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Simulation‐based diagnostics in random‐coefficient models

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  • Nicholas T. Longford

Abstract

Commonly applied diagnostic procedures in random‐coefficient (multilevel) analysis are based on an inspection of the residuals, motivated by established procedures for ordinary regression. The deficiencies of such procedures are discussed and an alternative based on simulation from the fitted model (parametric bootstrap) is proposed. Although computationally intensive, the method proposed requires little programming effort additional to implementing the model fitting procedure. It can be tailored for specific kinds of outliers. Some computationally less demanding alternatives are described.

Suggested Citation

  • Nicholas T. Longford, 2001. "Simulation‐based diagnostics in random‐coefficient models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(2), pages 259-273.
    • Handle: RePEc:bla:jorssa:v:164:y:2001:i:2:p:259-273
    DOI: 10.1111/1467-985X.00201
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    Cited by:

    1. Schützenmeister, André & Piepho, Hans-Peter, 2012. "Residual analysis of linear mixed models using a simulation approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1405-1416.
    2. Anders Skrondal & Sophia Rabe‐Hesketh, 2009. "Prediction in multilevel generalized linear models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(3), pages 659-687, June.
    3. Jay Verkuilen & Michael Smithson, 2012. "Mixed and Mixture Regression Models for Continuous Bounded Responses Using the Beta Distribution," Journal of Educational and Behavioral Statistics, , vol. 37(1), pages 82-113, February.
    4. E. Andres Houseman & Louise Ryan & Brent Coull, 2004. "Cholesky Residuals for Assessing Normal Errors in a Linear Model with Correlated Outcomes: Technical Report," Harvard University Biostatistics Working Paper Series 1019, Berkeley Electronic Press.
    5. McQuestion, Michael J. & Velasquez, Anibal, 2006. "Evaluating program effects on institutional delivery in Peru," Health Policy, Elsevier, vol. 77(2), pages 221-232, July.
    6. Eberly, Lynn E. & Thackeray, Lisa M., 2005. "On Lange and Ryan's plotting technique for diagnosing non-normality of random effects," Statistics & Probability Letters, Elsevier, vol. 75(2), pages 77-85, November.
    7. David I. Ohlssen & Linda D. Sharples & David J. Spiegelhalter, 2007. "A hierarchical modelling framework for identifying unusual performance in health care providers," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(4), pages 865-890, October.

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