Multivariate Statistical Modelling Based on Generalized Linear Models

Abstract: We present a general statistical modelling framework for handling multivariate mixed types of outcomes in the context of quantitative genetic analysis. The models are based on the multivariate covariance generalized linear models, where the matrix linear predictor is composed of an identity matrix combined with a relatedness matrix defined by a pedigree, representing the environmental and genetic components, respectively. We also propose a new index of heritability for non-Gaussian data. A case study on house sparrow (Passer domesticus) population with continuous, binomial and count outcomes is employed to motivate the new model. Simulation of multivariate marginal models is not trivial, thus we adapt the NORTA (Normal to anything) algorithm for simulation of multivariate covariance generalized linear models in the context of genetic data analysis. A simulation study is presented to assess the asymptotic properties of the estimating function estimators for the correlation between outcomes and the new heritability index parameters. The data set and R code are available in the supplementary material.

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John Ashworth Nelder. 8 October 1924—7 August 2010

Biographical Memoirs of Fellows of the Royal Society ◽

10.1098/rsbm.2019.0013 ◽

2019 ◽

Vol 67 ◽

pp. 307-326

Author(s):

Stephen Senn

Keyword(s):

Generalized Linear Models ◽

Linear Models ◽

Statistical Modelling ◽

Simplex Algorithm ◽

Function Optimization ◽

Research Station ◽

Wide Range ◽

Rothamsted Experimental Station ◽

Musical Interests ◽

General Balance

John Nelder was a statistician who made important contributions to applied statistical theory, of which three are notable: his work on general balance; his influential collaboration with Robert Wedderburn and later Peter McCullagh on the development of generalized linear models (GLMs); and his post-retirement collaboration with Youngjo Lee on hierarchical generalized linear models (HGLMs). John started his career at the National Vegetable Research Station in Wellesbourne in 1950, and was subsequently head of statistics at Rothamsted Experimental Station, Harpenden, from 1968 to his retirement in 1984, during which time he regularly gave a course of lectures on statistical computing at Imperial College London. He wrote several highly influential books and received many honours, including the Guy Medals in Silver and in Gold of the Royal Statistical Society (in 1977 and 2005) and an honorary doctorate from the Université Paul Sabatier, Toulouse, in 1981. His work on GLMs completely changed the world of statistical modelling, his theory of general balance was years ahead of its time and it is perhaps too early to judge his work on HGLMs. The simplex algorithm for function optimization developed with Roger Mead has proved extremely popular. John was an excellent pianist with a wide range of musical interests.

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From Generalized Linear Models to Neural Networks, and Back

SSRN Electronic Journal ◽

10.2139/ssrn.3491790 ◽

2019 ◽

Cited By ~ 5

Author(s):

Mario V. Wuthrich

Keyword(s):

Neural Networks ◽

Generalized Linear Models ◽

Linear Models

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Effect of Different Dentifrices, Bleaching with 35% Hydrogen Peroxide, and Red Wine on Surface Color and Roughness of Bovine Enamel

Current Dentistry ◽

10.2174/2542579x02999200817112951 ◽

2020 ◽

Vol 02 ◽

Author(s):

RM Garcia ◽

WF Vieira-Junior ◽

JD Theobaldo ◽

NIP Pini ◽

GM Ambrosano ◽

...

Keyword(s):

Hydrogen Peroxide ◽

Generalized Linear Models ◽

Repeated Measures ◽

Red Wine ◽

Linear Models ◽

Artificial Saliva ◽

Surface Color ◽

Dental Bleaching ◽

Surface Alteration ◽

Bovine Enamel

Objective: To evaluate color and roughness of bovine enamel exposed to dentifrices, dental bleaching with 35% hydrogen peroxide (HP), and erosion/staining by red wine. Methods: Bovine enamel blocks were exposed to: artificial saliva (control), Oral-B Pro-Health (stannous fluoride with sodium fluoride, SF), Sensodyne Repair & Protect (bioactive glass, BG), Colgate Pro-Relief (arginine and calcium carbonate, AR), or Chitodent (chitosan, CHI). After toothpaste exposure, half (n=12) of the samples were bleached (35% HP), and the other half were not (n=12). The color (CIE L*a* b*, ΔE), surface roughness (Ra), and scanning electron microscopy were evaluated. Color and roughness were assessed at baseline, post-dentifrice and/or -dental bleaching, and after red wine. The data were subjected to analysis of variance (ANOVA) (ΔE) for repeated measures (Ra), followed by Tukey ́s test. The L*, a*, and b* values were analyzed by generalized linear models (a=0.05). Results: The HP promoted an increase in Ra values; however, the SF, BG, and AR did not enable this alteration. After red wine, all groups apart from SF (unbleached) showed increases in Ra values; SF and AR promoted decreases in L* values; AR demonstrated higher ΔE values, differing from the control; and CHI decreased the L* variation in the unbleached group. Conclusion: Dentifrices did not interfere with bleaching efficacy of 35% HP. However, dentifrices acted as a preventive agent against surface alteration from dental bleaching (BG, SF, and AR) or red wine (SF). Dentifrices can decrease (CHI) or increase (AR and SF) staining by red wine.

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