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Modeling Response Bias in Count: A Structural Approach With an Application to the National Crime Victimization Survey Data

Author

Listed:
  • Tong Li
  • Pravin K. Trivedi

    (Indiana University, Bloomington)

  • Jiequn Guo

    (Fannie Mae)

Abstract

This article considers modeling response bias when the response is a count. The authors adopt a “structural approach†by using a generalized negative binomial mixture of Poisson distribution to model misreported counts, assuming that the distribution of the true response follows a negative binomial distribution. The model may be interpreted as a “stopped-sum†model. A simulated maximum likelihood estimator is proposed, and its finite sample performance is investigated through Monte Carlo simulations. The approach is then applied to analyzing school victimization data drawn from the National Crime Victimization Survey, which allows the authors to identify the individual- and school-related characteristics that could contribute to school crime victimization and to the possible biases on the reported number of repeat victimizations. The authors find that for the reported number of thefts, about 12 percent of respondents overreport the numbers, most of whom actually have not had any item stolen at school.

Suggested Citation

  • Tong Li & Pravin K. Trivedi & Jiequn Guo, 2003. "Modeling Response Bias in Count: A Structural Approach With an Application to the National Crime Victimization Survey Data," Sociological Methods & Research, , vol. 31(4), pages 514-544, May.
    • Handle: RePEc:sae:somere:v:31:y:2003:i:4:p:514-544
    DOI: 10.1177/0049124103251951
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    References listed on IDEAS

    as
    1. Hanke, Penelope J., 1996. "Putting school crime into perspective: Self-reported school victimizations of high school seniors," Journal of Criminal Justice, Elsevier, vol. 24(3), pages 207-226.
    2. Lab, Steven P. & Allen, Roy B., 1984. "Self-report and official measures: A further examination of the validity issue," Journal of Criminal Justice, Elsevier, vol. 12(5), pages 445-455.
    3. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    4. A. S. Whittemore & G. Gong, 1991. "Poisson Regression with Misclassified Counts: Application to Cervical Cancer Mortality Rates," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 40(1), pages 81-93, March.
    5. Hausman, J. A. & Abrevaya, Jason & Scott-Morton, F. M., 1998. "Misclassification of the dependent variable in a discrete-response setting," Journal of Econometrics, Elsevier, vol. 87(2), pages 239-269, September.
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    Cited by:

    1. Yingyao Hu & Zhongjian Lin, 2018. "Misclassification and the hidden silent rivalry," CeMMAP working papers CWP12/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Hossein Kavand & Marcel Voia, 2018. "Estimation of Health Care Demand and its Implication on Income Effects of Individuals," Springer Proceedings in Business and Economics, in: William H. Greene & Lynda Khalaf & Paul Makdissi & Robin C. Sickles & Michael Veall & Marcel-Cristia (ed.), Productivity and Inequality, pages 275-304, Springer.
    3. Lin, Zhongjian & Hu, Yingyao, 2024. "Binary choice with misclassification and social interactions, with an application to peer effects in attitude," Journal of Econometrics, Elsevier, vol. 238(1).
    4. Schennach, Susanne M., 2020. "Mismeasured and unobserved variables," Handbook of Econometrics, in: Steven N. Durlauf & Lars Peter Hansen & James J. Heckman & Rosa L. Matzkin (ed.), Handbook of Econometrics, edition 1, volume 7, chapter 0, pages 487-565, Elsevier.
    5. Paul Sullivan, 2009. "Estimation of an Occupational Choice Model when Occupations are Misclassified," Journal of Human Resources, University of Wisconsin Press, vol. 44(2).
    6. A. Colin Cameron & Tong Li & Pravin K. Trivedi & David M. Zimmer, 2004. "Modelling the differences in counted outcomes using bivariate copula models with application to mismeasured counts," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 566-584, December.
    7. Wing-Keung Wong & Guorui Bian, 2005. "Robust Estimation of Multiple Regression Model with Non-normal Error: Symmetric Distribution," Monash Economics Working Papers 09/05, Monash University, Department of Economics.
    8. Li, Tong & Hsiao, Cheng, 2004. "Robust estimation of generalized linear models with measurement errors," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 51-65.
    9. A. Colin Cameron & Tong Li & Pravin K. Trivedi & David M. Zimmer, 2004. "Modelling the differences in counted outcomes using bivariate copula models with application to mismeasured counts," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 566-584, December.
    10. Silvia Polettini & Serena Arima & Sara Martino, 2024. "An Investigation of Models for Under-Reporting in the Analysis of Violence Against Women in Italy," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 175(3), pages 1007-1026, December.

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