We present an hierarchical Bayes approach to modeling parameter heterogeneity in generalized linear models. The model assumes that there are relevant subpopulations and that within each subpopulation the individual-level regression coefficients have a multivariate normal distribution. However, class membership is not known a priori, so the heterogeneity in the regression coefficients becomes a finite mixture of normal distributions. This approach combines the flexibility of semiparametric, latent class models that assume common parameters for each sub-population and the parsimony of random effects models that assume normal distributions for the regression parameters. The number of subpopulations is selected to maximize the posterior probability of the model being true. Simulations are presented which document the performance of the methodology for synthetic data with known heterogeneity and number of sub-populations. An application is presented concerning preferences for various aspects of personal computers.

Functional extended redundancy analysis (FERA) was recently developed to integrate data reduction into functional linear models. This technique extracts a component from each of multiple sets of predictor data in such a way that the component accounts for the maximum variance of response data. Moreover, it permits predictor and/or response data to be functional. FERA can be of use in describing overall characteristics of each set of predictor data and in summarizing the relationships between predictor and response data. In this paper, we extend FERA into the framework of generalized linear models (GLM), so that it can deal with response data generated from a variety of distributions. Specifically, the proposed method reduces each set of predictor functions to a component and uses the component for explaining exponential-family responses. As in GLM, we specify the random, systematic, and link function parts of the proposed method. We develop an iterative algorithm to maximize a penalized log-likelihood criterion that is derived in combination with a basis function expansion approach. We conduct two simulation studies to investigate the performance of the proposed method based on synthetic data. In addition, we apply the proposed method to two examples to demonstrate its empirical usefulness.

A maximum likelihood estimation routine is presented for a generalized structural equation model that permits a combination of response variables from various distributions (e.g., normal, Poisson, binomial, etc.). The likelihood function does not have a closed-form solution and so must be numerically approximated, which can be computationally demanding for models with several latent variables. However, the dimension of numerical integration can be reduced if one or more of the latent variables do not directly affect any nonnormal endogenous variables. The method is demonstrated using an empirical example, and the full estimation details, including first-order derivatives of the likelihood function, are provided.

A wide variety of paired comparison, triple comparison, and ranking experiments may be viewed as generalized linear models. These include paired comparison models based on both the Bradley-Terry and Thurstone-Mosteller approaches, as well as extensions of these models that allow for ties, order of presentation effects, and the presence of covariates. Moreover, the triple comparison model of Pendergrass and Bradley, as well as models for complete rankings of more than three items, can also be represented as generalized linear models. All such models can be easily fit by maximum likelihood, using the widely available GLIM computer package. Additionally, GLIM enables the computation of likelihood ratio statistics for testing many hypotheses of interest. Examples are presented that cover a variety of cases, along with their implementation on GLIM.

Rating scales as predictors in regression models are typically treated as metrically scaled variables or, alternatively, are coded in dummy variables. The first approach implies a scale level that is not justified, the latter approach results in a large number of parameters to be estimated. Therefore, when rating scales are dummy-coded, applications are often restricted to the use of a few predictors. The penalization approach advocated here takes the scale level serious by using only the ordering of categories but is shown to work in the high dimensional case. We consider the proper modeling of rating scales as predictors and selection procedures by using penalization methods that are tailored to ordinal predictors. In addition to the selection of predictors, the clustering of categories is investigated. Existing methodology is extended to the wider class of generalized linear models. Moreover, higher order differences that allow shrinkage towards a polynomial as well as monotonicity constraints and alternative penalties are introduced. The proposed penalization approaches are illustrated by use of the Motivational States Questionnaire.

In this paper we discuss a general model framework within which manifest variables with different distributions in the exponential family can be analyzed with a latent trait model. A unified maximum likelihood method for estimating the parameters of the generalized latent trait model will be presented. We discuss in addition the scoring of individuals on the latent dimensions. The general framework presented allows, not only the analysis of manifest variables all of one type but also the simultaneous analysis of a collection of variables with different distributions. The approach used analyzes the data as they are by making assumptions about the distribution of the manifest variables directly.

We offer an introduction to the five papers that make up this special section. These papers deal with a range of the methodological challenges that face researchers analyzing fMRI data—the spatial, multilevel, and longitudinal nature of the data, the sources of noise, and so on. The papers all provide analyses of data collected by a multi-site consortium, the Function Biomedical Informatics Research Network. Due to the sheer volume of data, univariate procedures are often applied, which leads to a multiple comparisons problem (since the data are necessarily multivariate). The papers in this section include interesting applications, such as a state-space model applied to these data, and conclude with a reflection on basic measurement problems in fMRI. All in all, they provide a good overview of the challenges that fMRI data present to the standard psychometric toolbox, but also to the opportunities they offer for new psychometric modeling.

A general approach for analyzing categorical data when there are missing data is described and illustrated. The method is based on generalized linear models with composite links. The approach can be used (among other applications) to fill in contingency tables with supplementary margins, fit loglinear models when data are missing, fit latent class models (without or with missing data on observed variables), fit models with fused cells (including many models from genetics), and to fill in tables or fit models to data when variables are more finely categorized for some cases than others. Both Newton-like and EM methods are easy to implement for parameter estimation.

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.