A History of the GLIM Statistical Package

Aitkin, Murray

doi:10.1111/insr.12251

Cited by 3 publications

(3 citation statements)

References 18 publications

(13 reference statements)

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“…The ‘normal model’, a normal distribution regression model, prevailed as an analysis framework until ‘Theoretical and applied statistics were both convulsed by the publication of the GLM paper by Nelder and Wedderburn (1972)’. (Aitkin, 2018). The relaxation of the restrictive requirements of the normal model progressed from the GLM, in which the response distribution was extended from the normal to the exponential family distribution and the link function was introduced; to GAMs (Hastie and Tibshirani, 1990), which added smooth functions of the covariates to the linear predictor for the mean; to mean and dispersion modelling, in which modelling of the dispersion parameter of the response distribution was introduced (Aitkin, 1987; Smyth, 1989); to Generalized Additive Models for Location, Scale and Shape (GAMLSS) (Rigby and Stasinopoulos, 2005) which arguably represents the biggest leap forward of the regression methodology.…”

Section: Gamlssmentioning

confidence: 99%

P-splines and GAMLSS: a powerful combination, with an application to zero-adjusted distributions

Stasinopoulos,

Rigby,

Heller

et al. 2023

Statistical Modelling

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P-splines are a versatile statistical modelling tool, dealing with nonlinear relationships between the response and explanatory variable(s). GAMLSS is a distributional regression framework which allows modelling of a response variable using any parametric distribution. The combination of the two methodologies provides one of the most powerful tools in modern regression analysis. This article discusses the application of the two techniques when the response variable is zero-adjusted (or semi-continuous), which combines a point probability at zero with a positive continuous distribution.

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Section: Gamlssmentioning

confidence: 99%

P-splines and GAMLSS: a powerful combination, with an application to zero-adjusted distributions

Stasinopoulos,

Rigby,

Heller

et al. 2023

Statistical Modelling

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“…Relaxation of the classical linear model assumptions started with the GLM: “Theoretical and applied statistics were both convulsed by the publication of the GLM paper by Nelder & Wedderburn (1972).” [ 4 ]. The revolutionary aspects of the GLM were the extension of the choice of response distribution to any member of the exponential family of distributions, which includes the normal, Poisson, binomial, Gamma, inverse Gaussian and Tweedie distributions; inclusion of a link function g (·) in the model specification for μ i : where g (·) is any monotonic differentiable function; and an algorithm for the computation of the maximum likelihood estimates which was computationally feasible within computing constraints at the time.…”

Section: Introductionmentioning

confidence: 99%

Distributional regression in clinical trials: treatment effects on parameters other than the mean

Heller

Robledo²,

Marschner³

2022

BMC Med Res Methodol

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Background The classical linear model is widely used in the analysis of clinical trials with continuous outcomes. However, required model assumptions are frequently not met, resulting in estimates of treatment effect that can be inefficient and biased. In addition, traditional models assess treatment effect only on the mean response, and not on other aspects of the response, such as the variance. Distributional regression modelling overcomes these limitations. The purpose of this paper is to demonstrate its usefulness for the analysis of clinical trials, and superior performance to that of traditional models. Methods Distributional regression models are demonstrated, and contrasted with normal linear models, on data from the LIPID randomized controlled trial, which compared the effects of pravastatin with placebo in patients with coronary heart disease. Systolic blood pressure (SBP) and the biomarker midregional pro-adrenomedullin (MR-proADM) were analysed. Treatment effect was estimated in models that used response distributions more appropriate than the normal (Box-Cox-t and Johnson’s Su for MR-proADM and SBP, respectively), applied censoring below the detection limit of MR-proADM, estimated treatment effect on distributional parameters other than the mean, and included random effects for longitudinal observations. A simulation study was conducted to compare the performance of distributional regression models with normal linear regression, under conditions mimicking the LIPID study. The R package gamlss (Generalized Additive Models for Location, Scale and Shape), which implements maximum likelihood estimation for distributional regression modelling, was used throughout. Results In all cases the distributional regression models fit the data well, in contrast to poor fits obtained for traditional models; for MR-proADM a small but significant treatment effect on the mean was detected by the distributional regression model and not the normal model; and for SBP a beneficial treatment effect on the variance was demonstrated. In the simulation study distributional models strongly outperformed normal models when the response variable was non-normal and heterogeneous; and there was no disadvantage introduced by the use of distributional regression modelling when the response satisfied the normal linear model assumptions. Conclusions Distributional regression models are a rich framework, largely untapped in the clinical trials world. We have demonstrated a sample of the capabilities of these models for the analysis of trials. If interest lies in accurate estimation of treatment effect on the mean, or other distributional features such as variance, the use of distributional regression modelling will yield superior estimates to traditional normal models, and is strongly recommended. Trial registration The LIPID trial was retrospectively registered on ANZCTR on 27/04/2016, registration number ACTRN12616000535471.

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“…My attempt to develop GLIM into a more powerful modelling package was opposed by the RSS Council, and was abandoned, though Brian Francis later implemented in GLIM4 some of the facilities I had proposed. [The history of GLIM is given in detail in Aitkin (2018).] I left Lancaster for a sabbatical year in 1986 and did not return.…”

mentioning

confidence: 99%

Reflections on statistical modelling: A conversation with Murray Aitkin

Aitkin

Hinde

Francis

2021

Statistical Modelling

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A History of the GLIM Statistical Package

Abstract: Summary This article documents the history of the GLIM statistical package, from Royal Statistical Society documents, GLIM Working Party documents and recollections of the developers of GLIM and its supporting papers, manuals and books.

Cited by 3 publications

References 18 publications

P-splines and GAMLSS: a powerful combination, with an application to zero-adjusted distributions

P-splines and GAMLSS: a powerful combination, with an application to zero-adjusted distributions

Distributional regression in clinical trials: treatment effects on parameters other than the mean

Reflections on statistical modelling: A conversation with Murray Aitkin

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