Les modèles d'équations structurelles à variables latentes permettent de modéliser des relations entre des variables observables et non observables. Les deux paradigmes actuels d'estimation de ces modèles sont les méthodes de moindres carrés partiels sur composantes et l'analyse de la structure de covariance. Dans ce travail, après avoir décrit les deux principales méthodes d'estimation que sont PLS et LISREL, nous proposons une approche d'estimation fondée sur la maximisation par algorithme EM de la vraisemblance globale d'un modèle à facteurs latents et à une équation structurelle. Nous en étudions les performances sur des données simulées et nous montrons, via une application sur des données réelles environnementales, comment construire pratiquement un modèle et en évaluer la qualité. Enfin, nous appliquons l'approche développée dans le contexte d'un essai clinique en cancérologie pour l'étude de données longitudinales de qualité de vie. Nous montrons que par la réduction efficace de la dimension des données, l'approche EM simplifie l'analyse longitudinale de la qualité de vie en évitant les tests multiples. Ainsi, elle contribue à faciliter l'évaluation du bénéfice clinique d'un traitement. / Structural equation models enable the modeling of interactions between observed variables and latent ones. The two leading estimation methods are partial least squares on components and covariance-structure analysis. In this work, we first describe the PLS and LISREL methods and, then, we propose an estimation method using the EM algorithm in order to maximize the likelihood of a structural equation model with latent factors. Through a simulation study, we investigate how fast and accurate the method is, and thanks to an application to real environmental data, we show how one can handly construct a model or evaluate its quality. Finally, in the context of oncology, we apply the EM approach on health-related quality-of-life data. We show that it simplifies the longitudinal analysis of quality-of-life and helps evaluating the clinical benefit of a treatment.

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Introdução: O número de estudos relacionados à Síndrome Metabólica (SM) vem aumentando nos últimos anos, muitas vezes motivados pelo aumento do número de casos de sobrepeso/obesidade e diabetes Tipo II levando ao desenvolvimento de doenças cardiovasculares e, como consequência, infarto agudo do miocárdio e AVC, dentre outros desfechos desfavoráveis. A SM é uma doença multifatorial composta de cinco características, porém, para que um indivíduo seja diagnosticado com ela, possuir pelo menos três dessas características torna-se condição suficiente. Essas cinco características são: Obesidade visceral, caracterizada pelo aumento da circunferência da cintura, Glicemia de jejum elevada, Triglicérides aumentado, HDL-colesterol reduzido, Pressão Arterial aumentada. Objetivo: Estabelecer a rede de associações entre os fenótipos que compõem a Síndrome Metabólica através do aprendizado de estruturas de dependência, decompor a rede em componentes de correlação genética e ambiental e avaliar o efeito de ajustes por covariáveis e por variantes genéticas exclusivamente relacionadas à cada um dos fenótipos da rede. Material e Métodos: A amostra do estudo corresponderá a 79 famílias da cidade mineira de Baependi, composta por 1666 indivíduos. O aprendizado de estruturas de redes será feito por meio da Teoria de Grafos e Modelos de Equações Estruturais envolvendo o modelo linear misto poligênico para determinar as relações de dependência entre os fenótipos que compõem a Síndrome Metabólica / Introduction: The number of studies related to Metabolic Syndrome (MetS) has been increasing in the last years, encouraged by the increase on the overweight / obesity and Type II Diabetes cases, leading to the development of cardiovascular disease and, therefore, acute myocardial infarction and stroke, and others unfavorable outcomes. MetS is a multifactorial disease containing five characteristics, however, for an individual to be diagnosed with MetS, he/she may have at least three of them. These characteristics are: Truncal Obesity, characterized by increasing on the waist circumference, increasing on Fasting Blood Glucose, increasing on Triglycerides, decreasing on HDL cholesterol and increasing on Blood Pressure. Aims: Establish the best association network between MetS phenotypes through structured dependency learning between phenotypes considering genetic variants exclusively related to each phenotype. Materials and Methods: The study sample is composed of 79 families, 1666 individuals of a city in a rural area of Brazil, called Beapendi. Structured learning will use graph theory and Structural Equations Models to establish the dependency relations between MetS phenotypes

The estimation of latent variable models with ordinal and continuous, or ranking variables is the research focus of this thesis. The existing estimation methods are discussed and a composite likelihood approach is developed. The main advantages of the new method are its low computational complexity which remains unchanged regardless of the model size, and that it yields an asymptotically unbiased, consistent, and normally distributed estimator. The thesis consists of four papers. The first one investigates the two main formulations of the unrestricted Thurstonian model for ranking data along with the corresponding identification constraints. It is found that the extra identifications constraints required in one of them lead to unreliable estimates unless the constraints coincide with the true values of the fixed parameters. In the second paper, a pairwise likelihood (PL) estimation is developed for factor analysis models with ordinal variables. The performance of PL is studied in terms of bias and mean squared error (MSE) and compared with that of the conventional estimation methods via a simulation study and through some real data examples. It is found that the PL estimates and standard errors have very small bias and MSE both decreasing with the sample size, and that the method is competitive to the conventional ones. The results of the first two papers lead to the next one where PL estimation is adjusted to the unrestricted Thurstonian ranking model. As before, the performance of the proposed approach is studied through a simulation study with respect to relative bias and relative MSE and in comparison with the conventional estimation methods. The conclusions are similar to those of the second paper. The last paper extends the PL estimation to the whole structural equation modeling framework where data may include both ordinal and continuous variables as well as covariates. The approach is demonstrated through an example run in R software. The code used has been incorporated in the R package lavaan (version 0.5-11).

The dissertation “Informal Economic Activities” takes a comprehensive approach to the informal economy by studying traditional shadow economic activities, household DIY activities, and the smuggling of illegal and legal goods. Chapter 2 analyzes shadow economic and DIY activities and presents a dual estimation for the development of both types of informal economic activities in Germany from 1970 to 2005. It also considers the impact of German reunification on shadow economic and DIY activities and employs a proper estimate of domestic currency in circulation within Germany as an indicator variable for the shadow economy. Chapter 3 studies an informal economic activity that has attracted much attention recently: legal goods smuggling, or the illegal trade of otherwise legal goods. The main channel of this type of smuggling is the falsification of trade documents. By reporting false amounts of exports and/or imports to authorities smugglers, or trade misinvoicers, seek to avoid paying taxes and/or tariffs. Chapter 4 widens the analysis of smuggling to the smuggling of illegal goods and studies the smuggling of legal and illegal goods across the U.S.-Mexico border in order to improve the understanding of illegal trade. Studying the U.S.-Mexican case is particularly interesting as most illegal drugs and immigrants enter the United States via the Mexican border. The empirical analyses in the dissertation “Informal Economic Activities” are based on structural equation models (SEMs). The results demonstrate that the informal economy is significant and that growth of the informal economy is not exclusive to developing countries, although it is a more serious problem in these countries. Moreover, although the informal economy covers a wide range of rather diverse economic activities, the dissertation works out that a few similarities exist. These are important, especially for policymakers, in first understanding what drives informal economic activities and second designing appropriate policies to deter them.

Introdução: O número de estudos relacionados à Síndrome Metabólica (SM) vem aumentando nos últimos anos, muitas vezes motivados pelo aumento do número de casos de sobrepeso/obesidade e diabetes Tipo II levando ao desenvolvimento de doenças cardiovasculares e, como consequência, infarto agudo do miocárdio e AVC, dentre outros desfechos desfavoráveis. A SM é uma doença multifatorial composta de cinco características, porém, para que um indivíduo seja diagnosticado com ela, possuir pelo menos três dessas características torna-se condição suficiente. Essas cinco características são: Obesidade visceral, caracterizada pelo aumento da circunferência da cintura, Glicemia de jejum elevada, Triglicérides aumentado, HDL-colesterol reduzido, Pressão Arterial aumentada. Objetivo: Estabelecer a rede de associações entre os fenótipos que compõem a Síndrome Metabólica através do aprendizado de estruturas de dependência, decompor a rede em componentes de correlação genética e ambiental e avaliar o efeito de ajustes por covariáveis e por variantes genéticas exclusivamente relacionadas à cada um dos fenótipos da rede. Material e Métodos: A amostra do estudo corresponderá a 79 famílias da cidade mineira de Baependi, composta por 1666 indivíduos. O aprendizado de estruturas de redes será feito por meio da Teoria de Grafos e Modelos de Equações Estruturais envolvendo o modelo linear misto poligênico para determinar as relações de dependência entre os fenótipos que compõem a Síndrome Metabólica / Introduction: The number of studies related to Metabolic Syndrome (MetS) has been increasing in the last years, encouraged by the increase on the overweight / obesity and Type II Diabetes cases, leading to the development of cardiovascular disease and, therefore, acute myocardial infarction and stroke, and others unfavorable outcomes. MetS is a multifactorial disease containing five characteristics, however, for an individual to be diagnosed with MetS, he/she may have at least three of them. These characteristics are: Truncal Obesity, characterized by increasing on the waist circumference, increasing on Fasting Blood Glucose, increasing on Triglycerides, decreasing on HDL cholesterol and increasing on Blood Pressure. Aims: Establish the best association network between MetS phenotypes through structured dependency learning between phenotypes considering genetic variants exclusively related to each phenotype. Materials and Methods: The study sample is composed of 79 families, 1666 individuals of a city in a rural area of Brazil, called Beapendi. Structured learning will use graph theory and Structural Equations Models to establish the dependency relations between MetS phenotypes

The dissertation “Informal Economic Activities” takes a comprehensive approach to the informal economy by studying traditional shadow economic activities, household DIY activities, and the smuggling of illegal and legal goods. Chapter 2 analyzes shadow economic and DIY activities and presents a dual estimation for the development of both types of informal economic activities in Germany from 1970 to 2005. It also considers the impact of German reunification on shadow economic and DIY activities and employs a proper estimate of domestic currency in circulation within Germany as an indicator variable for the shadow economy. Chapter 3 studies an informal economic activity that has attracted much attention recently: legal goods smuggling, or the illegal trade of otherwise legal goods. The main channel of this type of smuggling is the falsification of trade documents. By reporting false amounts of exports and/or imports to authorities smugglers, or trade misinvoicers, seek to avoid paying taxes and/or tariffs. Chapter 4 widens the analysis of smuggling to the smuggling of illegal goods and studies the smuggling of legal and illegal goods across the U.S.-Mexico border in order to improve the understanding of illegal trade. Studying the U.S.-Mexican case is particularly interesting as most illegal drugs and immigrants enter the United States via the Mexican border. The empirical analyses in the dissertation “Informal Economic Activities” are based on structural equation models (SEMs). The results demonstrate that the informal economy is significant and that growth of the informal economy is not exclusive to developing countries, although it is a more serious problem in these countries. Moreover, although the informal economy covers a wide range of rather diverse economic activities, the dissertation works out that a few similarities exist. These are important, especially for policymakers, in first understanding what drives informal economic activities and second designing appropriate policies to deter them.

Causal models have been used in different areas of knowledge in order to comprehend the causal associations between variables. Over the past decades, the amount of studies using these models have been growing a lot, especially those related to biological systems where studying and learning causal relationships among traits are essential for predicting the consequences of interventions in such system. Graph analysis (GA) and structural equation modeling (SEM) are tools used to explore such associations. While GA allows searching causal structures that express qualitatively how variables are causally connected, fitting SEM with a known causal structure allows to infer the magnitude of causal effects. Also SEM can be viewed as multiple regression models in which response variables can be explanatory variables for others. In quantitative genetics studies, SEM aimed to study the direct and indirect genetic effects associated to individuals through information related to them, beyond the observed characteristics, such as the kinship relations. In those studies typically the assumptions of linear relationships among traits are made. However, in some scenarios, nonlinear relationships can be observed, which make unsuitable the mentioned assumptions. To overcome this limitation, this paper proposes to use a mixed effects polynomial structural equation model, second or superior degree, to model those nonlinear relationships. Two studies were developed, a simulation and an application to real data. The first study involved simulation of 50 data sets, with a fully recursive causal structure involving three characteristics in which linear and nonlinear causal relations between them were allowed. The second study involved the analysis of traits related to dairy cows of the Holstein breed. Phenotypic relationships between traits were calving difficulty, gestation length and also the proportion of perionatal death. We compare the model of multiple traits and polynomials structural equations models, under different polynomials degrees in order to assess the benefits of the SEM polynomial of second or higher degree. For some situations the inappropriate assumption of linearity results in poor predictions of the direct, indirect and total of the genetic variances and covariance, either overestimating, underestimating, or even assign opposite signs to covariances. Therefore, we conclude that the inclusion of a polynomial degree increases the SEM expressive power. / Modelos causais têm sido muitos utilizados em estudos em diferentes áreas de conhecimento, a fim de compreender as associações ou relações causais entre variáveis. Durante as últimas décadas, o uso desses modelos têm crescido muito, especialmente estudos relacionados à sistemas biológicos, uma vez que compreender as relações entre características são essenciais para prever quais são as consequências de intervenções em tais sistemas. Análise do grafo (AG) e os modelos de equações estruturais (MEE) são utilizados como ferramentas para explorar essas relações. Enquanto AG nos permite buscar por estruturas causais, que representam qualitativamente como as variáveis são causalmente conectadas, ajustando o MEE com uma estrutura causal conhecida nos permite inferir a magnitude dos efeitos causais. Os MEE também podem ser vistos como modelos de regressão múltipla em que uma variável resposta pode ser vista como explanatória para uma outra característica. Estudos utilizando MEE em genética quantitativa visam estudar os efeitos genéticos diretos e indiretos associados aos indivíduos por meio de informações realcionadas aos indivíduas, além das característcas observadas, como por exemplo o parentesco entre eles. Neste contexto, é tipicamente adotada a suposição que as características observadas são relacionadas linearmente. No entanto, para alguns cenários, relações não lineares são observadas, o que torna as suposições mencionadas inadequadas. Para superar essa limitação, este trabalho propõe o uso de modelos de equações estruturais de efeitos polinomiais mistos, de segundo grau ou seperior, para modelar relações não lineares. Neste trabalho foram desenvolvidos dois estudos, um de simulação e uma aplicação a dados reais. O primeiro estudo envolveu a simulação de 50 conjuntos de dados, com uma estrutura causal completamente recursiva, envolvendo 3 características, em que foram permitidas relações causais lineares e não lineares entre as mesmas. O segundo estudo envolveu a análise de características relacionadas ao gado leiteiro da raça Holandesa, foram utilizadas relações entre os seguintes fenótipos: dificuldade de parto, duração da gestação e a proporção de morte perionatal. Nós comparamos o modelo misto de múltiplas características com os modelos de equações estruturais polinomiais, com diferentes graus polinomiais, a fim de verificar os benefícios do MEE polinomial de segundo grau ou superior. Para algumas situações a suposição inapropriada de linearidade resulta em previsões pobres das variâncias e covariâncias genéticas diretas, indiretas e totais, seja por superestimar, subestimar, ou mesmo atribuir sinais opostos as covariâncias. Portanto, verificamos que a inclusão de um grau de polinômio aumenta o poder de expressão do MEE.

Causal models have been used in different areas of knowledge in order to comprehend the causal associations between variables. Over the past decades, the amount of studies using these models have been growing a lot, especially those related to biological systems where studying and learning causal relationships among traits are essential for predicting the consequences of interventions in such system. Graph analysis (GA) and structural equation modeling (SEM) are tools used to explore such associations. While GA allows searching causal structures that express qualitatively how variables are causally connected, fitting SEM with a known causal structure allows to infer the magnitude of causal effects. Also SEM can be viewed as multiple regression models in which response variables can be explanatory variables for others. In quantitative genetics studies, SEM aimed to study the direct and indirect genetic effects associated to individuals through information related to them, beyond the observed characteristics, such as the kinship relations. In those studies typically the assumptions of linear relationships among traits are made. However, in some scenarios, nonlinear relationships can be observed, which make unsuitable the mentioned assumptions. To overcome this limitation, this paper proposes to use a mixed effects polynomial structural equation model, second or superior degree, to model those nonlinear relationships. Two studies were developed, a simulation and an application to real data. The first study involved simulation of 50 data sets, with a fully recursive causal structure involving three characteristics in which linear and nonlinear causal relations between them were allowed. The second study involved the analysis of traits related to dairy cows of the Holstein breed. Phenotypic relationships between traits were calving difficulty, gestation length and also the proportion of perionatal death. We compare the model of multiple traits and polynomials structural equations models, under different polynomials degrees in order to assess the benefits of the SEM polynomial of second or higher degree. For some situations the inappropriate assumption of linearity results in poor predictions of the direct, indirect and total of the genetic variances and covariance, either overestimating, underestimating, or even assign opposite signs to covariances. Therefore, we conclude that the inclusion of a polynomial degree increases the SEM expressive power. / Modelos causais têm sido muitos utilizados em estudos em diferentes áreas de conhecimento, a fim de compreender as associações ou relações causais entre variáveis. Durante as últimas décadas, o uso desses modelos têm crescido muito, especialmente estudos relacionados à sistemas biológicos, uma vez que compreender as relações entre características são essenciais para prever quais são as consequências de intervenções em tais sistemas. Análise do grafo (AG) e os modelos de equações estruturais (MEE) são utilizados como ferramentas para explorar essas relações. Enquanto AG nos permite buscar por estruturas causais, que representam qualitativamente como as variáveis são causalmente conectadas, ajustando o MEE com uma estrutura causal conhecida nos permite inferir a magnitude dos efeitos causais. Os MEE também podem ser vistos como modelos de regressão múltipla em que uma variável resposta pode ser vista como explanatória para uma outra característica. Estudos utilizando MEE em genética quantitativa visam estudar os efeitos genéticos diretos e indiretos associados aos indivíduos por meio de informações realcionadas aos indivíduas, além das característcas observadas, como por exemplo o parentesco entre eles. Neste contexto, é tipicamente adotada a suposição que as características observadas são relacionadas linearmente. No entanto, para alguns cenários, relações não lineares são observadas, o que torna as suposições mencionadas inadequadas. Para superar essa limitação, este trabalho propõe o uso de modelos de equações estruturais de efeitos polinomiais mistos, de segundo grau ou seperior, para modelar relações não lineares. Neste trabalho foram desenvolvidos dois estudos, um de simulação e uma aplicação a dados reais. O primeiro estudo envolveu a simulação de 50 conjuntos de dados, com uma estrutura causal completamente recursiva, envolvendo 3 características, em que foram permitidas relações causais lineares e não lineares entre as mesmas. O segundo estudo envolveu a análise de características relacionadas ao gado leiteiro da raça Holandesa, foram utilizadas relações entre os seguintes fenótipos: dificuldade de parto, duração da gestação e a proporção de morte perionatal. Nós comparamos o modelo misto de múltiplas características com os modelos de equações estruturais polinomiais, com diferentes graus polinomiais, a fim de verificar os benefícios do MEE polinomial de segundo grau ou superior. Para algumas situações a suposição inapropriada de linearidade resulta em previsões pobres das variâncias e covariâncias genéticas diretas, indiretas e totais, seja por superestimar, subestimar, ou mesmo atribuir sinais opostos as covariâncias. Portanto, verificamos que a inclusão de um grau de polinômio aumenta o poder de expressão do MEE.

Enjeu important pour le marketing des seniors, le concept de bien vieillir demeure peu investigué par la recherche en marketing. Nous introduisons un nouveau concept, le Bien Vieillir Désiré (BVD), qui fait référence aux objectifs psychologiques, physiques, sociaux et financiers, poursuivis dans la quête du bien vieillir. Nous en proposons un modèle de mesure bifactoriel, fiable et valide, en quatre dimensions : le BVD général, le BVD physique, le BVD social et le BVD financier. Son influence est testée sur huit comportements de consommation relatifs aux secteurs suivants : alimentation, e-santé, chirurgie esthétique, loisirs, placements financiers, réseaux sociaux et sites de rencontres. L’échelle de mesure et un modèle global antécédents-manifestations-effets sont validés à partir d’un échantillon de 900 seniors âgés de 50 à 80 ans. Les résultats suggèrent le développement d’une nouvelle approche marketing des seniors : le marketing du bien vieillir. Son investigation et sa mise en œuvre sont ancrées dans quatre concepts clés : le BVD, le vieillissement perçu, les attentes d’ajustement au vieillissement et la consommation du bien vieillir. / Aging well is now a key stake for senior marketing, yet this concept remains little investigated by consumer research. A new concept is introduced in marketing research: Desired Aging Well (DAW), which refers to the psychological, physical, social and financial objectives, pursued in the quest for aging well. This research provides a reliable and valid bifactor measurement model for Desired Aging Well, in four dimensions: general DAW, physical DAW, social DAW and financial DAW. Its influence is tested on eight consumer behaviors related to the following sectors: food, e-health, plastic surgery, leisure, financial investments, social networks and dating sites. The Desired Aging Well scale and the overall antecedents-manifestations-effects model are validated on a sample of 900 French senior people aged from 50 to 80. The results suggest the development of a new marketing approach for seniors: aging well marketing. Its investigation and implementation are rooted in four key concepts: Desired Aging Well, perceived aging, adjustment to aging expectations and aging well consumption.