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We consider an application in electricity grid load prediction, where generalized additive models are appropriate, but where the data set's size can make their use practically intractable with existing methods. We therefore develop practical generalized additive model fitting methods for large data sets in the case in which the smooth terms in the model are represented by using penalized regression splines. The methods use iterative update schemes to obtain factors of the model matrix while requiring only subblocks of the model matrix to be computed at any one time. We show that efficient smoothing parameter estimation can be carried out in a well-justified manner. The grid load prediction problem requires updates of the model fit, as new data become available, and some means for dealing with residual auto-correlation in grid load. Methods are provided for these problems and parallel implementation is covered. The methods allow estimation of generalized additive models for large data sets by using modest computer hardware, and the grid load prediction problem illustrates the utility of reduced rank spline smoothing methods for dealing with complex modelling problems.

Recent work by Reiss and Ogden provides a theoretical basis for sometimes preferring restricted maximum likelihood (REML) to generalized cross-validation (GCV) for smoothing parameter selection in semiparametric regression. However, existing REML or marginal likelihood (ML) based methods for semiparametric generalized linear models (GLMs) use iterative REML or ML estimation of the smoothing parameters of working linear approximations to the GLM. Such indirect schemes need not converge and fail to do so in a non-negligible proportion of practical analyses. By contrast, very reliable prediction error criteria smoothing parameter selection methods are available, based on direct optimization of GCV, or related criteria, for the GLM itself. Since such methods directly optimize properly defined functions of the smoothing parameters, they have much more reliable convergence properties. The paper develops the first such method for REML or ML estimation of smoothing parameters. A Laplace approximation is used to obtain an approximate REML or ML for any GLM, which is suitable for efficient direct optimization. This REML or ML criterion requires that Newton-Raphson iteration, rather than Fisher scoring, be used for GLM fitting, and a computationally stable approach to this is proposed. The REML or ML criterion itself is optimized by a Newton method, with the derivatives required obtained by a mixture of implicit differentiation and direct methods. The method will cope with numerical rank deficiency in the fitted model and in fact provides a slight improvement in numerical robustness on the earlier method of Wood for prediction error criteria based smoothness selection. Simulation results suggest that the new REML and ML methods offer some improvement in mean-square error performance relative to GCV or Akaike's information criterion in most cases, without the small number of severe undersmoothing failures to which Akaike's information criterion and GCV are prone. This is achieved at the same computational cost as GCV or Akaike's information criterion. The new approach also eliminates the convergence failures of previous REML- or ML-based approaches for penalized GLMs and usually has lower computational cost than these alternatives. Example applications are presented in adaptive smoothing, scalar on function regression and generalized additive model selection.

Air pollution is a serious challenge in South Korea and worldwide, and negatively impacts human health and mortality rates. To assess air quality and the spatiotemporal characteristics of atmospheric particulate matter (PM), PM concentrations were compared with meteorological conditions and the concentrations of other airborne pollutants over South Korea from 2015 to 2020, using different linear and non-linear models such as linear regression, generalized additive, and multivariable linear regression models. The results showed that meteorological conditions played a significant role in the formation, transportation, and deposition of air pollutants. PM2.5 levels peaked in January, while PM10 levels peaked in April. Both were at their lowest levels in July. Further, PM2.5 was the highest during winter, followed by spring, autumn, and summer, whereas PM10 was the highest in spring followed by winter, autumn, and summer. PM concentrations were negatively correlated with temperature, relative humidity, and precipitation. Wind speed had an inverse relationship with air quality; zonal and vertical wind components were positively and negatively correlated with PM, respectively. Furthermore, CO, black carbon, SO2, and SO4 had a positive relationship with PM. The impact of transboundary air pollution on PM concentration in South Korea was also elucidated using air mass trajectories.

Many studies have reported that exposure to air pollution increases the likelihood of acquiring allergic rhinitis (AR). This study investigated associations between short-term air pollution exposure and AR outpatient visits. The Department of Otorhinolaryngology, Affiliated Hospital of Hangzhou Normal University provided AR outpatient data from January 1, 2019 to December 31, 2021. Daily air quality information for that period was gathered from the Hangzhou Air Quality Inspection Station. We used the Poisson's generalized additive model (GAM) to investigate relationships between daily outpatient AR visits and air pollution, and investigated lag-exposure relationships across days. Subgroup analyses were performed by age (adult (>18 years) and non-adult (<18 years)) and sex (male and female). We recorded 20,653 instances of AR during the study period. Each 10 g/m increase in fine particulate matter (PM10 and PM2.5) and carbon monoxide (CO) concentrations was associated with significant increases in AR outpatient Visits. The relative risks (RR) were: 1.007 (95% confidence interval (CI): 1.001-1.013), 1.026 (95% CI: 1.008-1.413), and 1.019 (95% CI: 1.008-1.047). AR visits were more likely due to elevated PM2.5, PM10, and CO levels. Additionally, children were more affected than adults. To better understand the possible effects of air pollution on AR, short-term exposure to ambient air pollution (PM2.5, PM10, and CO) may be linked to increased daily outpatient AR visits.

The study aims to investigate the heterogeneity of the Yangtze River’s impact on housing prices, using the data of 12,325 residential transactions within 8 kilometers of the Yangtze River in Wuhan, based on submarkets divided according to geographical location and buyer groups. The kernel density plots reveal that properties near the Yangtze River have the highest price and the lowest density, while properties further away from the river exhibit the opposite trend. Then the Spatial Generalized Additive Model and the Spatial Quantile Generalized Additive Model show the following results, respectively: (1) The Yangtze River has an influence range of roughly 5 kilometers on adjacent dwellings, with an average impact of 0.035%. However, within the chosen geographical interval, the impact rises from 1.582% to 2.072%. (2) The Yangtze River has the greatest impact on middle-priced houses, followed by high-priced houses, and the least impact on low-priced houses. (3) The Spatial Generalized Additive Model and the Spatial Quantile Generalized Additive Model have been proven to be effective at capturing spatial and temporal impacts on data. In conclusion, this article advises that the government should pay more attention to non-central locations with limited natural resources.

Generalized additive models for location, scale and shape (GAMLSSs) are a popular semiparametric modelling approach that, in contrast with conventional generalized additive models, regress not only the expected mean but also every distribution parameter (e.g. location, scale and shape) to a set of covariates. Current fitting procedures for GAMLSSs are infeasible for high dimensional data set-ups and require variable selection based on (potentially problematic) information criteria. The present work describes a boosting algorithm for high dimensional GAMLSSs that was developed to overcome these limitations. Specifically, the new algorithm was designed to allow the simultaneous estimation of predictor effects and variable selection. The algorithm proposed was applied to Munich rental guide data, which are used by landlords and tenants as a reference for the average rent of a flat depending on its characteristics and spatial features. The net rent predictions that resulted from the high dimensional GAMLSSs were found to be highly competitive and covariate-specific prediction intervals showed a major improvement over classical generalized additive models.

Genital size is a crucial index for the assessment of male sexual development, as abnormal penile or testicular size may be the earliest visible clinical manifestation of some diseases. However, there is a lack of data regarding penile and testicular size measurements for Chinese boys at all stages of childhood and puberty. This cross-sectional study aimed to develop appropriate growth curves and charts for male external genitalia among children and adolescents aged 0-17 years in Chongqing, China. A total of 2974 boys were enrolled in the present study. Penile length was measured using a rigid ruler, penile diameter was measured using a pachymeter, and testicular volume was determined using a Prader orchidometer. Age-specific percentile curves for penile length, penile diameter, and testicular volume were drawn using the generalized additive models for location, scale, and shape. Very similar growth curves were found for both penile length and penile diameter. Both of them gradually rose to 10 years of age and then sharply increased from 11 to 15 years of age. However, testicular volume changed little before the age of 10 years. This study contributes to the literature covering age-specific growth curve and charts about male external genitalia in Chinese children and adolescents. These age-related values are valuable in evaluating the growth and development status of male external genitalia and could be helpful in diagnosing genital disorders.

1. Estimating trends of populations distributed across wide areas is important for conservation and management of animals. Surveys in the form of annually repeated counts across a number of sites are used in many monitoring programmes, and from these, nonlinear trends may be estimated using generalized additive models (GAM). 2. I use generalized additive mixed models (GAMM) to decompose population change into a long-term, smooth, trend component and a component for short-term fluctuations. The longterm population trend is modelled as a smooth function of time and short-term fluctuations as temporal random effects. The methods are applied to analyse trends in goldcrest and greenfinch populations in Sweden using data from the Swedish Breeding Bird Survey. I use simulations to investigate statistical properties of the model. 3. The model separates short-term fluctuations from longer term population change. Depending on the amount of noise in the population fluctuations, estimated long-term trends can differ markedly from estimates based on standard GAMs. For the goldcrest with wide among-year fluctuations, trends estimated with GAMs suggest that the population has in recent years recovered from a decline. When filtering out, short-term fluctuations analyses suggest that the population has been in steady decline since the beginning of the survey. 4. Simulations suggest that trend estimation using the GAMM model reduces spurious detection of long-term population change found with estimates from a GAM model, but gives similar mean square errors. The simulations therefore suggest that the GAMM model, which decomposes population change, estimates uncertainty of long-term trends more accurately at little cost in detecting them. 5. Policy implications. Filtering out short-term fluctuations in the estimation of long-term smooth trends using temporal random effects in a generalized additive mixed model provides more robust inference about the long-term trends compared to when such random effects are not used. This can have profound effects on management decisions, as illustrated in an example for goldcrest in the Swedish breeding bird survey. In the example, if temporal random effects were not used, red listing would be highly influenced by the specific year in which it was done. When temporal random effects are used, red listing is stable over time. The methods are available in an R-package, pop trend.

Since the future output of wind power generation is uncertain due to weather conditions, there is an increasing need to manage the risks associated with wind power businesses, which have been increasingly implemented in recent years. This study introduces multiple weather derivatives of wind speed and temperature and examines their effectiveness in reducing (hedging) the fluctuation risk of future cash flows attributed to wind power generation. Given the diversification of hedgers and hedging needs, we propose new standardized derivatives with higher-order monomial payoff functions, such as “wind speed cubic derivatives” and “wind speed and temperature cross-derivatives,” to minimize the cash flow variance and develop a market-trading scheme to practically use these derivatives in wind power businesses. In particular, while demonstrating the importance of standardizing weather derivatives regarding market liquidity and efficiency, we propose a strategy to narrow down the required number (or volume) of traded instruments and improve trading efficiency by utilizing the least absolute shrinkage and selection operator (LASSO) regression. Empirical analysis reveals that higher-order, multivariate standardized derivatives can not only enhance the out-of-sample hedge effect but also help reduce trading volume. The results suggest that diversification of hedging instruments increases transaction flexibility and helps wind power generators find more efficient portfolios, which can be generalized to risk management practices in other businesses.

Changes in marine environments affect fishery resources at different spatial and temporal scales in marine ecosystems. Predictions from species distribution models are available to parameterize the environmental characteristics that influence the biology, range, and habitats of the species of interest. This study used generalized additive models (GAMs) fitted to two spatiotemporal fishery data sources, namely 1° spatial grid and observer record longline fishery data from 2006 to 2010, to investigate the relationship between catch rates of yellowfin tuna and oceanographic conditions by using multispectral satellite images and to develop a habitat preference model. The results revealed that the cumulative deviances obtained using the selected GAMs were 33.6% and 16.5% in the 1° spatial grid and observer record data, respectively. The environmental factors in the study were significant in the selected GAMs, and sea surface temperature explained the highest deviance. The results suggest that areas with a higher sea surface temperature, a sea surface height anomaly of approximately −10.0 to 20 cm, and a chlorophyll-a concentration of approximately 0.05–0.25 mg/m3 yield higher catch rates of yellowfin tuna. The 1° spatial grid data had higher cumulative deviances, and the predicted relative catch rates also exhibited a high correlation with observed catch rates. However, the maps of observer record data showed the high-quality spatial resolutions of the predicted relative catch rates in the close-view maps. Thus, these results suggest that models of catch rates of the 1° spatial grid data that incorporate relevant environmental variables can be used to infer possible responses in the distribution of highly migratory species, and the observer record data can be used to detect subtle changes in the target fishing grounds.