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Recursive residuals for linear mixed models

Author

Listed:
  • Ahmed Bani-Mustafa

    (Australian College of Kuwait)

  • K. M. Matawie

    (Western Sydney University)

  • C. F. Finch

    (Edith Cowan University)

  • Amjad Al-Nasser

    (Yarmouk University)

  • Enrico Ciavolino

    (University of Salento)

Abstract

This paper presents and extends the concept of recursive residuals and their estimation to an important class of statistical models, Linear Mixed Models (LMM). Recurrence formulae are developed and recursive residuals are defined. Recursive computable expressions are also developed for the model’s likelihood, together with its derivative and information matrix. The theoretical framework for developing recursive residuals and their estimation for LMM varies with the estimation method used, such as the fitting-of-constants or the Best Linear Unbiased Predictor method. These methods are illustrated through application to an LMM example drawn from a published study. Model fit is assessed through a graphical display of the developed recursive residuals and their Cumulative Sums.

Suggested Citation

  • Ahmed Bani-Mustafa & K. M. Matawie & C. F. Finch & Amjad Al-Nasser & Enrico Ciavolino, 2019. "Recursive residuals for linear mixed models," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(3), pages 1263-1274, May.
    • Handle: RePEc:spr:qualqt:v:53:y:2019:i:3:d:10.1007_s11135-018-0814-6
    DOI: 10.1007/s11135-018-0814-6
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    References listed on IDEAS

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    4. Sadeq Damrah & Mohammad I. Elian & Mohamad Atyeh & Fekri Ali Shawtari & Ahmed Bani-Mustafa, 2023. "A Linear Mixed Model Approach for Determining the Effect of Financial Inclusion on Bank Stability: Comparative Empirical Evidence for Islamic and Conventional Banks in Kuwait," Mathematics, MDPI, vol. 11(7), pages 1-17, April.

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