G.-L., Tang, M.-L.: Incomplete Categorical Data Design: Non-Randomized Response Techniques for Sensitive Questions in Surveys. Chapman & Hall, Boca Raton (2014)zbMATHGoogle Scholar
  68. Trappmann, M., Krumpal, I., Kirchner, A., Jann, B.: Item sum: a new technique for asking quantitative sensitive questions. J. Surv. Stat. Methodol. 2, 58–77 (2014)CrossRefGoogle Scholar
  69. van der Heijden, P.G.M., van Gils, G., Bouts, J., Hox, J.J.: A comparison of randomized response, computer-assisted self-interview, and face-to-face direct questioning. Soc. Methods Res. 28, 505–537 (2000)CrossRefGoogle Scholar
  70. Warner, S.L.: Randomized response: a survey technique for eliminating evasive answer bias. J. Am. Stat. Assoc. 60, 63–69 (1965)CrossRefzbMATHGoogle Scholar

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

Personalised recommendations