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Estimating the Proportion of a Categorical Variable With Probit Regression

Author

Listed:
  • Sergio Martínez
  • Maria Rueda
  • Antonio Arcos
  • Helena Martínez

Abstract

This article discusses the estimation of a population proportion, using the auxiliary information available, which is incorporated into the estimation procedure by a probit model fit. Three probit regression estimators are considered, using model-based and model-assisted approaches. The theoretical properties of the proposed estimators are derived and discussed. Monte Carlo experiments were carried out for simulated data and for real data taken from a database of confirmed dengue cases in Mexico. The probit estimates give valuable results in comparison to alternative estimators. Finally, the proposed methodology is applied to data obtained from an immigration survey.

Suggested Citation

  • Sergio Martínez & Maria Rueda & Antonio Arcos & Helena Martínez, 2020. "Estimating the Proportion of a Categorical Variable With Probit Regression," Sociological Methods & Research, , vol. 49(3), pages 809-834, August.
    • Handle: RePEc:sae:somere:v:49:y:2020:i:3:p:809-834
    DOI: 10.1177/0049124118761771
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    References listed on IDEAS

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    1. Hausman, Jerry A & Wise, David A, 1978. "A Conditional Probit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Econometrica, Econometric Society, vol. 46(2), pages 403-426, March.
    2. Wu C. & Sitter R. R, 2001. "A Model-Calibration Approach to Using Complete Auxiliary Information From Survey Data," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 185-193, March.
    3. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
    4. Cramer,J. S., 2011. "Logit Models from Economics and Other Fields," Cambridge Books, Cambridge University Press, number 9780521188036, October.
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