Document Type

Journal Article


Springer Netherlands


School of Medical and Health Sciences


This is a post-peer-review, pre-copyedit version of an article published in: Bani-Mustafa, A., Matawie, K. M., Finch, C. F., Al-Nasser, A., & Ciavolino, E. (2019). Recursive residuals for linear mixed models. Quality & Quantity, 53(3), 1263–1274. The final authenticated version is available here


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.



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