Recursive residuals for linear mixed models

Ahmed Bani‑Mustafa, K. M. Matawie, C. F. Finch, Amjad Al‑Nasser, Enrico Ciavolino

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)1263-1274
Number of pages12
JournalQuality and Quantity
Volume53
Issue number3
DOIs
Publication statusPublished - 2019

Keywords

  • linear models (statistics)
  • recursive functions

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