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Multistage Sampling Designs and Estimating Equations

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  • Alice S. Whittemore

Abstract

In some applications it is cost efficient to sample data in two or more stages. In the first stage a simple random sample is drawn and then stratified according to some easily measured attribute. In each subsequent stage a random subset of previously selected units is sampled for more detailed and costly observation, with a unit’s sampling probability determined by its attributes as observed in the previous stages. This paper describes multistage sampling designs and estimating equations based on the resulting data. Maximum likelihood estimates (MLEs) and their asymptotic variances are given for designs using parametric models. Horvitz–Thompson estimates are introduced as alternatives to MLEs, their asymptotic distributions are derived and their strengths and weaknesses are evaluated. The designs and the estimates are illustrated with data on corn production.

Suggested Citation

  • Alice S. Whittemore, 1997. "Multistage Sampling Designs and Estimating Equations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(3), pages 589-602.
    • Handle: RePEc:bla:jorssb:v:59:y:1997:i:3:p:589-602
    DOI: 10.1111/1467-9868.00084
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    Cited by:

    1. Michelle Ross & Jon Wakefield, 2013. "Bayesian Inference for Two-Phase Studies with Categorical Covariates," Biometrics, The International Biometric Society, vol. 69(2), pages 469-477, June.
    2. Qingning Zhou & Jianwen Cai & Haibo Zhou, 2018. "Outcome†dependent sampling with interval†censored failure time data," Biometrics, The International Biometric Society, vol. 74(1), pages 58-67, March.
    3. Qingning Zhou & Jianwen Cai & Haibo Zhou, 2020. "Semiparametric inference for a two-stage outcome-dependent sampling design with interval-censored failure time data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 85-108, January.
    4. Brady Ryan & Ananthika Nirmalkanna & Candemir Cigsar & Yildiz E. Yilmaz, 2023. "Evaluation of Designs and Estimation Methods Under Response-Dependent Two-Phase Sampling for Genetic Association Studies," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(2), pages 510-539, July.
    5. J. F. Lawless, 2018. "Two-phase outcome-dependent studies for failure times and testing for effects of expensive covariates," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 28-44, January.
    6. Jon Wakefield, 2004. "Ecological inference for 2 × 2 tables (with discussion)," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 167(3), pages 385-445, July.

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