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Estimation of regression models with nested error structure and unequal error variances under two and three stage cluster sampling

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  • Stukel, D. M.
  • Rao, J. N. K.

Abstract

A simple transformation method, proposed by Fuller and Battese (1973), for making inferences from one and two-fold nested error regression models with equal error variances under two and three-stage cluster sampling is extended here to the more realistic case of unequal error variances. The method permits the calculation of variance component estimates and making inferences on regression parameters, using only ordinary least squares on the transformed data. Normality of the random errors in the model is not assumed. The transformation method of estimating variance components may be regarded as an alternative technique for implementing the well-known Henderson's Method of Fitting Constants, but it remains numerically stable in situations where the Henderson method involves fitting a large number of parameters.

Suggested Citation

  • Stukel, D. M. & Rao, J. N. K., 1997. "Estimation of regression models with nested error structure and unequal error variances under two and three stage cluster sampling," Statistics & Probability Letters, Elsevier, vol. 35(4), pages 401-407, November.
    • Handle: RePEc:eee:stapro:v:35:y:1997:i:4:p:401-407
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    Cited by:

    1. A. F. Militino & M. D. Ugarte & T. Goicoa, 2007. "A BLUP Synthetic Versus an EBLUP Estimator: An Empirical Study of a Small Area Estimation Problem," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(2), pages 153-165.
    2. Lu Chen & Balgobin Nandram, 2023. "Bayesian Logistic Regression Model for Sub-Areas," Stats, MDPI, vol. 6(1), pages 1-23, January.
    3. Yolanda Marhuenda & Isabel Molina & Domingo Morales & J. N. K. Rao, 2017. "Poverty mapping in small areas under a twofold nested error regression model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1111-1136, October.

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