Reflections on statistical modelling: A conversation with Murray Aitkin

Abstract

A virtual interview with Murray Aitkin by Brian Francis and John Hinde, two of the original members of the Centre for Applied Statistics that Murray created at Lancaster University. The talk ranges over Murray's reflections of a career in statistical modelling and the many different collaborations across the world that have been such a significant part of it.

Reproductive performance effects of rearing the quasi-social parasitoid,Sclerodermus brevicornis(Hymenoptera: Bethylidae), on a factitious host

“…We employed generalized linear models (GLMs) and generalized linear mixed models (GLMMs) to explore the effects of experimental treatments on parasitoid performance. GLMs were used for analyses of a single response per replicate ( Aitkin et al 1989 ), and GLMMs were used when analyses concerned multiple observations per replicate ( Bolker et al 2009 ). Log-linear analysis, with a log link function, was used for analyses of integer response variables ( Aitkin et al 1989 , Crawley 1993 ) and logistic analyses, with a logit link function, were used for most analyses of proportional response variables ( Crawley 1993 , Wilson and Hardy 2002 ).…”

“…GLMs were used for analyses of a single response per replicate ( Aitkin et al 1989 ), and GLMMs were used when analyses concerned multiple observations per replicate ( Bolker et al 2009 ). Log-linear analysis, with a log link function, was used for analyses of integer response variables ( Aitkin et al 1989 , Crawley 1993 ) and logistic analyses, with a logit link function, were used for most analyses of proportional response variables ( Crawley 1993 , Wilson and Hardy 2002 ). In log-linear analysis and logistic analyses of grouped binary data, quasi-Poisson and quasi-binomial distributions of residuals were adopted, using empirically estimated scale parameters, to take potential over- or underdispersion into account ( Crawley 1993 , Wilson and Hardy 2002 , Hardy and Smith 2023 ).…”

Supplementary Methods from Modeling Cytostatic and Cytotoxic Responses to New Treatment Regimens for Ovarian Cancer

“…In the reqrowing tumors the fittings converged to the same solution independently on the starting position. Typical uncertainty for the best fit estimates of the four parameters, evaluated by likelihood-based 95% confidence intervals (17), were: k: 0.003, Del: 0.15, DR: 0.015, pQ 0.005, well lower than the biological variation between replicated tumors. A variation of the model was adopted for the "cured" mice, where tumor size fell below the detection limit in 2-3 weeks and only scar tissue was detected at the necropsy at the end of the observation time (day 180).…”

Generalized linear models.

“…More advanced books include Fahrmeir and Tutz (2001) and Hardin and Hilbe (2018). Books covering GLM in whole or in part, but oriented toward a particular software package, include Aitkin et al (2009) for R; Chambers and Hastie (1992) for S; and Venables and Ripley (2002) for R and Splus. For details on the GLM as originally conceptualized, the original article introducing the topic is Nelder and Wedderburn (1972), and the current authoritative source is McCullagh and Nelder (1989).…”