Recursive residuals in generalised linear models

McGilchrist, C. A.; Matawie, Kenan M

doi:10.1016/s0378-3758(97)00192-4

Cited by 3 publications

(7 citation statements)

References 40 publications

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“…Several types of residuals have been proposed for GLM models, with Pearson, deviance, and randomized quantile residuals being the most commonly used. McGilchrist et al 6 introduced the recursive residuals in the GLMs' framework. For count data, the most common choice is to use the Poisson, negative binomial distributions, and their variants like the zero-inflated Poisson and the Conway-Maxwell (COM) Poisson distribution.…”

Section: Introductionmentioning

confidence: 99%

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Gamma generalized linear model‐based control charts for high‐purity processes

Rizzo

Bucchianico

2023

Quality & Reliability Eng

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Statistical process monitoring of high‐purity manufacturing processes becomes challenging if the defect rate depends on the fluctuations of a set of covariates (e.g., inspected weight, volume, temperature). This paper applies the generalized linear model framework to statistical process control for detecting contextual anomalies in high‐purity processes. Different types of predictive residuals (i.e., Pearson, deviance, and quantile) and recursive residuals are considered, and the performance of these schemes is compared via a simulation study.

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Section: Introductionmentioning

confidence: 99%

“…Several types of residuals have been proposed for GLM models, with Pearson, deviance, and randomized quantile residuals being the most commonly used. McGilchrist et al 6 . introduced the recursive residuals in the GLMs' framework.…”

Section: Introductionmentioning

confidence: 99%

Gamma generalized linear model‐based control charts for high‐purity processes

Rizzo

Bucchianico

2023

Quality & Reliability Eng

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“…Tobing and McGilchrist (1992) derived formulae for recursive estimation of unknown parameters and the vector of recursive residuals for multivariate models. McGilchrist and Matawie (1998) introduced an extension of recursive residuals and estimation to Generalised Linear Models (GLM). Although, General and GLM diagnostic tools and the process of checking their components have been discussed using recursive residuals and estimates, these approaches have not yet been applied to model with both fixed and random effects.…”

Section: Introductionmentioning

confidence: 99%

“…The data are then entered progressively to estimate and update the already estimated parameters and to calculate the recursive residuals when they become available. This method of calculation has been used by various researchers including McGilchrist and colleagues, in developing recursive procedures for different models (McGilchrist et al 1983;McGilchrist and Matawie 1998;Lee and Nelder 1996;McGilchrist and Sandland 1979).…”

Section: Introductionmentioning

confidence: 99%

Recursive residuals for linear mixed models

et al. 2018

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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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“…They have frequently been suggested for testing model fit and model assumptions in linear regression [14][15][16][17][18]. Loynes [19] considered recursive residuals in non-linear models and McGilchrist and Matawie [20] introduced recursive residuals in generalized linear models. Magnus and Sinha [21] have a fresh look at recursive residuals and BLUS residuals in regression models.…”

Section: Introductionmentioning

confidence: 99%

Empirical process based on the recursive residuals in functional measurement error models

Rasekh¹

2006

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Recursive residuals are a linear transformation of ordinary residuals. They have frequently been suggested for testing model fit and model assumptions in linear regression. In this paper, we generalize the theory of the empirical process based on the residuals in the measurement error models to the recursive residuals in the measurement error models. We prove that recursive residuals in these models are asymptotically independent and identically distributed and show that, in this case, the weak convergence properties of the standardized residuals hold for the studentized recursive residuals. Furthermore, we look at some tests for goodness-of-fit based on the weak convergence of the empirical distribution of the recursive residuals. We justify the use of goodness-of-fit tests based on recursive residuals by carrying out a parametric bootstrap simulation study.

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Recursive residuals in generalised linear models

Abstract: Recursive estimation and recursive residuals are introduced for generalised linear models (GLIM). Their definitions parallel those of nonnal theory regression models and relate to one of the outlier model definitions of GLIM residuals. An example illustrates their use.

Cited by 3 publications

References 40 publications

Gamma generalized linear model‐based control charts for high‐purity processes

Gamma generalized linear model‐based control charts for high‐purity processes

Recursive residuals for linear mixed models

Empirical process based on the recursive residuals in functional measurement error models

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