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A Varying Coefficients Model For Estimating Finite Population Totals: A Hierarchical Bayesian Approach

Author

Listed:
  • Ciro Velasco-Cruz

    (Colegio de Postgraduados)

  • Luis Fernando Contreras-Cruz

    (Universidad Autónoma Chapingo)

  • Eric P. Smith

    (Virginia Tech)

  • José E. Rodríguez

    (Universidad de Guanajuato)

Abstract

In some finite sampling situations, there is a primary variable that is sampled, and there are measurements on covariates for the entire population. A Bayesian hierarchical model for estimating totals for finite populations is proposed. A nonparametric linear model is assumed to explain the relationship between the dependent variable of interest and covariates. The regression coefficients in the linear model are allowed to vary as a function of a subset of covariates nonparametrically based on B-splines. The generality of this approach makes it robust and applicable to data collected using a variety of sampling techniques, provided the sample is representative of the finite population. A simulation study is carried out to evaluate the performance of the proposed model for the estimation of the population total. Results indicate accurate estimation of population totals using the approach. The modeling approach is used to estimate the total production of avocado for a large group of groves in Mexico.

Suggested Citation

  • Ciro Velasco-Cruz & Luis Fernando Contreras-Cruz & Eric P. Smith & José E. Rodríguez, 2016. "A Varying Coefficients Model For Estimating Finite Population Totals: A Hierarchical Bayesian Approach," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 548-568, September.
    • Handle: RePEc:spr:jagbes:v:21:y:2016:i:3:d:10.1007_s13253-016-0250-9
    DOI: 10.1007/s13253-016-0250-9
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    References listed on IDEAS

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    1. Hogan J.W. & Tchernis R., 2004. "Bayesian Factor Analysis for Spatially Correlated Data, With Application to Summarizing Area-Level Material Deprivation From Census Data," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 314-324, January.
    2. Little R.J., 2004. "To Model or Not To Model? Competing Modes of Inference for Finite Population Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 546-556, January.
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