Neste trabalho, apresentamos as equações de estimação generalizadas desenvolvidas por Liang e Zeger (1986), sob a ótica da teoria de funções de estimação apresentada por Godambe (1991). Essas equações de estimação são obtidas para os modelos lineares generalizados (MLGs) considerando medidas repetidas. Apresentamos também um processo iterativo para estimação dos parâmetros de regressão, assim como testes de hipóteses para esses parâmetros. Para a análise de resíduos, generalizamos para dados com medidas repetidas algumas técnicas de diagnóstico usuais em MLGs. O gráfico de probabilidade meio-normal com envelope simulado é uma proposta para avaliarmos a adequação do ajuste do modelo. Para a construção desse gráfico, simulamos respostas correlacionadas por meio de algoritmos que descrevemos neste trabalho. Por fim, realizamos aplicações a conjuntos de dados reais. / In this work, we consider the generalized estimation equations developed by Liang and Zeger (1986) focusing the theory of estimating functions presented by Godambe (1991). These estimation equations are an extension of generalized linear models (GLMs) to the analysis of repeated measurements. We present an iterative procedure to estimate the regression parameters as well as hypothesis testing of these parameters. For the residual analysis, we generalize to repeated measurements some diagnostic methods available for GLMs. The half-normal probability plot with a simulated envelope is useful for diagnosing model inadequacy and detecting outliers. To obtain this plot, we consider an algorithm for generating a set of nonnegatively correlated variables having a specified correlation structure. Finally, the theory is applied to real data sets.

Nesta tese, desenvolvemos refinamentos assintóticos em modelos lineares generalizados heteroscedásticos (Smyth, 1989). Inicialmente, obtemos a matriz de covariâncias de segunda ordem dos estimadores de máxima verossimilhança corrigidos pelos viés de primeira ordem. Com base na matriz obtida, sugerimos modificações na estatística de Wald. Posteriormente, derivamos os coeficientes do fator de correção tipo-Bartlett para a estatística do teste gradiente. Em seguida, obtemos o coeficiente de assimetria assintótico da distribuição dos estimadores de máxima verossimilhança dos parâmetros do modelo. Finalmente, exibimos o coeficiente de curtose assintótico da distribuição dos estimadores de máxima verossimilhança dos parâmetros do modelo. Analisamos os resultados obtidos através de estudos de simulação de Monte Carlo. / In this thesis, we have developed asymptotic refinements in heteroskedastic generalized linear models (Smyth, 1989). Initially, we obtain the second-order covariance matrix for the maximum likelihood estimators corrected by the bias of first-order. Based on the obtained matrix, we suggest changes in Wald statistics. In addition, we derive the coeficients of the Bartlett-type correction factor for the statistical gradient test. After, we get asymptotic skewness of the distribution of the maximum likelihood estimators of the model parameters. Finally, we show the asymptotic kurtosis coeficient of the distribution of the maximum likelihood estimators of the model parameters. Monte Carlo simulation studies are developed to evaluate the results obtained.

O mapeamento e a estimação de riscos e incidências são ferramentas muito úteis para a Epidemiologia pois, auxiliam na prevenção de agravos da saúde e, também auxiliam no planejamento e avaliação dos serviços de saúde. Este trabalho busca utilizar uma ferramenta estatística que incorpora de forma adequada este tipo de análise ao estudo de outras características que estejam relacionadas a estes agravos. No presente trabalho utiliza-se como aplicação dados do estudo caso-controle espacial com base populacional de acidentes de trabalho com a proposta de estimar a distribuição espacial do risco de sofrer acidente de trabalho na área urbana do município de Piracicaba/SP entre trabalhadores que se encontravam na situação de precarização do trabalho em associação com outras variáveis de interesse através de modelos aditivos generalizados (MAG) e, através disso, mostrar que ao incorporar de forma explícita o espaço no processo de modelagem dos dados ocorre um ganho significativo na explicação da variação do risco. O modelo MAG utilizado tem variável resposta binomial (caso e controle) e multinomial (caso e controle separados pela gravidade do acidente sofrido). Com os modelos ajustados, mapas foram desenhados com indicações de diferentes cores para a intensidade do risco de sofrer acidente de trabalho. Outra abordagem utilizada para os dados espaciais de acidentes de trabalho foi a INLA (INTEGRATED NESTED LAPLACE APPROXIMATIONS), a qual é utilizada como processo de modelagem para a família dos modelos Gaussianos latentes através de novos métodos para esta família de modelos. A intenção foi mostrar como essa nova abordagem lida com dados do tipo espacial e, fazer uma comparação com a abordagem feita pela modelagem GAM / Mapping and estimation of risks and impacts are very useful tools for Epidemiology at the assistance in prevention of injuries and health, also assists in planning and evaluation of health services. This paper seeks to use a statistical tool that adequately incorporates this type of analysis to the study of other characteristics that are related these illnesses. In the present work is used as application data from case-control study space-based population accidents with the proposal to estimate the spatial distribution of risk of suffering an accident at work in the urban area of Piracicaba/SP among workers who were in employed as casual labor in combination with other variables of interest using generalized additive models (GAM) and, thereby, show that by incorporating explicitly space in the process of data modeling is a gain significant in explaining the variation in risk. The GAM model have used binomial response variable (case and control) and multinomial (case and control separated by the severity of the accident suffered). With the adjusted models, maps were drawn with indications of different colors to the intensity of the risk of accident. Another approach used for spatial data on accidents at work was the INLA (INTEGRATED NESTED LAPLACE APPROXIMATIONS), which is used as a modeling process for the family of latent Gaussian models through new methods for this family of models. The intention was to show how this new approach deals with spatial data and a comparison with the approach made by GAM modeling.

Os frutos cítricos são uma das principais fontes de exportação do Brasil, sendo que São Paulo responde por cerca de 80% da produção total. Dentre os fatores que limitam a produção citrícola brasileira, especialmente no estado de São Paulo, vem se sobressaindo nos últimos anos, a clorose variegada dos citros (CVC), a podridão floral, o minador-dos-citros e o bicho-furão-dos-citros, Ecdytolopha aurantiana (Lima, 1927) (Lepidoptera: Tortricidae), além dos ácaros, moscas-das-frutas, pinta preta e mais recentemente a morte súbita. O presente trabalho teve como objetivo desenvolver um modelo para previsão de ocorrência de E. aurantiana, baseado em dados de monitoramento através de armadilhas de feromônio sexual e desenvolver um sistema computacional que possa utilizar este modelo para gerar as previsões de ocorrência, além de fornecer um local de troca de informações entre o citricultor e a comunidade científica. O tipo de solo, temperatura do local, variedade de citros, idade das plantas e uso de agroquímicos para controle de E. aurantiana, influenciaram na dinâmica populacional deste inseto. A maior influência sobre a flutuação do bicho-furão foi exercida pelo tipo de solo, seguido pela temperatura local, variedade de citros, idade das plantas e uso de agroquímicos para controle de E. aurantiana. A ocorrência de E. aurantiana em função da temperatura é diferente para cada combinação de tipo de solo, variedade de citros, idade das plantas e uso de agroquímicos. O modelo desenvolvido pode prever o potencial de ocorrência de E. aurantiana em função da temperatura ou dos meses do ano, levando-se em consideração o tipo de solo, variedade de citros, idade das plantas e aplicação de agroquímicos. O programa (BF) elaborado na linguagem R conta com equações para simular as diversas situações de ocorrência de E. aurantiana. O SIAC (Sistema Integrado de Apoio ao Citricultor) é um sistema que facilita o uso do modelo, sem a necessidade de conhecimento de R e fornece uma gama de recursos que visa facilitar o acesso do citricultor às informações e ao pesquisador aos problemas do citricultor, criando com isto uma maior interação de ambos. O modelo de previsão de ocorrência de bicho-furão pode ser aperfeiçoado com coleta de dados mais regulares e de forma contínua. / Citrus fruits are Brazil’s major exporting sources, and São Paulo is accountable for approximately 80% of the total production. Among the factors that limit the Brazilian citriculture, especially in the state of São Paulo, one points in the past few years the citrus variegated chlorosis (CVC), flower rot, citrus leaf miner and citrus fruit borer, Ecdytolopha aurantiana (Lima, 1927) (Lepidoptera: Tortricidae), in addition to mites, fruit flies, black spot, and more recently, sudden death. The goal of this work was to develop a model to predict the occurrence of E. aurantiana, based on monitoring data collected through sexual pheromone traps, and to develop a computer system capable of using such model to generate occurrence predictions and to provide a place for information exchange between citriculturists and the scientific community. Soil type, site temperature, citrus variety, age of plants and use of chemicals to control E. aurantiana influenced the population dynamics of the insect. The highest influence on the citrus fruit borer dynamics was exerted by the soil type, followed by site temperature, citrus variety, age of plants and use of chemicals for E. aurantiana control. The occurrence of E. aurantiana according to temperature is different for each combination of soil type, citrus variety, age of plants and use of chemicals. The model developed can predict the occurrence potential of E. aurantiana according to temperature or months of the year, taking into account soil type, citrus variety, age of plants and chemicals spraying. The elaborated software (BF), designed in R language, includes equations that simulate the various situations of E. aurantiana occurrence. SIAC ("Sistema Integrado de Apoio ao Citricultor") is a system that simplifies the use of the model, does not require previous knowledge on R, and provides a wide range of resources to facilitates the access of citriculturists to information and that of researchers to citriculturists’ problems, thus creating a better interaction between them. The predicting model of citrus fruit borer occurrence can be improved with more frequent and continuous data collecting.

Neste trabalho apresentamos os modelos lineares parciais generalizados com uma variável explicativa contínua tratada de forma não paramétrica e os modelos lineares parciais aditivos generalizados com no mínimo duas variáveis explicativas contínuas tratadas de tal forma. São utilizados os P-splines para descrever a relação da variável resposta com as variáveis explicativas contínuas. Sendo assim, as funções de verossimilhança penalizadas, as funções escore penalizadas e as matrizes de informação de Fisher penalizadas são desenvolvidas para a obtenção das estimativas de máxima verossimilhança penalizadas por meio da combinação do algoritmo backfitting (Gauss-Seidel) e do processo iterativo escore de Fisher para os dois tipos de modelo. Em seguida, são apresentados procedimentos para a estimação do parâmetro de suavização, bem como dos graus de liberdade efetivos. Por fim, com o objetivo de ilustração, os modelos propostos são ajustados à conjuntos de dados reais. / In this work we present the generalized partial linear models with one continuous explanatory variable treated nonparametrically and the generalized additive partial linear models with at least two continuous explanatory variables treated in such a way. The P-splines are used to describe the relationship among the response and the continuous explanatory variables. Then, the penalized likelihood functions, penalized score functions and penalized Fisher information matrices are derived to obtain the penalized maximum likelihood estimators by the combination of the backfitting (Gauss-Seidel) algorithm and the Fisher escoring iterative method for the two types of model. In addition, we present ways to estimate the smoothing parameter as well as the effective degrees of freedom. Finally, for the purpose of illustration, the proposed models are fitted to real data sets.

O mapeamento e a estimação de riscos e incidências são ferramentas muito úteis para a Epidemiologia pois, auxiliam na prevenção de agravos da saúde e, também auxiliam no planejamento e avaliação dos serviços de saúde. Este trabalho busca utilizar uma ferramenta estatística que incorpora de forma adequada este tipo de análise ao estudo de outras características que estejam relacionadas a estes agravos. No presente trabalho utiliza-se como aplicação dados do estudo caso-controle espacial com base populacional de acidentes de trabalho com a proposta de estimar a distribuição espacial do risco de sofrer acidente de trabalho na área urbana do município de Piracicaba/SP entre trabalhadores que se encontravam na situação de precarização do trabalho em associação com outras variáveis de interesse através de modelos aditivos generalizados (MAG) e, através disso, mostrar que ao incorporar de forma explícita o espaço no processo de modelagem dos dados ocorre um ganho significativo na explicação da variação do risco. O modelo MAG utilizado tem variável resposta binomial (caso e controle) e multinomial (caso e controle separados pela gravidade do acidente sofrido). Com os modelos ajustados, mapas foram desenhados com indicações de diferentes cores para a intensidade do risco de sofrer acidente de trabalho. Outra abordagem utilizada para os dados espaciais de acidentes de trabalho foi a INLA (INTEGRATED NESTED LAPLACE APPROXIMATIONS), a qual é utilizada como processo de modelagem para a família dos modelos Gaussianos latentes através de novos métodos para esta família de modelos. A intenção foi mostrar como essa nova abordagem lida com dados do tipo espacial e, fazer uma comparação com a abordagem feita pela modelagem GAM / Mapping and estimation of risks and impacts are very useful tools for Epidemiology at the assistance in prevention of injuries and health, also assists in planning and evaluation of health services. This paper seeks to use a statistical tool that adequately incorporates this type of analysis to the study of other characteristics that are related these illnesses. In the present work is used as application data from case-control study space-based population accidents with the proposal to estimate the spatial distribution of risk of suffering an accident at work in the urban area of Piracicaba/SP among workers who were in employed as casual labor in combination with other variables of interest using generalized additive models (GAM) and, thereby, show that by incorporating explicitly space in the process of data modeling is a gain significant in explaining the variation in risk. The GAM model have used binomial response variable (case and control) and multinomial (case and control separated by the severity of the accident suffered). With the adjusted models, maps were drawn with indications of different colors to the intensity of the risk of accident. Another approach used for spatial data on accidents at work was the INLA (INTEGRATED NESTED LAPLACE APPROXIMATIONS), which is used as a modeling process for the family of latent Gaussian models through new methods for this family of models. The intention was to show how this new approach deals with spatial data and a comparison with the approach made by GAM modeling.

Die vorliegende Dissertationsschrift widmet sich der Beschreibung des Geschwindigkeits-verhaltens von Kraftfahrern auf innerörtlichen Straßen sowie dessen Auswirkungen auf die Verkehrssicherheit. Grundlage bilden manuelle und automatische Querschnittsmessungen von Einzelgeschwindigkeiten in Hauptverkehrs- und Erschließungs¬straßen mit zulässigen Höchstgeschwindigkeiten von 50 bzw. 30 km/h. Die Beschreibung von Wunschgeschwindigkeiten über unterschiedliche Abgrenzungen freifahrender Fahrzeuge, deren Geschwindigkeiten die Grundlage für die folgenden Modelle bilden, sowie die Überprüfung der Übertragbarkeit von Querschnittsmessungen auf die Strecke und die Analyse von Geschwindigkeitsganglinien dienen der Einordnung der in dieser Untersuchung vorgelegten Ergebnisse. Ziel des ersten Teils der Arbeit ist die Beschreibung möglicher Einflussfaktoren aus der Gestaltung, dem Betrieb sowie der Lage im Netz und dem Umfeld einer Straße auf die Wahl der Geschwindigkeit von Pkw-Fahrern. Erste Ansätze werden aus dem Vergleich von fahrtrichtungsbezogenen Geschwindigkeiten an einem Querschnitt mit asymmetrischer Gestaltung abgeleitet. Auf Basis querschnittsbezogener mittlerer und v85-Geschwindigkeiten werden verschiedene multiple Regressionsmodelle aufgestellt und miteinander verglichen. Die Modelle basieren auf Messungen im Straßennetz Dresdens und werden anhand von Messungen aus anderen deutschen Städten validiert. Signifikante Einflussgrößen ergeben sich aus den Bereichen Verkehrsbedeutung, Querschnittsgestaltung, Umfeldnutzung und Fahrbahnoberfläche eines Straßenquerschnitts. Die Einflussgrößen sowie deren Abhängigkeiten untereinander werden diskutiert und Potenziale für Maßnahmen zur Geschwindigkeitsreduzierung aufgezeigt. Im zweiten Teil der Arbeit werden für Tempo-50-Straßen verallgemeinerte lineare Modelle zur Beschreibung des Einflusses der Geschwindigkeit auf die Verkehrssicherheit abgeleitet. Für unterschiedliche Unfallkollektive bezüglich räumlicher Abgrenzung, Unfallschwere und Verkehrsbeteiligung wird der Geschwindigkeitseinfluss auf die Unfallzahl anhand einer Potenzfunktion (Power-Modell) unter Kontrolle der Randbedingungen Verkehrsaufkommen des motorisierten Individual-verkehrs und Umfeldnutzung beschrieben. Die Zahl der Unfälle mit Personenschaden steigt progressiv mit der mittleren Geschwindigkeit und degressiv mit dem DTV an. / Driving speeds of personal vehicles on urban roads are analyzed and their influence on traffic safety is modeled. The speed data is measured at cross sections on major and minor roads with speed limits of 50 and 30 km/h. Different kinds of classification of free-flow-vehicles were analyzed for the description of the desired speed of a driver. Also local speeds along road sections as well as time variation curves of driving speeds are documented in order to interpret and classify the provided findings. The first part of this work deals with the prediction of local driving speeds based on parameters of the roadway environment determining road design as well as the land-use next to the road. One first simple approach is to compare both driving directions at non-symmetric cross sections. Then several multiple regression models for mean speeds and 85-percentiles of the speed distribution are estimated and compared with each other. The models are based on the road network of the city of Dresden and are validated with speed measurements in other German cities. Road classification, cross section characteristics, land-use and the road surface condition are found to be significant parameters that correlate with driving speed. The possible influences on the choice of speed and their interdependencies as well as their practical relevance are discussed. In the second part of this work the influence of speeds on the occurrence of traffic accidents is estimated using Generalized Linear Models. This is done for different accident groups under consideration of the annual daily traffic and a parameter that describes the length and type of land-use of the adjacent buildings next to the road section. The relationship between speed and accident counts can be described using a power function. Accident numbers rise progressively with increasing speeds and rise in a declining manner with increasing amount of traffic.

No description available.

Elasmobranchs are among the oldest and most successful predators in the ocean, yet one of the most vulnerable to the direct and indirect effects of fishing. Many populations are rapidly declining around the world, and an increasing number is listed as threatened or endangered. The broader ecosystem consequences of these declines, and whether other marine predators can replace sharks, are open questions. In this thesis, I used a diverse set of data and modeling techniques to analyze long-term changes in elasmobranch populations in the Mediterranean Sea, and the consequences of shark declines on marine ecosystems. Because of its long history of fishing, the Mediterranean offers a unique perspective on the response of marine communities to exploitation over long time scales. Here, I reconstructed the history of elasmobranch exploitation over the past 200 years in pelagic, coastal and demersal communities. Results were combined meta-analytically to derive a general pattern of change for the entire region. Overall, I detected multiple cases of regional species extirpations, a strong correlation between historical intensity of exploitation and the stage of community degradation, and some cases of compensatory species increases. My results suggest that compared to other marine ecosystems worldwide, the Mediterranean Sea might be in an advanced stage of overexploitation. To gain more general conclusions about the patterns and consequences of shark declines in the ocean, I reviewed and reanalyzed documented changes in exploited elasmobranch communities around the world, and synthesized the effects of sharks on their prey and wider communities. This work revealed that sharks are abundant and diverse in little exploited or unexploited marine ecosystems but vulnerable to even light levels of fishing. The decline in large sharks has reduced natural mortality in a range of their prey, contributing to changes in abundance, distribution, and behaviour of marine megafauna that have few other predators. In some cases, this has resulted in cascading changes in prey populations and food-web structure. Overall, my thesis greatly enhanced our knowledge about the critical state of elasmobranchs in the Mediterranean Sea and the consequences of the declines of these important marine predators on marine ecosystems.

En écologie, dans le cadre par exemple d’études des services fournis par les écosystèmes, les modélisations descriptive, explicative et prédictive ont toutes trois leur place distincte. Certaines situations bien précises requièrent soit l’un soit l’autre de ces types de modélisation ; le bon choix s’impose afin de pouvoir faire du modèle un usage conforme aux objectifs de l’étude. Dans le cadre de ce travail, nous explorons dans un premier temps le pouvoir explicatif de l’arbre de régression multivariable (ARM). Cette méthode de modélisation est basée sur un algorithme récursif de bipartition et une méthode de rééchantillonage permettant l’élagage du modèle final, qui est un arbre, afin d’obtenir le modèle produisant les meilleures prédictions. Cette analyse asymétrique à deux tableaux permet l’obtention de groupes homogènes d’objets du tableau réponse, les divisions entre les groupes correspondant à des points de coupure des variables du tableau explicatif marquant les changements les plus abrupts de la réponse. Nous démontrons qu’afin de calculer le pouvoir explicatif de l’ARM, on doit définir un coefficient de détermination ajusté dans lequel les degrés de liberté du modèle sont estimés à l’aide d’un algorithme. Cette estimation du coefficient de détermination de la population est pratiquement non biaisée. Puisque l’ARM sous-tend des prémisses de discontinuité alors que l’analyse canonique de redondance (ACR) modélise des gradients linéaires continus, la comparaison de leur pouvoir explicatif respectif permet entre autres de distinguer quel type de patron la réponse suit en fonction des variables explicatives. La comparaison du pouvoir explicatif entre l’ACR et l’ARM a été motivée par l’utilisation extensive de l’ACR afin d’étudier la diversité bêta. Toujours dans une optique explicative, nous définissons une nouvelle procédure appelée l’arbre de régression multivariable en cascade (ARMC) qui permet de construire un modèle tout en imposant un ordre hiérarchique aux hypothèses à l’étude. Cette nouvelle procédure permet d’entreprendre l’étude de l’effet hiérarchisé de deux jeux de variables explicatives, principal et subordonné, puis de calculer leur pouvoir explicatif. L’interprétation du modèle final se fait comme dans une MANOVA hiérarchique. On peut trouver dans les résultats de cette analyse des informations supplémentaires quant aux liens qui existent entre la réponse et les variables explicatives, par exemple des interactions entres les deux jeux explicatifs qui n’étaient pas mises en évidence par l’analyse ARM usuelle. D’autre part, on étudie le pouvoir prédictif des modèles linéaires généralisés en modélisant la biomasse de différentes espèces d’arbre tropicaux en fonction de certaines de leurs mesures allométriques. Plus particulièrement, nous examinons la capacité des structures d’erreur gaussienne et gamma à fournir les prédictions les plus précises. Nous montrons que pour une espèce en particulier, le pouvoir prédictif d’un modèle faisant usage de la structure d’erreur gamma est supérieur. Cette étude s’insère dans un cadre pratique et se veut un exemple pour les gestionnaires voulant estimer précisément la capture du carbone par des plantations d’arbres tropicaux. Nos conclusions pourraient faire partie intégrante d’un programme de réduction des émissions de carbone par les changements d’utilisation des terres. / In ecology, in ecosystem services studies for example, descriptive, explanatory and predictive modelling all have relevance in different situations. Precise circumstances may require one or the other type of modelling; it is important to choose the method properly to insure that the final model fits the study’s goal. In this thesis, we first explore the explanatory power of the multivariate regression tree (MRT). This modelling technique is based on a recursive bipartitionning algorithm. The tree is fully grown by successive bipartitions and then it is pruned by resampling in order to reveal the tree providing the best predictions. This asymmetric analysis of two tables produces homogeneous groups in terms of the response that are constrained by splitting levels in the values of some of the most important explanatory variables. We show that to calculate the explanatory power of an MRT, an appropriate adjusted coefficient of determination must include an estimation of the degrees of freedom of the MRT model through an algorithm. This estimation of the population coefficient of determination is practically unbiased. Since MRT is based upon discontinuity premises whereas canonical redundancy analysis (RDA) models continuous linear gradients, the comparison of their explanatory powers enables one to distinguish between those two patterns of species distributions along the explanatory variables. The extensive use of RDA for the study of beta diversity motivated the comparison between its explanatory power and that of MRT. In an explanatory perspective again, we define a new procedure called a cascade of multivariate regression trees (CMRT). This procedure provides the possibility of computing an MRT model where an order is imposed to nested explanatory hypotheses. CMRT provides a framework to study the exclusive effect of a main and a subordinate set of explanatory variables by calculating their explanatory powers. The interpretation of the final model is done as in nested MANOVA. New information may arise from this analysis about the relationship between the response and the explanatory variables, for example interaction effects between the two explanatory data sets that were not evidenced by the usual MRT model. On the other hand, we study the predictive power of generalized linear models (GLM) to predict individual tropical tree biomass as a function of allometric shape variables. Particularly, we examine the capacity of gaussian and gamma error structures to provide the most precise predictions. We show that for a particular species, gamma error structure is superior in terms of predictive power. This study is part of a practical framework; it is meant to be used as a tool for managers who need to precisely estimate the amount of carbon recaptured by tropical tree plantations. Our conclusions could be integrated within a program of carbon emission reduction by land use changes.