We propose a novel framework for fitting additive quantile regression models, which provides well calibrated inference about the conditional quantiles and fast automatic estimation of the smoothing parameters, for model structures as diverse as those usable with distributional GAMs, while maintaining equivalent numerical efficiency and stability. The proposed methods are at once statistically rigorous and computationally efficient, because they are based on the general belief updating framework of Bissiri et al. (2016) to loss based inference, but compute by adapting the stable fitting methods of Wood et al. (2016). We show how the pinball loss is statistically suboptimal relative to a novel smooth generalisation, which also gives access to fast estimation methods. Further, we provide a novel calibration method for efficiently selecting the 'learning rate' balancing the loss with the smoothing priors during inference, thereby obtaining reliable quantile uncertainty estimates. Our work was motivated by a probabilistic electricity load forecasting application, used here to demonstrate the proposed approach. The methods described here are implemented by the qgam R package, available on the Comprehensive R Archive Network (CRAN).

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In the last two decades the growth of computational resources has made it possible to handle Generalized Additive Models (GAMs) that formerly were too costly for serious applications. However, the growth in model complexity has not been matched by improved visualisations for model development and results presentation. Motivated by an industrial application in electricity load forecasting, we identify the areas where the lack of modern visualisation tools for GAMs is particularly severe, and we address the shortcomings of existing methods by proposing a set of visual tools that a) are fast enough for interactive use, b) exploit the additive structure of GAMs, c) scale to large data sets and d) can be used in conjunction with a wide range of response distributions. The new visual methods proposed here are implemented by the mgcViz R package, available on the Comprehensive R Archive Network 1 .

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Generalized additive models (GAMs) are flexible non-linear regression models, which can be fitted efficiently using the approximate Bayesian methods provided by the mgcv R package. While the GAM methods provided by mgcv are based on the assumption that the response distribution is modeled parametrically, here we discuss more flexible methods that do not entail any parametric assumption. In particular, this article introduces the qgam package, which is an extension of mgcv providing fast calibrated Bayesian methods for fitting quantile GAMs (QGAMs) in R. QGAMs are based on a smooth version of the pinball loss of Koenker (2005), rather than on a likelihood function, hence jointly achieving satisfactory accuracy of the quantile point estimates and coverage of the corresponding credible intervals requires adopting the specialized Bayesian fitting framework of Fasiolo, Wood, Zaffran, Nedellec, and Goude (2021b). Here we detail how this framework is implemented in qgam and we provide examples illustrating how the package should be used in practice.

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BackgroundWhile current research priorities include investigations of age-related hearing loss, there are concerns regarding effects on childhood hearing, for example through increased personal headphone use. By utilising historical data, it is possible to assess what factors may have increased hearing problems in children in the past, and this may be used to inform current public health policies to protect children against hearing loss and in turn reduce the long-term burden on individuals and services that may possible evolve. The aim of this study was to investigate which factors in early life significantly impacted on hearing level in childhood using existing data from the Newcastle Thousand Families Study, a 1947 birth cohort.MethodsData on early life factors, including growth, socio-economic status and illness, and hearing at age 14 years were collated for a representative subset of individuals from the cohort (n = 147). Factors were assessed using linear regression analysis to identify associations with hearing thresholds.ResultsMales were found to have lower hearing thresholds at 250 Hz, 500 Hz and 1 kHz. Main analyses showed no associations between hearing thresholds and early life growth or socio-economic indicators. An increasing number of ear infections from birth to age 13 years was associated with hearing thresholds at 250Hz (p = 0.04) and 500Hz (p = 0.03), which remained true for females (p = 0.050), but not males (p = 0.213) in sex-specific analysis. Scarlet fever and bronchitis were associated with hearing thresholds at 8 kHz. After adjustment for all significant predictors at each frequency, results remained unchanged.ConclusionsWe found no associations between childhood hearing thresholds and early life growth and socio-economic status. Consistent with other studies, we found associations between childhood infections and hearing thresholds. Current public health strategies aimed at reducing childhood infections may also have a beneficial effect upon childhood hearing.