Generalized additive models (GAMs) are a leading model class for interpretable machine learning. GAMs were originally defined with smooth shape functions of the predictor variables and trained using smoothing splines. Recently, tree-based GAMs where shape functions are gradient-boosted ensembles of bagged trees were proposed, leaving the door open for the estimation of a broader class of shape functions (e.g. Explainable Boosting Machine (EBM)). In this paper, we introduce a competing three-step GAM learning approach where we combine (i) the knowledge of the way to split the covariates space brought by an additive tree model (ATM), (ii) an ensemble of predictive linear scores derived from generalized linear models (GLMs) using a binning strategy based on the ATM, and (iii) a final GLM to have a prediction model that ensures auto-calibration. Numerical experiments illustrate the competitive performances of our approach on several datasets compared to GAM with splines, EBM, or GLM with binarsity penalization. A case study in trade credit insurance is also provided.

Classical generalized linear models assume that marginal effects are homogeneous in the population given the observed covariates. Researchers can never be sure a priori if that assumption is adequate. Recent literature in statistics and political science have proposed models that use Dirichlet process priors to deal with the possibility of latent heterogeneity in the covariate effects. In this paper, we extend and generalize those approaches and propose a hierarchical Dirichlet process of generalized linear models in which the latent heterogeneity can depend on context-level features. Such a model is important in comparative analyses when the data comes from different countries and the latent heterogeneity can be a function of country-level features. We provide a Gibbs sampler for the general model, a special Gibbs sampler for gaussian outcome variables, and a Hamiltonian Monte Carlo within Gibbs to handle discrete outcome variables. We demonstrate the importance of accounting for latent heterogeneity with a Monte Carlo exercise and with two applications that replicate recent scholarly work. We show how Simpson’s paradox can emerge in the empirical analysis if latent heterogeneity is ignored and how the proposed model can be used to estimate heterogeneity in the effect of covariates.

We start by describing how, in some cases, we can use variance-related premium principles in ratemaking, when the claim numbers and individual claim amounts are independent. We use quasi-likelihood generalized linear models, under the assumption that the variance function is a power function of the mean of the underlying random variable. We extend this approach to the cases where the claim numbers are correlated. Some alternatives to deal with dependent risks are presented, taking explicitly into account overdispersion. We present regression models covering the bivariate Poisson, the generalized bivariate negative binomial and the bivariate Poisson–Laguerre polynomial, which nest the bivariate negative binomial. We apply these models to a portfolio of the Portuguese insurance company Tranquilidade and compare the results obtained.

Recent extinction rates suggest that humans are now causing the sixth mass extinction, and the Mediterranean islands are at the forefront of many of the environmental issues involved. This study provides an alternative approach for investigating documented local plant extinctions that occurred in Sardinia (western Mediterranean) during the last half century. A total of 190 local extinctions of 62 plant species were used to investigate the independent effects of eight ecological and anthropogenic variables and to model the areas of potential extinctions where plant conservation efforts could be focused. If all analysed plant species were considered together, ecological factors explained local extinctions more than anthropogenic factors. The independent effects of each factor considerably varied among species of different lifeforms and altitude ranges. Accordingly, distribution models of local extinctions outscored areas that are potentially rich in plant species with conservation interest, but which are particularly affected by humans. This paper suggests a reproducible, operational framework for analysing which extinction factors may play important roles in similar contexts and where they might be relevant.

Rice planthopper (RPH) populations of Nilaparvata lugens and Sogatella furcifera periodically have erupted across Asia. Predicting RPH population dynamics and identifying their source areas are crucial for the management of these migratory pests in China, but the origins of the migrants to temperate and subtropical regions in China remains unclear. In particular, their early migration to China in March and April have not yet been explored due to a lack of research data available from potential source areas, Central Vietnam and Laos. In this study, we examined the population dynamics and migratory paths of N. lugens and S. furcifera in Vietnam and South China in 2012 and 2013. Trajectory modeling showed that in March and April in 2012 and 2013, RPH emigrated from source areas in Central Vietnam where rice was maturing to the Red River Delta and South China. Early migrants originated from Southern Central Vietnam (14–16°N), but later most were from Northern Central Vietnam (16–19°N). Analysis of meteorological and light-trap data from Hepu in April (1977–2013) using generalized linear models showed that immigration increased with precipitation in Southern Central Vietnam in January, but declined with precipitation in Northern Central Vietnam in January. These results determined that the RPH originate from overwintering areas in Central Vietnam, but not from southernmost areas of Vietnam. Winter precipitation, rather than temperature was the most important factor determining the number of RPH migrants. Based on their similar population dynamics and low population densities in Central Vietnam, we further speculated that RPH migrate to track ephemeral food resources whilst simultaneously avoiding predators. Migrations do not seem to be initiated by interspecific competition, overcrowding or host deterioration. Nevertheless, S. furcifera establishes populations earlier than N. lugens South China, perhaps to compensate for interspecific competition. We provide new information that could assist with forecasting outbreaks and implementing control measures against these migratory pests.

Probit-based models relating a proportional response variable to a temporal explanatory variable, assuming that the times to response are normally distributed within the population, have been used in seed biology for describing the rate of loss of viability during seed ageing and the progress of germination over time in response to environmental signals (e.g. water, temperature). These models may be expressed as generalized linear models (GLMs) with a probit (cumulative normal distribution) link function, and, using GLM fitting procedures in current statistical software, parameters of these models are efficiently estimated while taking into account the binomial error distribution of the dependent variable. The fitted parameters can then be used to calculate the ‘traditional’ model parameters, such as the hydro- or hydrothermal time constant, the mean or median response of the seeds (e.g. mean time to death, median base water potential), and the standard deviation of the normal distribution of that response. Furthermore, through consideration of the deviance and residuals, performing model evaluation and modification can lead to improved understanding of the underlying physiological/ecological processes. However, fitting a binomial GLM is not appropriate for the cumulative count data often collected from germination studies, as successive observations are not independent, and time-to-event/survival analysis should be considered instead. This review discusses well-known probit-based models, providing advice on how to collect appropriate data and fit the models to those data, and gives an overview of alternative analysis approaches to improve understanding of the underlying mechanisms of seed dormancy and germination behaviour.

Statistical analysis is increasingly used in seed germination/viability studies across different disciplines. The objective of this opinion piece is to assess current trends in statistical analysis of such data, and draw attention of readers to the limitations of the usual inferential statistics in controlling error rates. The assessments are based on a survey of 429 papers published in 139 peer-reviewed journals in the past 11 years. My intention is to identify areas of concern across a wide range of studies. Accordingly, the areas of greatest concern found in the analysis of percentage seed germination and viability data were: (1) pseudoreplication and/or use of a few replicates; (2) ignoring assumptions of ANOVA and non-parametric tests (NPARTs); (3) uncritical data transformation; (4) arbitrary choice of multiple comparison tests; and (5) lack of emphasis on effect sizes. Given the prevalence of these problems, in my opinion we would be building a body of knowledge on a shaky ground. The discussions that follow will: (1) describe situations where germination data violate assumptions of ANOVA and NPARTs; (2) highlight the implications of the various problems to Type I and Type II error rates; and (3) indicate remedial measures based on the recent statistical literature.

The prediction of adequate claims reserves is a major subject in actuarial practice and science. Due to their simplicity, the chain ladder (CL) and Bornhuetter–Ferguson (BF) methods are the most commonly used claims reserving methods in practice. However, in contrast to the CL method, no estimator for the conditional mean square error of prediction (MSEP) of the ultimate claim has been derived in the BF method until now, and as such, this paper aims to fill that gap. This will be done in the framework of generalized linear models (GLM) using the (overdispersed) Poisson model motivation for the use of CL factor estimates in the estimation of the claims development pattern.

Flatfishes represent an important resource in Portuguese fisheries. Although flatfish landings represent a low percentage of total fish weight landed, their importance is higher when commercial value is considered (11%). Official data on flatfish landings from 1992 to 2005 for all landing ports in Portugal were analysed, together with vessel characteristics, in order to detect patterns in flatfish fisheries. Fleet characteristics were heterogeneous, but most of the vessels were multi-gear. Three landing profiles were identified in the flatfish fishery, and the target species of these métiers showed variation in space and in time. Small vessels caught species that occur in coastal areas, mainly soles, bastard sole, flounder, turbot and brill, and usually also presented high landings of octopuses, cuttlefish and rays. Megrims and spotted flounder were caught with others species, like small pelagic fishes and seabreams by coastal trawlers. For this fleet component, catches of flatfish were usually bycatch. Generalized Linear Models (GLM) were used to analyse flatfish landings (LPUE, landings per unit effort and landings in terms of value) between 1992 and 2005 and to evaluate their relationships with several variables. The main effects in the models included year, month, landing port, vessel length class and total landings (kg). The models explained between 15% and 60% of the variability of the LPUE, and 46% to 82% of the variability of landing value, for the flatfish groups considered, with the most important factors being landing port, vessel length class, month, total landing (kg) and landing port: vessel length interaction. These results suggest high spatial and temporal variability. The results of this study may have implications for fishery management, because the LPUE was highest during the important periods of flatfish life cycles, like the spawning season. This fishing pattern has a negative impact on the stocks because of increased fishing pressure during a sensitive period for these species. The adoption of spatial and temporal closures should be implemented.

Discontinuity between suitable aquatic and terrestrial habitats forces many amphibian species with aquatic larvae to undertake risky breeding migrations through disturbed environments, potentially contributing to population declines by reducing survival of adults and juveniles (Becker et al. 2007). The north-western region of the state of São Paulo, Brazil, is characterized by fragments of mesophytic semideciduous forest and savanna, surrounded by a matrix of pasture, plantations and urban areas with only 4% of the remaining original vegetation of the state (Ribeiro et al. 2009). Currently, 36 anuran species have been recorded in this region, corresponding to almost 15% of the state's species (Araújo et al. 2009). The anuran species of this region are associated with open environments or are widely distributed in the different Brazilian biomes (Duellman 1999). Silva & Rossa-Feres (2007) showed the importance of forest fragments in this region for 12 anuran species that breed in pools located in a pasture matrix.

We revisit the stochastic model of Alai et al. (2009) for the Bornhuetter-Ferguson claims reserving method, Bornhuetter & Ferguson (1972). We derive an estimator of its conditional mean square error of prediction (MSEP) using an approach that is based on generalized linear models and maximum likelihood estimators for the model parameters. This approach leads to simple formulas, which can easily be implemented in a spreadsheet.

Habitat distribution models are one of the most up to date methods to study the habitat usage of wildlife populations. They allow animal distribution to be related to environmental features and also the prediction of the distribution of animals based on this relationship. Seasonal aerial surveys were conducted in central Spanish Mediterranean waters from June 2000 to March 2003 to obtain information on the distribution of cetacean species. Data from the three most common cetacean species (striped dolphin, Stenella coeruleoalba, bottlenose dolphin, Tursiops truncatus, and Risso's dolphin, Grampus griseus) were related, using generalized linear models, to local environmental features: depth, slope, sea surface temperature and chlorophyll concentration. For bottlenose dolphins, no significant relationship was found with any covariate and no dolphins were observed in waters greater than 1000 m. The distribution of both striped and Risso's dolphin was significantly related to depth. The striped dolphin showed a preference for waters between 900 and 1500 m deep and Risso's dolphin for waters more than 1500 m deep. In addition, for the latest two species, maps of distribution were predicted by means of the spatial models. The areas of higher probabilities of occurrence coincide to a large extent with the marine protected areas previously proposed for the conservation of oceanic cetacean species.

Kaas, Dannenburg & Goovaerts (1997) generalized Jewell’s theorem on exact credibility, from the classical Bühlmann model to the (weighted) Bühlmann-Straub model. We extend this result further to the “Bühlmann-Straub model with a priori differences” (Bühlmann & Gisler, 2005). It turns out that exact credibility holds for a class of Tweedie models, including the Poisson, gamma and compound Poisson distribution – the most important distributions for insurance applications of generalized linear models (GLMs). Our results can also be viewed as an alternative to the HGLM approach for combining credibility and GLMs, see Nelder and Verrall (1997).

The purpose of this paper is to obtain approximations to the transition intensities defined for a multiple state model for Permanent Health Insurance (PHI) which enables us to analyse PHI claims by cause of disability.

The approximations to the transition intensities are obtained using a set of PHI data classified by 18 sickness categories and the graduations of the transition intensities defined for a simpler model proposed in Continuous Mortality Investigation Reports, 12 (1991).

In order to derive the approximations to the recovery and mortality of the sick intensities for our model, we carry out tests of hypotheses based on the distributions of average sickness durations. The approximations to the sickness intensities are obtained by estimating a statistical model for the number of claim inceptions, which can be formulated as a generalized linear model.

We reconsider the problem of producing fair and accurate tariffs based on aggregated insurance data giving numbers of claims and total costs for the claims. Jørgensen and de Souza (Scand Actuarial J., 1994) assumed Poisson arrival of claims and gamma distributed costs for individual claims. Jørgensen and de Souza (1994) directly modelled the risk or expected cost of claims per insured unit, μ say. They observed that the dependence of the likelihood function on μ is as for a linear exponential family, so that modelling similar to that of generalized linear models is possible. In this paper we observe that, when modelling the cost of insurance claims, it is generally necessary to model the dispersion of the costs as well as their mean. In order to model the dispersion we use the framework of double generalized linear models. Modelling the dispersion increases the precision of the estimated tariffs. The use of double generalized linear models also allows us to handle the case where only the total cost of claims and not the number of claims has been recorded.

We investigate the influence of initial selection (the impact of underwriting during the early years of a policy's life) on individual Permanent Health Insurance claim inceptions. In Gutiérrez-Delgado (1999) a decreasing trend was found. In this paper we include the effect of cause of disability and fit a generalized linear model in order to gain a greater understanding of the phenomenon. Both effects, policy duration and cause of disability, are found to have a significant effect on the number of claims. We describe their influence using factors that collect the information available through the fitted model. Results from both factors suggest that the grouping of diseases selected for the research helps to explain partially our earlier results. In addition there is some evidence of moral hazard in mental disorders and musculoskeletal diseases which also contributes to the understanding of the negative trend found.

This paper shows how credibility theory can be encompassed within the theory of Hierarchical Generalized Linear Models. It is shown that credibility estimates are obtained by including random effects in the model. The framework of Hierarchical Generalized Linear Models allows a more extensive range of models to be used than straightforward credibility theory. The model fitting and testing procedures can be carried out using a standard statistical package. Thus, the paper contributes a further range of models which may be useful in a wide range of actuarial applications, including premium rating and claims reserving.

An overview of the potential of Generalized Linear Models as a means of modelling the salient features of the claims process in the presence of rating factors is presented. Specific attention is focused on the rich variety of modelling distributions which can be implemented in this context.