The Annals of Applied Statistics

Bayesian randomized response technique with multiple sensitive attributes: The case of information systems resource misuse

Ray S. W. Chung, Amanda M. Y. Chu, and Mike K. P. So

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


The randomized response technique (RRT) is a classical and effective method used to mitigate the distortion arising from dishonest answers. The traditional RRT usually focuses on the case of a single sensitive attribute, and discussion of the case of multiple sensitive attributes is limited. Here, we study a business case to identify some individual and organizational determinants driving information systems (IS) resource misuse in the workplace. People who actually engage in IS resource misuse are probably not willing to provide honest answers, given the sensitivity of the topic. Yet, to develop the causal relationship between IS resource misuse and its determinants, a version of the RRT for multivariate analysis is required. To implement the RRT with multiple sensitive attributes, we propose a Bayesian approach for estimating covariance matrices with incomplete information (resulting from the randomization procedure in the RRT case). The proposed approach (i) accommodates the positive definite condition and other intrinsic parameter constraints in the posterior to improve statistical precision, (ii) incorporates Bayesian shrinkage estimation for covariance matrices despite incomplete information, and (iii) adopts a quasi-likelihood method to achieve Bayesian semiparametric inference for enhancing flexibility. We show the effectiveness of the proposed method in a simulation study. We also apply the Bayesian RRT method and structural equation modeling to identify the causal relationship between IS resource misuse and its determinants.

Article information

Ann. Appl. Stat., Volume 12, Number 3 (2018), 1969-1992.

Received: July 2016
Revised: November 2017
First available in Project Euclid: 11 September 2018

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Causal modeling Markov chain Monte Carlo quasi-likelihood sensitive responses shrinkage estimation of covariance matrix unrelated question design


Chung, Ray S. W.; Chu, Amanda M. Y.; So, Mike K. P. Bayesian randomized response technique with multiple sensitive attributes: The case of information systems resource misuse. Ann. Appl. Stat. 12 (2018), no. 3, 1969--1992. doi:10.1214/18-AOAS1139.

Export citation


  • Ando, T. (2011). Predictive Bayesian model selection. Amer. J. Math. Management Sci. 31 13–38.
  • Blair, G. and Imai, K. (2012). Statistical analysis of list experiments. Polit. Anal. 20 47–77.
  • Blair, G., Imai, K. and Zhou, Y.-Y. (2015). Design and analysis of the randomized response technique. J. Amer. Statist. Assoc. 110 1304–1319.
  • Blair, G. and Zhou, Y.-Y. (2016). Bayesian randomized response regression. The rr R package [Online]. Available at
  • Chaudhuri, A. (2011). Randomized Response and Indirect Questioning Techniques in Surveys. CRC Press, Boca Raton, FL.
  • Chen, C. C. and Singh, S. (2011). Pseudo-Bayes and pseudo-empirical Bayes estimators in randomized response sampling. J. Stat. Comput. Simul. 81 779–793.
  • Christofides, T. C. (2005). Randomized response technique for two sensitive characteristics at the same time. Metrika 62 53–63.
  • Chu, A. M. Y. and Chau, P. Y. K. (2014). Development and validation of instruments of information security deviant behavior. Decis. Support Syst. 66 93–101.
  • Chu, A. M. Y., Chau, P. Y. K. and So, M. K. P. (2015). Developing a typological theory using a quantitative approach: A case of information security deviant behavior. Commun. Assoc. Inf. Syst. 37 510–535.
  • Chung, R. S., Chu, A. M. and So, M. K. (2018). Supplement to “Bayesian Randomized Response Technique with Multiple Sensitive Attributes: The Case of Information Systems Resource Misuse.” DOI:10.1214/18-AOAS1139SUPP.
  • Cohen, A. (1996). On the discriminant validity of the Meyer and Allen measure of organizational commitment: How does it fit with the work commitment construct? Educ. Psychol. Meas. 56 494–503.
  • 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). Sociol. Methods Res. 40 169–193.
  • Cruyff, M. J. L. F., van den Hout, A. and van der Heijden, P. G. M. (2008). The analysis of randomized response sum score variables. J. R. Stat. Soc. Ser. B. Stat. Methodol. 70 21–30.
  • D’Arcy, J. and Devaraj, S. (2012). Employee misuse of information technology resources: Testing a contemporary deterrence model. Decis. Sci. 43 1091–1124.
  • D’Arcy, J., Hovav, A. and Galletta, D. (2009). User awareness of security countermeasures and its impact on information systems misuse: A deterrence approach. Inf. Syst. Res. 20 79–98.
  • Fox, J. A. and Tracy, P. E. (1984). Measuring associations with randomized response. Soc. Sci. Res. 13 188–197.
  • Fox, J. A. and Tracy, P. E. (1986). Randomized Response: A Method for Sensitive Surveys. SAGE Publications, Thousand Oaks, CA.
  • Gjestvang, C. R. and Singh, S. (2006). A new randomized response model. J. R. Stat. Soc. Ser. B. Stat. Methodol. 68 523–530.
  • Greenberg, B. G., Abul-Ela, A.-L. A., Simmons, W. R. and Horvitz, D. G. (1969). The unrelated question randomized response model: Theoretical framework. J. Amer. Statist. Assoc. 64 520–539.
  • Greenberg, B. G., Kuebler, R. R., Abernathy, J. R. and Horvitz, D. G. (1971). Application of the randomized response technique in obtaining quantitative data. J. Amer. Statist. Assoc. 66 243–250.
  • Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica 50 1029–1054.
  • Höglinger, M., Jann, B. and Diekmann, A. (2016). Sensitive questions in online surveys: An experimental evaluation of different implementations of the randomized response technique and the crosswise model. Surv. Res. Methods 10 171–187.
  • Horvitz, D. G., Shah, B. V. and Simmons, W. R. (1967). The unrelated question randomized response model. In Proceedings of Social Statistics Section 65–72. Amer. Statist. Assoc., Alexandria, VA.
  • Hsieh, J. J. P.-A., Rai, A. and Keil, M. (2008). Understanding digital inequality: Comparing continued use behavioral models of the socio-economically advantaged and disadvantaged. MIS Q. 32 97–126.
  • Huang, J. Z., Liu, N., Pourahmadi, M. and Liu, L. (2006). Covariance matrix selection and estimation via penalised normal likelihood. Biometrika 93 85–98.
  • Imai, K. (2011). Multivariate regression analysis for the item count technique. J. Amer. Statist. Assoc. 106 407–416.
  • Imai, K., Park, B. and Greene, K. F. (2015). Using the predicted responses from list experiments as explanatory variables in regression models. Polit. Anal. 23 180–196.
  • Jaros, S. J. (1997). An assessment of Meyer and Allen’s (1991) three-component model of organizational commitment and turnover intentions. J. Vocat. Behav. 51 319–337.
  • Jayaraj, A., Odumade, O. and Singh, S. (2014). A new quasi-empirical Bayes estimate in randomized response technique. JSM 2014.
  • Kaplan, D. (2009). Structural Equation Modeling, 2nd ed. SAGE Publications, Inc., Thousand Oaks, CA.
  • Kuk, A. Y. C. (1990). Asking sensitive questions indirectly. Biometrika 77 436–438.
  • Kwan, S. S. K., So, M. K. P. and Tam, K. Y. (2010). Research note—Applying the randomized response technique to elicit truthful responses to sensitive questions in IS research: The case of software piracy behavior. Inf. Syst. Res. 21 941–959.
  • Lee, C. S., Sedory, S. A. and Singh, S. (2016). Cramer–Rao lower bounds of variance for estimating two proportions and their overlap by using two-decks of cards. In Handbook of Statistics 34 353–385.
  • Lin, C.-P. and Ding, C. G. (2003). Modeling information ethics: The joint moderating role of locus of control and job insecurity. J. Bus. Ethics 48 335–346.
  • Liu, J. S., Liang, F. and Wong, W. H. (2000). The multiple-try method and local optimization in Metropolis sampling. J. Amer. Statist. Assoc. 95 121–134.
  • Locander, W., Sudman, S. and Blackburn, N. (1976). An investigation of interview method, threat and response distortion. J. Amer. Statist. Assoc. 71 269–275.
  • Mangat, N. S. (1994). An improved randomized response strategy. J. Roy. Statist. Soc. Ser. B 56 93–95.
  • Mangat, N. S. and Singh, R. (1990). An alternative randomized response procedure. Biometrika 77 439–442.
  • Meyer, J. P., Allen, N. J. and Smith, C. A. (1993). Commitment to organizations and occupations: Extension and test of a three-component conceptualization. J. Appl. Psychol. 78 538–551.
  • Minsky-Kelly, D., Hamberger, L. K., Pape, D. A. and Wolff, M. (2005). We’ve had training, now what? Qualitative analysis of barriers to domestic violence screening and referral in a health care setting. J. Interpers. Violence 20 1288–1309.
  • Muirhead, R. J. (2005). Aspects of Multivariate Statistical Theory. Wiley-Interscience, New York.
  • Nuno, A. and St. John, F. A. V. (2015). How to ask sensitive questions in conservation: A review of specialized questioning techniques. Biol. Conserv. 189 5–15.
  • Panaccio, A. and Vandenberghe, C. (2009). Perceived organizational support, organizational commitment and psychological well-being: A longitudinal study. J. Vocat. Behav. 75 224–236.
  • Park, T. and Casella, G. (2008). The Bayesian lasso. J. Amer. Statist. Assoc. 103 681–686.
  • Peace, A. G., Galletta, D. F. and Thong, J. Y. L. (2003). Software piracy in the workplace: A model and empirical test. J. Manage Inf. Syst. 20 153–177.
  • Pollock, K. H. and Bek, Y. (1976). A comparison of three randomized response models for quantitative data. J. Amer. Statist. Assoc. 71 884–886.
  • Raghavarao, D. and Federer, W. T. (1979). Block total response as an alternative to the randomized response method in surveys. J. Roy. Statist. Soc. Ser. B 41 40–45.
  • Rosenfeld, B., Imai, K. and Shapiro, J. N. (2016). An empirical validation study of popular survey methodologies for sensitive questions. Amer. J. Polit. Sci. 60 783–802.
  • Shao, J. (2003). Mathematical Statistics, 2nd ed. Springer, New York.
  • Shephard, N. and Pitt, M. K. (1997). Likelihood analysis of non-Gaussian measurement time series. Biometrika 84 653–667.
  • Singh, S. (2003). Advanced Sampling Theory with Applications: How Michael ‘Selected’ Amy, Vol. I. Kluwer Academic, Dordrecht.
  • Singh, S. and Sedory, S. A. (2011). Cramer–Rao lower bound of variance in randomized response sampling. Sociol. Methods Res. 40 536–546.
  • So, M. K. P., Chen, C. W. S. and Chen, M.-T. (2005). A Bayesian threshold nonlinearity test for financial time series. J. Forecast. 24 61–75.
  • Tamhane, A. C. (1981). Randomized response techniques for multiple sensitive attributes. J. Amer. Statist. Assoc. 76 916–923.
  • Tan, M. T., Tian, G.-L. and Tang, M.-L. (2009). Sample surveys with sensitive questions: A nonrandomized response approach. Amer. Statist. 63 9–16.
  • Warner, S. L. (1965). Randomized response: A survey technique for eliminating evasive answer bias. J. Amer. Statist. Assoc. 60 63–69.
  • Yin, G. (2009). Bayesian generalized method of moments. Bayesian Anal. 4 191–207.

Supplemental materials

  • Supplement: Rmarkdown file. The supplementary R Markdown and HTML files for implementing the Bayesian methods in the paper.