Electronic Journal of Statistics

Improvements and extensions of the item count technique

Heiko Groenitz

Full-text: Open access


The item count technique (ICT) is a helpful tool to conduct surveys on sensitive characteristics such as tax evasion, corruption, insurance fraud, social fraud or drug consumption. The ICT yields cooperation of the respondents by protecting their privacy. There have been several interesting developments on the ICT in recent years. However, some approaches are incomplete while some research questions can not be tackled by the ICT so far. For these reasons, we broaden the existing literature in two main directions. First, we generalize the single sample count (SSC) technique, which is a simplified version of the original ICT, and derive an admissible estimate for the proportion of persons bearing a stigmatizing attribute, bootstrap variance estimates and bootstrap confidence intervals. Moreover, we present both a Bayesian and a covariate extension of the generalized SSC technique. The Bayesian set up allows the incorporation of prior information (e.g., available from a previous study) into the estimation and thus can lead to more efficient estimates. Our covariate extension is useful to conduct regression analysis, i.e., to estimate the effects of explanatory variables on the sensitive characteristic. Second, we establish a new ICT that is applicable to multicategorical sensitive variables such as the number of times a respondent has evaded taxes or the amount of money earned by undeclared work (recorded in classes). The estimation of the distribution of such attributes was not at all treated in the literature on the ICT so far. Therefore, we derive estimates for the marginal distribution of the sensitive characteristic, Bayesian estimates and regression estimates corresponding to our multicategorical ICT.

Article information

Electron. J. Statist., Volume 8, Number 2 (2014), 2321-2351.

First available in Project Euclid: 6 November 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Sensitive question socially desired answer randomized response missing data problem Bayesian inference logistic regression


Groenitz, Heiko. Improvements and extensions of the item count technique. Electron. J. Statist. 8 (2014), no. 2, 2321--2351. doi:10.1214/14-EJS951. https://projecteuclid.org/euclid.ejs/1415285927

Export citation


  • [1] Bar-Lev, S.K., Bobovitch, E. and Boukai, B. (2004). A note on randomized response models for quantitative data. Metrika 60, 255–260.
  • [2] Blair, G. and Imai, K. (2012). Statistical analysis of list experiments. Political Analysis 20, 47–77.
  • [3] Chaudhuri, A. (2011). Randomized Response and Indirect Questioning Techniques in Surveys. Chapman &, Hall/CRC.
  • [4] Chaudhuri, A. and Christofides, T.C. (2007). Item count technique in estimating the proportion of people with a sensitive feature. Journal of Statistical Planning and Inference 137, 589–593.
  • [5] Chaudhuri, A. and Christofides, T.C. (2013). Indirect Questioning in Sample Surveys., Springer.
  • [6] Coutts, E. and Jann, B. (2011). Sensitive questions in online surveys: Experimental results for the randomized response technique (RRT) and the unmatched count technique (UCT). Sociological Methods & Research 40, 169–193.
  • [7] Dempster, A.P., Laird, N.M. and Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society B 39, 1–38.
  • [8] Eichhorn, B.H. and Hayre, L.S. (1983). Scrambled randomized response methods for obtaining sensitive quantitative data. Journal of Statistical Planning and Inference 7, 307–316.
  • [9] Groenitz, H. (2013). Using prior information in privacy-protecting survey designs for categorical sensitive variables. Statistical Papers, DOI, 10.1007/s00362-013-0573-3.
  • [10] Gupta, S., Shabbir, J. and Sehra, S. (2010). Mean and sensitivity estimation in optional randomized response models. Journal of Statistical Planning and Inference 140, 2870–2874.
  • [11] Holbrook, A.L. and Krosnick, J.A. (2010). Social desirability bias in voter turnout reports: Tests using the item count technique. Public Opinion Quarterly 74, 37–67.
  • [12] Imai, K. (2011). Multivariate regression analysis for the item count technique. Journal of the American Statistical Association 106, 407–416.
  • [13] Kuha, J. and Jackson, J. (2014). The item count method for sensitive survey questions: Modelling criminal behaviour. Journal of the Royal Statistical Society C 63, 321–341.
  • [14] Miller, J.D. (1984). A New Survey Technique for Studying Deviant Behavior. PhD thesis, The George Washington, University.
  • [15] Petroczi, A., Nepusz, T., Cross, P., Taft, H., Shah, S., Deshmukh, N., Schaffer, J., Shane, M., Adesanwo, C., Barker, J. and Naughton, D.P. (2011). New non-randomised model to assess the prevalence of discriminating behaviour: A pilot study on mephedrone. Substance Abuse Treatment, Prevention, and Policy, 6:20.
  • [16] Pollock, K.H. and Bek, Y. (1976). A comparison of three randomized response models for quantitative data. Journal of the American Statistical Association 71, 884–886.
  • [17] Schafer, J.L. (2000). Analysis of Incomplete Multivariate Data. Chapman &, Hall/CRC.
  • [18] Tanner, M.A. and Wong, W.H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association 82, 528–540.
  • [19] Tian, G.L. and Tang, M.L. (2014). Incomplete categorical data design: Non-randomized response techniques for sensitive questions in surveys. CRC, Press.
  • [20] Trappmann, M., Krumpal, I., Kirchner, A. and Jann, B. (2014). Item sum: A new technique for asking quantitative sensitive questions. Journal of Survey Statistics and Methodology 2, 58–77.
  • [21] Tsuchiya, T. (2005). Domain estimators for the item count technique. Survey Methodology 31, 41–51.
  • [22] Tsuchiya, T., Hirai, Y. and Ono, S. (2007). A study of the properties of the item count technique. Public Opinion Quarterly 71, 253–272.