Skip to main content
SpringerLink
Log in

Estimating Induced Abortion and Foreign Irregular Presence Using the Randomized Response Crossed Model

  • Published:
Social Indicators Research Aims and scope Submit manuscript

Abstract

We present the theoretical framework and the results of a pilot survey conducted in Calabria, a region in the south of Italy, to investigate the prevalence of two sensitive characteristics, namely induced abortion among foreign women residing in this region, and irregular immigrant status. Collecting data on these two attributes by means of traditional survey modes typically produces underestimates of the diffusion of the phenomena due to the stigmatizing nature of the investigated topics. In order to overcome this problem, we employ an alternative data collection method known as the Randomized Response Technique. In particular, we focus on the implementation of the crossed model recently proposed by Lee et al. (Stat Probab Lett 83:399–409, 2013) to estimate two sensitive characteristics and some related measures of association.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Arnab, R., & Singh, S. (2010). Randomized response techniques: An application to the Botswana AIDS impact survey. Journal of Statistical Planning and Inference, 140, 941–953.

    Article  Google Scholar 

  • Barabesi, L., Diana, G., & Perri, P. F. (2013). Design-based distribution function estimation for stigmatized populations. Metrika, 76, 919–935.

    Article  Google Scholar 

  • Barabesi, L., Diana, G., & Perri, P. F. (2014). Horvitz-Thompson estimation with randomized response and nonresponse. Model Assisted Statistics and Applications: Special Issues on Randomized Response Sampling, 9, 3–10.

    Google Scholar 

  • Barabesi, L., Diana, G., & Perri, P. F. (2015). Gini index estimation in randomized response surveys. AStA Advances in Statistical Analysis, 99, 45–62.

    Article  Google Scholar 

  • Blair, G., Zhou, Y.-Y., & Imai, K. (2015). rr: Statistical methods for the randomized response technique. Available at The Comprehensive R Archive Network (CRAN). http://CRAN.R-project.org/package=rr.

  • Boruch, R. F. (1971). Assuring confidentiality of response in social research: A note on strategies. The American Sociologist, 6, 308–311.

    Google Scholar 

  • Chaudhuri, A. (2011). Randomized response and indirect questioning techniques in surveys. Boca Raton, FL: Chapman & Hall/CRC.

    Google Scholar 

  • Chaudhuri, A., & Christofides, T. (2013). Indirect questioning in sample surveys. Berlin: Springer.

    Book  Google Scholar 

  • Chaudhuri, A., & Mukerjee, R. (1988). Randomized response: Theory and techniques. New York: Marcel Dekker Inc.

    Google Scholar 

  • Chaudhuri, A., & Stenger, H. (2005). Survey sampling: Theory and methods. Boca Raton, FL: Chapman & Hall/CRC.

    Book  Google Scholar 

  • Cobo, B., Rueda, M., & Arcos, A. (2015). RRTCS: Randomized response techniques for complex surveys. R package version 0.0.2. http://CRAN.R-project.org/package=RRTCS.

  • Cochran, W. G. (1977). Sampling techniques. New York: Wiley.

    Google Scholar 

  • Dietz, P., Striegel, H., Franke, A. G., Lieb, K., Simon, P., & Ulrich, R. (2013). Randomized response estimates for the 12-month prevalence of cognitive-enhancing drug use in university students. Pharmacotherapy, 33, 44–50.

    Article  Google Scholar 

  • Duncan, B., & Duncan, O. D. (1955). A methodological analysis of segregation indexes. American Sociological Review, 20, 210–217.

    Article  Google Scholar 

  • Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. New York: Chapman & Hall.

    Book  Google Scholar 

  • Fondazione Ismu. (2014). Diciannovesimo rapporto sulle migrazioni 2013. Milano: Franco Angeli.

    Google Scholar 

  • Fox, J. A., & Tracy, P. E. (1986). Randomized response: A method for sensitive survey. Newbury Park: Sage Publication Inc.

    Book  Google Scholar 

  • Greenberg, B. G., Abul-Ela, A. L. A., Simmons, W. R., & Horvitz, D. G. (1969). The unrelated question randomized response model: Theoretical framework. Journal of the American Statistical Association, 64, 520–539.

    Article  Google Scholar 

  • Heck, D.W., & Moshagen M. (2014). Correlation and regression analyses for randomized response data (Version 0.2.0). http://psycho3.uni-mannheim.de/Home/Research/Software/RRreg/.

  • Hedayat, A. S., & Sinha, B. K. (1991). Design and inference in finite population sampling. Toronto: Wiley.

    Google Scholar 

  • Holbrook, A. L., & Krosnick, J. A. (2010). Measuring voter turnout by using the randomized response technique: Evidence calling into question the method’s validity. Public Opinion Quarterly, 74, 328–343.

    Article  Google Scholar 

  • Istat. (2014a). Induced abortion, Year 2012. http://www.istat.it/en/archive/141810.

  • Istat. (2014b). Foreign resident population at January 1, 2014 by age and sex. Data from population registers. http://demo.istat.it/strasa2014/index.html.

  • Istat. (2014c). Foreign citizens. Resident population and demographic balance at December 31, 2014. Region Calabria. Data from population registers. http://demo.istat.it/str2014/index.html.

  • Istituto Superiore di Sanità. (2006). L’interruzione volontaria di gravidanza tra le donne straniere in Italia. In A. Spinelli, E. Forcella, S. Di Rollo, & M. E. Grandolfo (Eds.), Rapporti ISTISAN 06/17, Istituto Superiore di Sanità, Roma.

  • James, R. A., Nepusz, T., Naughton, D. P., & Petróczi, A. (2013). A potential inflating effect in estimation models: Cautionary evidence from comparing performance enhancing drug and herbal hormonal supplement use estimates. Psychology of Sports and Exercise, 14, 84–96.

    Article  Google Scholar 

  • Jann, B., Jerke, J., & Krumpal, I. (2012). Asking sensitive questions using the crosswise model: An experimental survey measuring plagiarism. Public Opinion Quarterly, 76, 32–49.

    Article  Google Scholar 

  • Korndörfer, M., Krumpal, I., & Schmukle, S. C. (2014). Measuring and explain tax evasion: Improving self-reports using the crosswise model. Journal of Economic Psychology, 45, 18–32.

    Article  Google Scholar 

  • Krumpal, I. (2012). Estimating the prevalence of xenophobia and anti-semitism in Germany: A comparison of the randomized response technique and direct questioning. Social Science Research, 41, 1387–1403.

    Article  Google Scholar 

  • Lara, D., García, S. G., Ellertson, C., Camlin, C., & Suaréz, J. (2006). The measure of induced abortion in Mexico using random response technique. Sociological Methods & Research, 35, 279–301.

    Article  Google Scholar 

  • Lara, D., Strickler, J., Olavarrieta, C. D., García, S. G., & Ellertson, C. (2004). Measuring induced abortion in Mexico: A comparison of four methodologies. Sociological Methods & Research, 32, 529–558.

    Article  Google Scholar 

  • Lee, C.-S., Sedory, S. A., & Singh, S. (2013). Estimating at least seven measures of qualitative variables from a single sample using randomized response technique. Statistics and Probability Letters, 83, 399–409.

    Article  Google Scholar 

  • Lensvelt-Mulders, G. J. L. M., van der Heijden, P. G. M., Laudy, O., & van Gils, G. (2006). A validation of a computer-assisted randomized response survey to estimate the prevalence of fraud in social security. Journal of the Royal Statistical Society A, 169, 305–318.

    Article  Google Scholar 

  • Lensvelt-Mulders, G. J. L. M., Hox, J. J., van der Heijden, P. G. M., & Mass, C. J. M. (2005). Meta-analysis of randomized response research: Thirty-five years of validation. Sociological Methods & Research, 33, 319–348.

    Article  Google Scholar 

  • Ministero della Salute. (2014). Relazione del Ministro della Salute sulla attuazione della legge contenente norme per la tutela sociale della maternità e per l’interruzione volontaria di gravidanza (Legge 194/78)—Dati preliminari 2013 e dati definitivi 2012. Roma, 15 Ottobre 2014.

  • Oliveras, E., & Letamo, G. (2010). Examples of methods to address underreporting of induced abortion: Preceding birth technique and randomized response technique. In S. Singh, L. Remez, & A. Tartaglione (Eds.), Methodologies for estimating abortion incidence and abortion-related morbidity: A review. New York City: Guttmacher Institute; and Paris: International Union for the Scientific Study of the Population.

  • Ostapczuk, M., Musch, J., & Mashagen, M. (2009). A randomized-response investigation of the education effect in attitudes towards foreigners. European Journal of Social Psychology, 39, 920–931.

    Article  Google Scholar 

  • Simon, P., Striegel, H., Aust, F., Dietz, K., & Ulrich, R. (2006). Doping in fitness sports: Estimated number of unreported cases and individual probability of doping. Addiction, 101, 1640–1644.

    Article  Google Scholar 

  • Singh, S. (2003). Advanced sampling theory with applications (Vol. 2). Dordrecht: Kluwer Academic Publishers.

    Book  Google Scholar 

  • Singh, R., & Mangat, N. S. (1996). Elements of survey sampling. Dordrecht: Kluwer Academic Publishers.

    Book  Google Scholar 

  • Stranges, M. (2008). Foreign women in Italy turning to voluntary interruption of pregnancy (VPI): Extent and characteristics. International Journal of Migration and Transcultural Medicine, 2, 392–406.

    Google Scholar 

  • Striegel, H., Ulrich, R., & Simon, P. (2010). Randomized response estimates for doping and illicit drug use in elite athletes. Drug and Alcohol Dependence, 106, 230–232.

    Article  Google Scholar 

  • Stubbe, J. H., Chorus, A. M. J., Frank, L. E., de Hon, O., & van der Heijden, P. G. M. (2013). Prevalence of use of performance enhancing drugs by fitness center members. Drug Testing and Analysis, 6, 434–438.

    Google Scholar 

  • van der Heijden, P. G. M., van Gils, G., Bouts, J., & Hox, J. J. (2000). A comparison of randomized response, computer-assisted self-interview, and face-to-face direct questioning. Sociological Methods & Research, 28, 505–537.

    Article  Google Scholar 

  • Warner, S. L. (1965). Randomized response: A survey technique for eliminating evasive answer bias. Journal of the American Statistical Association, 60, 63–69.

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the three anonymous reviewers for their valuable comments and suggestions which have truly improved the early version of the paper. The work of Perri P.F. has been supported by the Italian project PRIN-2012F42NS8 “Household wealth and youth unemployment: new survey methods to meet current challenges”.

Author information

Authors and Affiliations

  1. Department of Economics, Statistics and Finance, University of Calabria, Via P. Bucci, 87036, Arcavacata di Rende, Italy

    Pier Francesco Perri, Elvira Pelle & Manuela Stranges

Authors
  1. Pier Francesco Perri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elvira Pelle
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Manuela Stranges
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pier Francesco Perri.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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). https://doi.org/10.1007/s11205-015-1136-x

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11205-015-1136-x

Keywords

Mathematics Subject Classification

Search

Navigation