Os modelos multiníveis representam uma classe de modelos utilizada para ajustes de dados que apresentam estrutura de hierarquia. O presente trabalho propõe uma generalizacão dos modelos normais multiníveis, denominada modelos elípticos multiníveis. Esta proposta sugere o uso de distribuicões de probabilidade pertencentes à classe elíptica, envolvendo portanto todas as distribuições contínuas simétricas, incluindo a distribuição normal como caso particular. As distribuições elípticas podem apresentar caudas mais leves ou mais pesadas que as caudas da distribuição normal. No caso da presença de observações aberrantes, é sugerido o uso de distribuições com caudas pesadas no intuito de obter um melhor ajuste do modelo aos dados considerados discrepantes. Nesta dissertação, alguns aspectos dos modelos elípticos multiníveis são desenvolvidos, como o processo de estimação dos parâmetros via máxima verossimilhança, testes de hipóteses para os efeitos fixos e parâmetros de variância e covariância e análise de resíduos para verificação de características relacionadas aos ajustes e às suposições estabelecidas. / Multilevel models represent a class of models used to adjust data which have hierarchical structure. The present work proposes a generalization of the multilevel normal models, named multilevel elliptical models. This proposal suggests the use of probability distributions belonging to the elliptical class, thus involving all symmetric continuous distributions, including the normal distribution as a particular case. Elliptical distributions may have lighter or heavier tails than the normal ones. In case of presence of outlying observations, it is suggested the use of heavy-tailed distributions in order to obtain a better fitted model to the discrepant observations. In this dissertation some aspects of the multilevel elliptical models are developed, such as the process of parameter estimation by maximum likelihood, hypothesis tests for fixed effects and variance-covariance parameters and residual analysis to check features related to the fitting and established assumptions.

The persistence of shame-based reactions to child maltreatment (CM) has been associated with poor posttraumatic adjustment. Despite evidence that the postpartum period is a vulnerable time for women with CM histories, little is known about the consequences of maltreatment-specific (MS) shame for postpartum functioning. The current study examined individual differences in MS shame among a sample of women during the postpartum period (n = 100) as well as prospective relations from MS shame to postpartum psychopathology at 6-, 12-, 15-, and 18-month postpartum. Linear growth curve (LGC) analyses showed that MS shame predicted higher levels of depression symptoms but not post-traumatic stress disorder (PTSD) symptoms at all time points whereas path analyses showed that shame mediated the relations from multi-maltreatment to both depression and PTSD symptoms at all time points. Results point to the long-term consequences of MS shame during postpartum and the importance of attending to shame in clinical care of maltreatment survivors who present with postpartum psychopathology.

Rumberger (2020) observed that "dropping out of school has economic and social consequences both for dropouts themselves and for the country as a whole" (p. 151). Every year, many Brazilians drop out of school due to work, early pregnancies, marriage, drug consumption, crime, etc. Dropping out of school can occur due to learning challenges, poor attendance, discipline problems, or a lack of access to high school institutions. Dropouts can experience depression and anxiety and are more likely to attempt suicide. The present dissertation includes two different papers about dropouts. The first paper uses fixed effect regression to show the main characteristics of dropouts who both left high school before completing it and registered for the Brazilian National Exam (ENEM). The results demonstrate that dropouts who take the ENEM are males, hail from low-income families, are younger (less than 17 years old), and are less likely to possess computers. When analyzing the 2015 and 2016 data set, which included dropouts who took the ENEM to receive high school certification, the results show that thew are more likely to have dropped out of school during their basic education (1st to 9th grade). In the second paper, I evaluated differences in achievement "between dropout registrants and current students, and dropout registrants and graduates" each comparison using the same data set (ENEM), but restricted to 2015 and 2016, due to the availability of a larger number of predictive variables of dropouts. The results indicate that dropout registrants did worse than all groups in essay writing but performed similarly to current students in math and language in 2016. When comparing the achievement of dropout registrants and graduates, the results show more pronounced differences, but in essay writing, the effect size varied from 0.22SD to 0.35SD.

Yes / The complex healthcare system that provides patients with medicines places them at risk when care is transferred between healthcare organisations, for example discharge from hospital. Consequently, under-standing and improving medicines management, particularly at care transfers, is a priority.Objectives: This study aimed to explore the medicines management system as patients experience it and determine differences in the patient-perceived importance of people in the system.Methods: We used a Social Network Analysis framework, collecting ego-net data about the importance of people patients had contact with concerning their medicines after hospital discharge. Single- and multi-level logistic regression models of patients' networks were constructed, and model residuals were explored at the patient level.This enabled us to identify patients' networks with support tie patterns different from the general patterns suggested by the model results. Qualitative data for those patients were then analysed to understand their differing experiences.Results: Networks comprised clinical and administrative healthcare staff and friends and family members.Networks were highly individual and the perceived importance of alters varied both within and between patients. Ties to spouses were significantly more likely to be rated as highly important and ties to community pharmacy staff (other than pharmacists) and to GP receptionists were less likely to be highly rated. Patients with low-value medicines management networks described having limited information about their medicines and alack of understanding or help. Patients with high-value networks described appreciating support and having confidence in staff.Conclusions: Patients experienced medicines management as individual systems within which they interacted with healthcare staff and informal support to manage their treatment. Multilevel models indicated that there are unexplained variables impacting on patients' assessments of their medicines management networks. Qualitative exploration of the model residuals can offer an understanding of networks that do not have the typical range of support ties. / National Institute for Health Research (NIHR) Yorkshire and Humber Patient Safety Translational Research Centre (NIHR Yorkshire and Humber PSTRC)

Bien que les données soient relativement rares, les élèves français semblent particulièrement anxieux en milieu scolaire (OCDE, 2014). Parallèlement, un grand nombre d’entre eux présentent d’importantes lacunes dans la maitrise des savoirs élémentaires, notamment en compréhension de l’écrit (OCDE, 2011), habileté pourtant indispensable à toute forme d’apprentissage comme à l’insertion sociale et professionnelle. Ce double constat fonde le présent travail. En effet, nous nous interrogeons sur le rôle joué par l’anxiété dans la variabilité des acquisitions des élèves en lecture. Si la littérature sur les anxiétés académiques compte d’innombrables travaux relatifs à l’anxiété face aux mathématiques (e.g., Ashcraft & Moore, 2009) ou en contexte évaluatif (e.g., Pekrun & Stephens, 2015), aucun d’entre eux n’envisage l’existence d’anxiétés spécifiques à la lecture ou à l’environnement scolaire, plus largement. Nous avons précisément choisi de nous acquitter de cette tâche et de rendre compte de leurs effets au plan des performances en compréhension écrite et en fluence de lecture. Pour cela, nous avons mené deux études longitudinales impliquant plusieurs centaines d’élèves de CM2 et de 6ème. Dans la première, nous avons eu recours à des modélisations multiniveaux et avons montré que l’anxiété à l’égard du contexte scolaire entretient une relation quadratique avec la compréhension écrite à la fin de l’école primaire. Nous avons, de plus, montré que les croyances d’efficacité personnelle pouvaient partiellement médiatiser cet effet. Dans la seconde, l’usage de modèles multiniveaux de croissance nous a permis de révélé que l’anxiété en lecture conditionne le rythme de progression des performances en fluence des élèves suivis en CM2 et en 6ème. / Although data are quite rare, French pupils seem particularly anxious in school (OCDE, 2014). A significant number of them also show important gaps in elementary abilities – such as written comprehension (OCDE, 2011) – that are yet crucial for any form of learning as much as for social and professional insertion. The present research emerges from both these observations. We interrogate the effect of anxiety on the variability of students’ acquisitions in reading. Numerous research have been lead on academic anxiety related to mathematics (e.g., Ashcraft & Moore, 2009) or evaluation context (e.g., Pekrun & Stephens, 2015). But none have considered the existence of specific anxieties related either to reading or to academic environment. We tackle this task by giving an account of the effects of these two specific academic anxieties on reading comprehension and reading fluency. To do so, we led two longitudinal studies involving several hundreds of 5th and 6th graders. In the first study, we used multilevel models and have shown that anxiety related to academic context has a quadratic relation with reading comprehension at the end of primary school. Moreover, we have shown that self-efficacy beliefs could partially mediate this effect. In the second study, the use of growth curve models underline that anxiety related to reading helps to predict, for the pupils followed up in 5th and 6th grade, the rhythm of progression of their fluency performances.

Um dos temas mais discutidos na área de finanças é a forma como os mercados se estruturam sob perspectiva informacional, precificando ativos financeiros. Uma das teorias centrais de discussão é a Hipótese de Eficiência dos Mercados (HEM) de Eugene Fama (1970), derivada da teoria de utilidade. Um dos pontos centrais de discussão e critica da HEM são seus pressupostos quanto à modelagem do comportamento humano, totalmente racional e oportunista. Uma segunda linha de estudos apresenta um contraponto a esse modelo de ser humano utilizado nas teorias neoclássicas de finanças, utilizando um modelo de agente que possui falhas no processo de tomada de decisão financeira em função de uma racionalidade limitada e de vieses cognitivos, que impactam sobre o preço dos ativos negociados (Tversky & Kahneman, 1979; Thaler, 1985). A Hipótese de Mercados Adaptativos (HMA), de Andrew Lo (2004, 2005), é uma das teorias que conciliam a estrutura neoclássica da HEM com o comportamento não ótimo do agente, considerando novas estruturas de tomada de decisão financeira pelo investidor, como aprendizado, adaptação e vieses comportamentais, apresentando dinâmicas de mercado semelhantes a características biológicas, com impactos do ambiente e seleção natural como direcionadores da eficiência dos mercados. Desta forma, esse trabalho tem como objetivo verificar se existe aderência do conceito de evolução e do impacto do ambiente macroeconômico sobre a eficiência informacional dos mercados financeiros, verificando a capacidade de adaptação do mercado a mudanças do ambiente, e quais fatores apresentam maior grau de explicação no processo de adaptação e eficiência dos mercados em diferentes países. Para isso foram analisados os índices de preços e retornos de 48 economias, assim como informações econômico-institucionais sobre os países aos quais estavam relacionados, por meio do desenvolvimento de uma métrica de ineficiência informacional relativa dos mercados e posterior análise por meio de modelos descritivos e multinível. Foi identificado que há comportamentos cíclicos de eficiência ao longo do tempo, e os graus de eficiência diferem-se entre as economias estudadas, assim como há evidências de que há variação do comportamento de eficiência quando da mudança do cenário econômico. Adicionalmente foi identificado que características ambientais (como instituições e comportamento geral da economia) também apresentam efeitos sobre o grau de ineficiência relativa de mercados, e sua relação está associada ao comportamento previsto na HMA. / One of the most discussed topics in finance research is the way of markets are structured from an informational perspective, pricing financial assets. One of the central theories of discussion is Eugene Fama\'s Market Efficiency Hypothesis (HEM) (1970), derived from utility theory. One of the central points of discussion and critics of HEM is its assumptions about the modeling of human behavior, totally rational and opportunistic. The second line of studies shows a counterpoint to this model of human behavior used in neoclassical finance theories, by an agent model that has flaws in financial decision-making process due to a bounded rationality and cognitive biases impacting on the price of the traded assets (Tversky & Kahneman, 1979; Thaler, 1985). The Andrew Lo\'s (2004, 2005) Adaptive Market Hypothesis (HMA) is one of the theories that reconcile the neoclassical structure of HEM with the agent\'s non-optimal behavior, considering new structures of financial decision-making by the investor, such as learning, adaptation and behavioral biases, presenting market dynamics like biological characteristics with environmental impacts and natural selection as drivers of market efficiency. In this way, the objective of this work is to verify if there is adherence to the concept of evolution and the impact of the macroeconomic environment on the informational efficiency of the financial markets, observing the adaptability of the market to changes in the environment, and which factors present a greater degree of explanation in the process of adaptation and efficiency of markets in different countries. To do so, we analyzed the price and return indices of 48 economies, as well as economic-institutional information about the related countries, through the development of a metric of relative informational inefficiency and subsequent analysis through descriptive and multilevel models. It has been identified that there are cyclical efficiency behaviors over time, and the efficiency levels differ between the studied economies, and evidence about the changes in the efficiency behavior when the economic scenario changes. Additionally, it was identified that environmental characteristics (such as institutions and general economic behavior) also have effects on the degree of relative market inefficiency, and their relation is associated with the behavior predicted in the HMA

Quando um conjunto de dados possui uma estrutura hierárquica, uma possível abordagem são os modelos de regressão multiníveis, que se justifica pelo fato de haver uma porção significativa da variabilidade dos dados que pode ser explicada por níveis macro. Neste trabalho, desenvolvemos a seleção de modelos de regressão multinível aplicados a dados educacionais. Esta análise divide-se em duas partes: seleção de variáveis e seleção de modelos. Esta última subdivide-se em dois casos: modelagem clássica e modelagem bayesiana. Buscamos através de critérios como o Lasso, AIC, BIC, WAIC entre outros, encontrar quais são os fatores que influenciam no desempenho em matemática dos alunos do nono ano do ensino fundamental do estado de São Paulo. Também investigamos o funcionamento de cada um dos critérios de seleção de variáveis e de modelos. Foi possível concluir que, sob a abordagem frequentista, o critério de seleção de modelos BIC é o mais eficiente, já na abordagem bayesiana, o critérioWAIC apresentou melhores resultados. Utilizando o critério de seleção de variáveis Lasso para abordagem clássica, houve uma diminuição de 34% dos preditores do modelo. Por fim, identificamos que o desempenho em matemática dos estudantes do nono ano do ensino fundamental do estado de São Paulo é influenciado pelas seguintes covariáveis: grau de instrução da mãe, frequência de leitura de livros, tempo gasto com recreação em dia de aula, o fato de gostar de matemática, o desempenho em matemática global da escola, desempenho em língua portuguesa do aluno, dependência administrativa da escola, sexo, grau de instrução do pai, reprovações e distorção idade-série. / When a dataset contains a hierarchical data structure, a possible approach is the multilevel regression modelling, which is justified by the significative amout of the data variability that can be explained by macro level processes. In this work, a selection of multilevel regression models for educational data is developed. This analysis is divided into two parts: variable selection and model selection. The latter is subdivided into two categories: classical and Bayesian modeling. Traditional criteria for model selection such as Lasso, AIC, BIC, and WAIC, among others are used in this study as an attempt to identify the factors influencing ninth grade students performance in Mathematics of elementary education in the State of São Paulo. Likewise, an investigation was conducted to evaluate the performance of each variable selection criteria and model selection methods applied to fitted models that will be mentioned throughout this work. It was possible to conclude that, under the frequentist approach, BIC is the most efficient, whereas under the bayesian approach, WAIC presented better results. Using Lasso under the frequentist approach, a decrease of 34% on the number of predictors was observed. Finally, we identified that the performance in Mathematics of students in the ninth year of elementary school in the state of São Paulo is most influenced by the following covariates: mothers educational level, frequency of book reading, time spent with recreation in classroom, the fact of liking Math, school global performance in Mathematics, performance in Portuguese, school administrative dependence, gender, fathers educational degree, failures and age-grade distortion.

Um dos temas mais discutidos na área de finanças é a forma como os mercados se estruturam sob perspectiva informacional, precificando ativos financeiros. Uma das teorias centrais de discussão é a Hipótese de Eficiência dos Mercados (HEM) de Eugene Fama (1970), derivada da teoria de utilidade. Um dos pontos centrais de discussão e critica da HEM são seus pressupostos quanto à modelagem do comportamento humano, totalmente racional e oportunista. Uma segunda linha de estudos apresenta um contraponto a esse modelo de ser humano utilizado nas teorias neoclássicas de finanças, utilizando um modelo de agente que possui falhas no processo de tomada de decisão financeira em função de uma racionalidade limitada e de vieses cognitivos, que impactam sobre o preço dos ativos negociados (Tversky & Kahneman, 1979; Thaler, 1985). A Hipótese de Mercados Adaptativos (HMA), de Andrew Lo (2004, 2005), é uma das teorias que conciliam a estrutura neoclássica da HEM com o comportamento não ótimo do agente, considerando novas estruturas de tomada de decisão financeira pelo investidor, como aprendizado, adaptação e vieses comportamentais, apresentando dinâmicas de mercado semelhantes a características biológicas, com impactos do ambiente e seleção natural como direcionadores da eficiência dos mercados. Desta forma, esse trabalho tem como objetivo verificar se existe aderência do conceito de evolução e do impacto do ambiente macroeconômico sobre a eficiência informacional dos mercados financeiros, verificando a capacidade de adaptação do mercado a mudanças do ambiente, e quais fatores apresentam maior grau de explicação no processo de adaptação e eficiência dos mercados em diferentes países. Para isso foram analisados os índices de preços e retornos de 48 economias, assim como informações econômico-institucionais sobre os países aos quais estavam relacionados, por meio do desenvolvimento de uma métrica de ineficiência informacional relativa dos mercados e posterior análise por meio de modelos descritivos e multinível. Foi identificado que há comportamentos cíclicos de eficiência ao longo do tempo, e os graus de eficiência diferem-se entre as economias estudadas, assim como há evidências de que há variação do comportamento de eficiência quando da mudança do cenário econômico. Adicionalmente foi identificado que características ambientais (como instituições e comportamento geral da economia) também apresentam efeitos sobre o grau de ineficiência relativa de mercados, e sua relação está associada ao comportamento previsto na HMA. / One of the most discussed topics in finance research is the way of markets are structured from an informational perspective, pricing financial assets. One of the central theories of discussion is Eugene Fama\'s Market Efficiency Hypothesis (HEM) (1970), derived from utility theory. One of the central points of discussion and critics of HEM is its assumptions about the modeling of human behavior, totally rational and opportunistic. The second line of studies shows a counterpoint to this model of human behavior used in neoclassical finance theories, by an agent model that has flaws in financial decision-making process due to a bounded rationality and cognitive biases impacting on the price of the traded assets (Tversky & Kahneman, 1979; Thaler, 1985). The Andrew Lo\'s (2004, 2005) Adaptive Market Hypothesis (HMA) is one of the theories that reconcile the neoclassical structure of HEM with the agent\'s non-optimal behavior, considering new structures of financial decision-making by the investor, such as learning, adaptation and behavioral biases, presenting market dynamics like biological characteristics with environmental impacts and natural selection as drivers of market efficiency. In this way, the objective of this work is to verify if there is adherence to the concept of evolution and the impact of the macroeconomic environment on the informational efficiency of the financial markets, observing the adaptability of the market to changes in the environment, and which factors present a greater degree of explanation in the process of adaptation and efficiency of markets in different countries. To do so, we analyzed the price and return indices of 48 economies, as well as economic-institutional information about the related countries, through the development of a metric of relative informational inefficiency and subsequent analysis through descriptive and multilevel models. It has been identified that there are cyclical efficiency behaviors over time, and the efficiency levels differ between the studied economies, and evidence about the changes in the efficiency behavior when the economic scenario changes. Additionally, it was identified that environmental characteristics (such as institutions and general economic behavior) also have effects on the degree of relative market inefficiency, and their relation is associated with the behavior predicted in the HMA

My doctoral research dissertation focuses on two aspects of functional data analysis (FDA): FDA under spatial interdependence and FDA for multi-level data. The first part of my thesis focuses on developing modeling and inference procedure for functional data under spatial dependence. The methodology introduced in this part is motivated by a research study on inequities in accessibility to financial services. The first research problem in this part is concerned with a novel model-based method for clustering random time functions which are spatially interdependent. A cluster consists of time functions which are similar in shape. The time functions are decomposed into spatial global and time-dependent cluster effects using a semi-parametric model. We also assume that the clustering membership is a realization from a Markov random field. Under these model assumptions, we borrow information across curves from nearby locations resulting in enhanced estimation accuracy of the cluster effects and of the cluster membership. In a simulation study, we assess the estimation accuracy of our clustering algorithm under a series of settings: small number of time points, high noise level and varying dependence structures. Over all simulation settings, the spatial-functional clustering method outperforms existing model-based clustering methods. In the case study presented in this project, we focus on estimates and classifies service accessibility patterns varying over a large geographic area (California and Georgia) and over a period of 15 years. The focus of this study is on financial services but it generally applies to any other service operation. The second research project of this part studies an association analysis of space-time varying processes, which is rigorous, computational feasible and implementable with standard software. We introduce general measures to model different aspects of the temporal and spatial association between processes varying in space and time. Using a nonparametric spatiotemporal model, we show that the proposed association estimators are asymptotically unbiased and consistent. We complement the point association estimates with simultaneous confidence bands to assess the uncertainty in the point estimates. In a simulation study, we evaluate the accuracy of the association estimates with respect to the sample size as well as the coverage of the confidence bands. In the case study in this project, we investigate the association between service accessibility and income level. The primary objective of this association analysis is to assess whether there are significant changes in the income-driven equity of financial service accessibility over time and to identify potential under-served markets. The second part of the thesis discusses novel statistical methodology for analyzing multilevel functional data including a clustering method based on a functional ANOVA model and a spatio-temporal model for functional data with a nested hierarchical structure. In this part, I introduce and compare a series of clustering approaches for multilevel functional data. For brevity, I present the clustering methods for two-level data: multiple samples of random functions, each sample corresponding to a case and each random function within a sample/case corresponding to a measurement type. A cluster consists of cases which have similar within-case means (level-1 clustering) or similar between-case means (level-2 clustering). Our primary focus is to evaluate a model-based clustering to more straightforward hard clustering methods. The clustering model is based on a multilevel functional principal component analysis. In a simulation study, we assess the estimation accuracy of our clustering algorithm under a series of settings: small vs. moderate number of time points, high noise level and small number of measurement types. We demonstrate the applicability of the clustering analysis to a real data set consisting of time-varying sales for multiple products sold by a large retailer in the U.S. My ongoing research work in multilevel functional data analysis is developing a statistical model for estimating temporal and spatial associations of a series of time-varying variables with an intrinsic nested hierarchical structure. This work has a great potential in many real applications where the data are areal data collected from different data sources and over geographic regions of different spatial resolution.

The starting point of this research is the question, may reading acquisition be more or less effective depending on the language in which it is perform? Two categories for classifying the languages have been developed. First the notion of linguistic family is employed to describe the languages from a cultural and historical perspective. Secondly, the notion of orthographic depth is used for differentiating the languages according to the correspondence between orthography and phonetic. These categories have been related to the databases PIRLS 2001 and 2006 (international assessments about reading developed by the IEA), the aim being to connect reading achievement to the language in which students answered the test. However, it is clear that the language is not an isolated factor, but part of a complex structure of determinants of reading. Therefore, factors related to students and schools have also been incorporated to this research. Moreover, the multidimensionality of the reading process has been taken into account by distinguishing in the analysis the different aspects that made the process according to PIRLS: informative reading, literary reading, process comprehension of high and low order. To answer to the questions proposed by this research a hierarchical statistical model (multilevel) was developed, it was able to account for the connection between reading achievement, language and other associated factors. As a result, contextual factors (home and school) were more significant than language. Moreover, determinacy may vary if taking into account educational systems.