Academic literature on the topic 'Generalised linear modelling (GLM)'

Abstract. Multivariable regression models have been used extensively as spatial modelling tools. However, other regression approaches are emerging as more efficient techniques. This paper attempts to present a synthesis of Generalised Regression Models (Generalized Linear Models, GLMs, Generalized Additive Models, GAMs), and a Geographically Weighted Regression, GWR, implemented in a GAM, explaining their statistical formulations and assessing improvements in predictive accuracy compared with linear regressions. The problems associated with these approaches are also discussed. A digital database developed with Geographic Information Systems (GIS), including environmental maps and bird species richness distribution in northern Spain, is used for comparison of the techniques. GWR using splines has shown the highest improvement in accounted deviance when compared with traditional linear regression approach, followed by GAM and GLM.

Ordered categorical data occur in many applied fields, such as geochemistry, econometrics, sociology and demography or even transportation research, for example, in the form of results from various questionnaires. There are different possibilities for modelling proportions of individual categories. Generalised linear models (GLMs) are traditionally used for this purpose, but also methods of compositional data analysis (CoDa) can be considered. Here, both approaches are compared in depth. Particularly, different assumptions of the models on variability are highlighted. Advantages and disadvantages of individual models are pointed out. While the CoDa model may be inappropriate when the variability of the compositional coordinates depends on the regressors, for example, due to different total counts on which the coordinates are based, the GLM may underestimate the uncertainty of the predictions considerably in case of large-scale data.

The aim of this research was to determine the variables that characterize slate exploitability and to model spatial distribution. A generalized linear spatial model (GLSMs) was fitted in order to explore relationship between exploitability and different explanatory variables that characterize slate quality. Modelling the influence of these variables and analysing the spatial distribution of the model residuals yielded a GLSM that allows slate exploitability to be predicted more effectively than when using generalized linear models (GLM), which do not take spatial dependence into account. Studying the residuals and comparing the prediction capacities of the two models lead us to conclude that the GLSM is more appropriate when the response variable presents spatial distribution.

Wildfire ignition distribution models are powerful tools for predicting the probability of ignitions across broad areas, and identifying their drivers. Several approaches have been used for ignition-distribution modelling, yet the performance of different model types has not been compared. This is unfortunate, given that conceptually similar species-distribution models exhibit pronounced differences among model types. Therefore, our goal was to compare the predictive performance, variable importance and the spatial patterns of predicted ignition-probabilities of three ignition-distribution model types: one parametric, statistical model (Generalised Linear Models, GLM) and two machine-learning algorithms (Random Forests and Maximum Entropy, Maxent). We parameterised the models using 16 years of ignitions data and environmental data for the Huron–Manistee National Forest in Michigan, USA. Random Forests and Maxent had slightly better prediction accuracies than did GLM, but model fit was similar for all three. Variables related to human population and development were the best predictors of wildfire ignition locations in all models (although variable rankings differed slightly), along with elevation. However, despite similar model performance and variables, the map of ignition probabilities generated by Maxent was markedly different from those of the two other models. We thus suggest that when accurate predictions are desired, the outcomes of different model types should be compared, or alternatively combined, to produce ensemble predictions.

Wildland and cropland fires, which differ considerably in fire regime characteristics, have often been evaluated jointly to estimate regional or global fire regimes using satellite-based fire activity data. We hypothesised that excluding cropland fires will change the output of the models regarding the drivers of natural fire activity. We modelled MODIS fire activity data of western and southern Turkey for the years 2000–2015 using binomial generalised linear models in which many climatic, anthropogenic and geographic factors were included as predictor variables. For modelling, we used different datasets created by the exclusion of various cropland and vegetation land cover classes. More fire activity was observed as the number of cropland-dominated cells increased in a dataset. The explained deviance (%) of the binomial GLM differed substantially in the separate datasets for most of the variables. Moreover, excluding croplands gradually from the overall dataset resulted in a substantial decrease in the explained deviance (%) in the models for all variables. The results suggest that cropland fires have a significant effect on the output of fire regime models. Therefore, a clear distinction should be drawn between wildland and cropland fires in such models for a better understanding of natural fire activity.

This study describes the development of macro-level (i.e., neighbourhood or traffic zone level) collision prediction models using data from 577 neighbourhoods across the Greater Vancouver Regional District. The objective is to provide a safety planning decision-support tool that facilitates a proactive approach to community planning which addresses road safety before problems emerge. The models are developed using the generalized linear regression modelling (GLM) technique assuming a negative binomial error structure. The resulting models relate traffic collisions to neighbourhood characteristics such as traffic volume, demographics, network shape, and transportation demand management. Several models are presented for total or severe collisions in rural or urban zones using measured and (or) modelled data. It is hoped that quantifying a predictive traffic safety – neighbourhood planning relationship will facilitate improved decisions by community planners and engineers and, ultimately, facilitate improved neighbourhood traffic safety for residents and other road users.Key words: neighbourhood safety, macro-level collision prediction models, road safety, safety planning, transportation demand management, sociodemographic, generalized linear regression modelling.

BackgroundBicycle injuries are of concern in Canada. Since helmet use was mandated in 1996 in the province of British Columbia, Canada, use has increased and head injuries have decreased. Despite the law, many cyclists do not wear a helmet. Health action process approach (HAPA) model explains intention and behaviour with self-efficacy, risk perception, outcome expectancies and planning constructs. The present study examines the impact of a social marketing campaign on HAPA constructs in the context of bicycle helmet use.MethodA questionnaire was administered to identify factors determining helmet use. Intention to obey the law, and perceived risk of being caught if not obeying the law were included as additional constructs. Path analysis was used to extract the strongest influences on intention and behaviour. The social marketing campaign was evaluated through t-test comparisons after propensity score matching and generalised linear modelling (GLM) were applied to adjust for the same covariates.Results400 cyclists aged 25–54 years completed the questionnaire. Self-efficacy and Intention were most predictive of intention to wear a helmet, which, moderated by planning, strongly predicted behaviour. Perceived risk and outcome expectancies had no significant impact on intention. GLM showed that exposure to the campaign was significantly associated with higher values in self-efficacy, intention and bicycle helmet use.ConclusionSelf-efficacy and planning are important points of action for promoting helmet use. Social marketing campaigns that remind people of appropriate preventive action have an impact on behaviour.

Possible changes in streamflow in response to climate variation are crucial for anthropological and ecological systems. However, estimates of precipitation under future climate scenarios are notoriously uncertain. In this article, rainfall time series are generated by the generalized linear model (GLM) approach in which stochastic time series are generated using alternative climate model output variables and potential evaporation series estimated by a temperature method. These have been input to a conceptual rainfall–runoff model (pd4-2par) to simulate the daily streamflows for six UK catchments for a set of climate scenarios using seven global circulation models (GCMs) and regional circulation models (RCMs). The performance of the combined methodology in reproducing observed streamflows is generally good. Results of future climate scenarios show significant variability between different catchments, and very large variability between different climate models. It is concluded that the GLM methodology is promising, and can readily be extended to support distributed hydrological modelling.

AbstractEnergy securityis one of the major components of energy sustainability in the world’s energy performance. In this study,energy securityis taken as an ordinal response variable coming from the multinomial distribution with the energy grade levelsA,B,C, andD. Thereafter, the worldenergy securitydata is tried to be statistically modelled by usinggeneralized linear model (GLM)approach for the ordinal response variable under different cumulative link functions. The cumulative link functions comparatively used in this study are cumulative logit, cumulative probit, cumulative complementary log-log, cumulative Cauchit, and cumulative negative log-log. In order to avoid a multicollinearity problem in the data structure, principal component analysis (PCA) technique is integrated with theGLMapproach for the ordinal response variable. In this study, statistically, the importance of determining the best cumulative link function on the accuracy of parameter estimates, confidence intervals, and hypothesis tests in theGLMfor the multinomially distributed response variable is highlighted. In terms of energy evaluation, by usingcumulative logitas the best cumulative link function,energy sources consumptions,electricity productions from nuclear energy,natural gas,oil,coal,and hydroelectric,energy use per capita and energy importsare found to have statistically significant effects onenergy securityin the world’s energy performance.

My Masters research aims to deepen our understanding of the behaviour of robust methods in logistic regression. Logistic regression is a special case of Generalized Linear Modelling (GLM), which is a powerful and popular technique for modelling a large variety of data. Robust methods are useful in reducing the effect of outlying values in the response variable on parameter estimates. A literature survey shows that we are still at the beginning of being able to detect extreme observations in logistic regression analyses, to apply robust methods in logistic regression and to present informatively the results of logistic regression analyses. In Chapter 1 I have made a basic introduction to logistic regression, with an example, and to robust methods in general. In Chapters 2 through 4 of the thesis I have described traditional methods and some relatively new methods for presenting results of logistic regression using powerful visualization techniques as well as the concepts of outliers in binomial data. I have used different published data sets for illustration, such as the Prostate Cancer data set, the Damaged Carrots data set and the Recumbent Cow data set. In Chapter 4 I summarize and report on the modem concepts of graphical methods, such as central dimension reduction, and the use of graphics as pioneered by Cook and Weisberg (1999). In Section 4.6 I have then extended the work of Cook and Weisberg to robust logistic regression. In Chapter 5 I have described simulation studies to investigate the effects of outlying observations on logistic regression (robust and non-robust). In Section 5.2 I have come to the conclusion that, in the case of classical or robust multiple logistic regression with no outliers, robust methods do not necessarily provide more reasonable estimates of the parameters for the data that contain no st~ong outliers. In Section 5.4 I have looked into the cases where outliers are present and have come to the conclusion that either the breakdown method or a sensitivity analysis provides reasonable parameter estimates in that situation. Finally, I have identified areas for further study.

Uncertainty is pervasive in risk assessment. In ecotoxicological risk assessments, it arises from such sources as a lack of data, the simplification and abstraction of complex situations, and ambiguities in assessment endpoints (Burgman 2005; Suter 1993). When evaluating and managing risks, uncertainty needs to be explicitly considered in order to avoid erroneous decisions and to be able to make statements about the confidence that we can place in risk estimates. Although informative, previous approaches to dealing with uncertainty in ecotoxicological modelling have been found to be limited, inconsistent and often based on assumptions that may be false (Ferson & Ginzburg 1996; Suter 1998; Suter et al. 2002; van der Hoeven 2004; van Straalen 2002a; Verdonck et al. 2003a). In this thesis a Generalised Linear Modelling approach is proposed as an alternative, congruous framework for the analysis and prediction of a wide range of ecotoxicological effects. This approach was used to investigate the results of toxicity experiments on the effect of 2,4-Dichlorophenoxyacetic Acid (2,4-D) formulations and 4-Chlorophenol (4-CP, an associated breakdown product) on Daphnia carinata. Differences between frequentist Maximum Likelihood (ML) and Bayesian Markov-Chain Monte-Carlo (MCMC) approaches to statistical reasoning and model estimation were also investigated. These approaches are inferentially disparate and place different emphasis on aleatory and epistemic uncertainty (O'Hagan 2004). Bayesian MCMC and Probability Bounds Analysis methods for propagating uncertainty in risk models are also compared for the first time. For simple models, Bayesian and frequentist approaches to Generalised Linear Model (GLM) estimation were found to produce very similar results when non-informative prior distributions were used for the Bayesian models. Potency estimates and regression parameters were found to be similar for identical models, signifying that Bayesian MCMC techniques are at least a suitable and objective replacement for frequentist ML for the analysis of exposureresponse data. Applications of these techniques demonstrated that Amicide formulations of 2,4-D are more toxic to Daphnia than their unformulated, Technical Acid parent. Different results were obtained from Bayesian MCMC and ML methods when more complex models and data structures were considered. In the analysis of 4-CP toxicity, the treatment of 2 different factors as fixed or random in standard and Mixed-Effect models was found to affect variance estimates to the degree that different conclusions would be drawn from the same model, fit to the same data. Associated discrepancies in the treatment of overdispersion between ML and Bayesian MCMC analyses were also found to affect results. Bayesian MCMC techniques were found to be superior to the ML ones employed for the analysis of complex models because they enabled the correct formulation of hierarchical (nested) datastructures within a binomial logistic GLM. Application of these techniques to the analysis of results from 4-CP toxicity testing on two strains of Daphnia carinata found that between-experiment variability was greater than that within-experiments or between-strains. Perhaps surprisingly, this indicated that long-term laboratory culture had not significantly affected the sensitivity of one strain when compared to cultures of another strain that had recently been established from field populations. The results from this analysis highlighted the need for repetition of experiments, proper model formulation in complex analyses and careful consideration of the effects of pooling data on characterising variability and uncertainty. The GLM framework was used to develop three dimensional surface models of the effects of different length pulse exposures, and subsequent delayed toxicity, of 4-CP on Daphnia. These models described the relationship between exposure duration and intensity (concentration) on toxicity, and were constructed for both pulse and delayed effects. Statistical analysis of these models found that significant delayed effects occurred following the full range of pulse exposure durations, and that both exposure duration and intensity interacted significantly and concurrently with the delayed effect. These results indicated that failure to consider delayed toxicity could lead to significant underestimation of the effects of pulse exposure, and therefore increase uncertainty in risk assessments. A number of new approaches to modelling ecotoxicological risk and to propagating uncertainty were also developed and applied in this thesis. In the first of these, a method for describing and propagating uncertainty in conventional Species Sensitivity Distribution (SSD) models was described. This utilised Probability Bounds Analysis to construct a nonparametric 'probability box' on an SSD based on EC05 estimates and their confidence intervals. Predictions from this uncertain SSD and the confidence interval extrapolation methods described by Aldenberg and colleagues (2000; 2002a) were compared. It was found that the extrapolation techniques underestimated the width of uncertainty (confidence) intervals by 63% and the upper bound by 65%, when compared to the Probability Bounds (P3 Bounds) approach, which was based on actual confidence estimates derived from the original data. An alternative approach to formulating ecotoxicological risk modelling was also proposed and was based on a Binomial GLM. In this formulation, the model is first fit to the available data in order to derive mean and uncertainty estimates for the parameters. This 'uncertain' GLM model is then used to predict the risk of effect from possible or observed exposure distributions. This risk is described as a whole distribution, with a central tendency and uncertainty bounds derived from the original data and the exposure distribution (if this is also 'uncertain'). Bayesian and P-Bounds approaches to propagating uncertainty in this model were compared using an example of the risk of exposure to a hypothetical (uncertain) distribution of 4-CP for the two Daphnia strains studied. This comparison found that the Bayesian and P-Bounds approaches produced very similar mean and uncertainty estimates, with the P-bounds intervals always being wider than the Bayesian ones. This difference is due to the different methods for dealing with dependencies between model parameters by the two approaches, and is confirmation that the P-bounds approach is better suited to situations where data and knowledge are scarce. The advantages of the Bayesian risk assessment and uncertainty propagation method developed are that it allows calculation of the likelihood of any effect occurring, not just the (probability)bounds, and that the same software (WinBugs) and model construction may be used to fit regression models and predict risks simultaneously. The GLM risk modelling approaches developed here are able to explain a wide range of response shapes (including hormesis) and underlying (non-normal) distributions, and do not involve expression of the exposure-response as a probability distribution, hence solving a number of problems found with previous formulations of ecotoxicological risk. The approaches developed can also be easily extended to describe communities, include modifying factors, mixed-effects, population growth, carrying capacity and a range of other variables of interest in ecotoxicological risk assessments. While the lack of data on the toxicological effects of chemicals is the most significant source of uncertainty in ecotoxicological risk assessments today, methods such as those described here can assist by quantifying that uncertainty so that it can be communicated to stakeholders and decision makers. As new information becomes available, these techniques can be used to develop more complex models that will help to bridge the gap between the bioassay and the ecosystem.

Factor score regression has recently received growing interest as an alternative for structural equation modelling. Two issues causing uncertainty for researchers are addressed in this thesis. Firstly, more knowledge is needed on how different approaches to calculating factor score estimates compare when estimating factor score regression models. Secondly, many applications are left without guidance because of the focus on normally distributed outcomes in the literature. This thesis examines how factor scoring methods compare when estimating regression coefficients in generalised linear factor score regression. An evaluation is made of the regression, correlation-preserving, total sum, and weighted sum method in ordinary, logistic, and Poisson factor score regression. In contrast to previous studies, both the mean and variance of loading coefficients and the degree of inter-factor correlation are varied in the simulations. A meta-analysis demonstrates that the choice of factor scoring method can substantially influence research conclusions. The regression and correlation-preserving method outperform the other two methods in terms of coefficient and standard error bias, accuracy, and empirical Type I error rates. Moreover, the regression method generally has the best performance. It is also noticed that performance can differ notably across the considered regression models.

There has been an ongoing debate regarding appropriate strategies for the management of carious primary teeth. Studies appear to provide evidence that both selective, symptom-based interventions and traditional restorative strategies are advantageous. However, the analysis and quantification of childhood caries may be affected by clustering of data, and the concurrent risk of exfoliation of primary teeth. Multilevel generalised linear models for the occurrence of primary caries were derived utilising data from a cohort study of 2,654 children aged 4-5 years at baseline undertaken 1999-2003. These models, which assumed underlying hierarchies with clustering at child, tooth and surface levels, identified higher rates of caries occurrence in primary molar teeth to be associated with boys, poor socio-economic background, lack of water fluoridation, 2nd mandibular molars and occlusal surfaces. Significant risk factors identified were carried forward for inclusion in parametric competing risks multivariate multilevel survival models, utilising cohort study data augmented with Dental Practice Board treatment data. Analysis of sound teeth and surfaces found the concurrent risk of exfoliation did not alter inferences of parameter significance, but restricted the extent of caries occurrence and reduced distinction in survival experience between different types of teeth and surfaces in children from different demographic backgrounds. Further competing risks survival models were derived to analyse the same teeth and surfaces in the untreated carious and filled states, to assess the effect of restorative treatment on subsequent exfoliation and extraction. Survival rates extrapolated to 14 years without further treatment for filled molar teeth were approximately double those of untreated teeth. Time of caries occurrence and treatment also affected survival, with later occurrence or treatment of caries associated with higher survival rates. However, early filling of carious teeth resulted in the greatest reductions in the expected time that decay is present in the mouth.

Une meilleure connaissance des frayères des principaux poissons commerciaux de la mer du Nord semble nécessaire pour leur surveillance. La composition et l'abondance des espèces d'oeufs collectés par le CUFES (Continuous Underway Fish Egg Sampler) sont comparées à celle collectées par le VET (Vertical Egg Trawl) permettant de prouver l'efficacité du CUFES en Manche et mer du Nord. L'identification des œufs de poissons principalement basée sur des critères morphologiques n'est pas toujours fiable. En effet, certaines espèces comme la morue (Gadus morhua) et le merlan (Merlangius merlangus) ont la même gamme de taille, ainsi des méthodes altenatives ont été développées. Premièrement, une technique de biologie moléculaire par PCR-RFLP puis un nouveau système d'analyse d'images, le ZooScan ont été développés pour identifier les œufs de poissons. Des cartes annuelles des frayères hivernales ont été réalisées et comparées entre elles afin de déterminer des zones de ponte récurrentes. Les œufs sont généralement bien distribués sur la zone d'étude, à l'exception de la zone Nord-Ouest de la mer du Nord, près des côtes écossaises. Et enfin, l'habitat de ponte des poissons a été modélisé en utilisant les méthodes GLM (Generalised Linear Model) et RQ (Regression Quantile) en fonction des paramètres environnementaux disponibles afin de prédire les frayères. Les résultats de cette étude multidisciplinaire ont permis d'améliorer les connaissances sur les frayères hivernales en Manche Orientale et sud mer du Nord et ont été discutés dans une perspective de protection et de conservation de ces zones
A better knowledge and monitoring of principal commercial fish spawning grounds have become necessary in the North Sea. The efficiency of CUFES was proved by sampling pelagic fish eggs in winter in Eastern Channel and Southern North Sea. Fish egg taxonomic identification based on visual criteria cannot always be carried out effectively. In particular, cod (Gadus morhua), and whiting (Merlangius merlangus) or flounder (Platichthys flesus) and dab (Limanda limanda) have the same range of egg diameter and similar morphologies. Alternative identification methods using molecular techniques were developed to improve the accuracy of egg taxonomic identification. First, PCR-RFLP method, then, in order to accelerate egg identification, the use of a new laboratory imaging system, the ZooScan, able to produce high resolution images of zooplankton samples, was adapted to fish eggs and allower their automated identification using supervised learning algorithms. The location of winter spawning grounds of fishes in the Southern North Sea and the Eastern Channel was illustrated using yearly maps and analysed over the available period to define recurrent, occasional and unfavorable spawning areas. Generally, fish eggs were found over the study area, except for the North Western of the North Sea, near Scottish coasts. Important spawning areas were clearly localised along the Belgian, Dutch and Danish coasts. Habitat modelling of these fish spawning areas was carried out using both GLM (Generalised Linear Model) and QR (Regression Quantile) and associated egg abundance to physical conditions such as temperature, salinity, bedstress, chlorophyll a concentration and bottom sediment types to characterize spawning habitat conditions and predict their extent and location. The results of this approach improve the understanding of spawning grounds distribution and were discussed in the context of the protection and conservation of critical spawning grounds

This chapter discusses general and generalised linear models (GLM and GLZ respectively). It outlines GLMs (mean, properties of GLMs and the mean), samples and populations, comparison of two groups of data, multiple regression and the GLM, analysis of variance (ANOVA) and the GLM, GLM in SPSS, and the GLZ).

Abstract This chapter employs generalized linear modelling using the function glm when we know that variances are not constant with one or more explanatory variables and/or we know that the errors cannot be normally distributed, for example, they may be binary data, or count data where negative values are impossible, or proportions which are constrained between 0 and 1. A glm seeks to determine how much of the variation in the response variable can be explained by each explanatory variable, and whether such relationships are statistically significant. The data for generalized linear models take the form of a continuous response variable and a combination of continuous and discrete explanatory variables.

Abstract This chapter employs generalized linear modelling using the function glm when we know that variances are not constant with one or more explanatory variables and/or we know that the errors cannot be normally distributed, for example, they may be binary data, or count data where negative values are impossible, or proportions which are constrained between 0 and 1. A glm seeks to determine how much of the variation in the response variable can be explained by each explanatory variable, and whether such relationships are statistically significant. The data for generalized linear models take the form of a continuous response variable and a combination of continuous and discrete explanatory variables.

The major drawback of magnetorheological dampers (MR) lies in their non-linear and hysteretic force-velocity response. To take full advantage of the operating characteristics of these devices a high fidelity model is required for control analysis and design. In this contribution the ability of a generalised PI operator-based model to represent the characteristics of a commercially available MR damper is examined. This approach allows the user to define the PI operator to best match the hysteresis characteristics. For the MR damper the force-velcoity hysteresis characteristic is ‘S’ shaped and constrained. Two possibilities will be examined here for the generalised play operator; an hyperbolic tan function and a symmetric sigmoid function.