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The Efficiency of Split Panel Designs in an Analysis of Variance Model

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  • Xin Liu
  • Wei-Guo Wang
  • Hai-Jun Liu

Abstract

We consider split panel design efficiency in analysis of variance models, that is, the determination of the cross-sections series optimal proportion in all samples, to minimize parametric best linear unbiased estimators of linear combination variances. An orthogonal matrix is constructed to obtain manageable expression of variances. On this basis, we derive a theorem for analyzing split panel design efficiency irrespective of interest and budget parameters. Additionally, relative estimator efficiency based on the split panel to an estimator based on a pure panel or a pure cross-section is present. The analysis shows that the gains from split panel can be quite substantial. We further consider the efficiency of split panel design, given a budget, and transform it to a constrained nonlinear integer programming. Specifically, an efficient algorithm is designed to solve the constrained nonlinear integer programming. Moreover, we combine one at time designs and factorial designs to illustrate the algorithm’s efficiency with an empirical example concerning monthly consumer expenditure on food in 1985, in the Netherlands, and the efficient ranges of the algorithm parameters are given to ensure a good solution.

Suggested Citation

  • Xin Liu & Wei-Guo Wang & Hai-Jun Liu, 2016. "The Efficiency of Split Panel Designs in an Analysis of Variance Model," PLOS ONE, Public Library of Science, vol. 11(5), pages 1-20, May.
    • Handle: RePEc:plo:pone00:0154913
    DOI: 10.1371/journal.pone.0154913
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    1. repec:hal:wpspec:info:hdl:2441/f6h8764enu2lskk9p2m9mgp8l is not listed on IDEAS
    2. Geert Dhaene & Koen Jochmans, 2015. "Split-panel Jackknife Estimation of Fixed-effect Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(3), pages 991-1030.
    3. Alinne Veiga & Peter W. F. Smith & James J. Brown, 2014. "The use of sample weights in multivariate multilevel models with an application to income data collected by using a rotating panel survey," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(1), pages 65-84, January.
    4. repec:hal:spmain:info:hdl:2441/f6h8764enu2lskk9p2m9mgp8l is not listed on IDEAS
    5. Nijman, Theo & Verbeek, Marno & van Soest, Arthur, 1991. "The efficiency of rotating-panel designs in an analysis-of-variance model," Journal of Econometrics, Elsevier, vol. 49(3), pages 373-399, September.
    6. Nijman, T.E., 1990. "Estimation of time dependent parameters in linear models using cross sections, panels or both," Other publications TiSEM 3efbf7de-1ca7-4f9f-b515-3, Tilburg University, School of Economics and Management.
    7. Nijman, T.E. & Verbeek, M.J.C.M., 1990. "Estimation of time-dependent parameters in linear models using cross-sections, panels, or both," Other publications TiSEM 1b042f06-e9e2-4712-8460-c, Tilburg University, School of Economics and Management.
    8. Nijman, Theo & Verbeek, Marno, 1990. "Estimation of time-dependent parameters in linear models using cross-sections, panels, or both," Journal of Econometrics, Elsevier, vol. 46(3), pages 333-346, December.
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