Les études cliniques permettent de mesurer de nombreuses variables répétées dans le temps. Lorsque l'objectif est de les relier à un critère clinique d'intérêt, les méthodes de régularisation de type LASSO, généralisées aux Generalized Estimating Equations (GEE) permettent de sélectionner un sous-groupe de variables en tenant compte des corrélations intra-patients. Les bases de données présentent souvent des données non renseignées et des problèmes de mesures ce qui entraîne des données manquantes inévitables. L'objectif de ce travail de thèse est d'intégrer ces données manquantes pour la sélection de variables en présence de données longitudinales. Nous utilisons la méthode d'imputation multiple et proposons une fonction d'imputation pour le cas spécifique des variables soumises à un seuil de détection. Nous proposons une nouvelle méthode de sélection de variables pour données corrélées qui intègre les données manquantes : le Multiple Imputation Penalized Generalized Estimating Equations (MI-PGEE). Notre opérateur utilise la pénalité group-LASSO en considérant l'ensemble des coefficients de régression estimés d'une même variable sur les échantillons imputés comme un groupe. Notre méthode permet une sélection consistante sur l'ensemble des imputations, et minimise un critère de type BIC pour le choix du paramètre de régularisation. Nous présentons une application sur l'arthrose du genoux où notre objectif est de sélectionner le sous-groupe de biomarqueurs qui expliquent le mieux les différences de largeur de l'espace articulaire au cours du temps. / Clinical studies enable us to measure many longitudinales variables. When our goal is to find a link between a response and some covariates, one can use regularisation methods, such as LASSO which have been extended to Generalized Estimating Equations (GEE). They allow us to select a subgroup of variables of interest taking into account intra-patient correlations. Databases often have unfilled data and measurement problems resulting in inevitable missing data. The objective of this thesis is to integrate missing data for variable selection in the presence of longitudinal data. We use mutiple imputation and introduce a new imputation function for the specific case of variables under detection limit. We provide a new variable selection method for correlated data that integrate missing data : the Multiple Imputation Penalized Generalized Estimating Equations (MI-PGEE). Our operator applies the group-LASSO penalty on the group of estimated regression coefficients of the same variable across multiply-imputed datasets. Our method provides a consistent selection across multiply-imputed datasets, where the optimal shrinkage parameter is chosen by minimizing a BIC-like criteria. We then present an application on knee osteoarthritis aiming to select the subset of biomarkers that best explain the differences in joint space width over time.

Indiana University-Purdue University Indianapolis (IUPUI) / Useful medical indices pose important roles in predicting medical outcomes. Medical indices, such as the well-known Body Mass Index (BMI), Charleson Comorbidity Index, etc., have been used extensively in research and clinical practice, for the quantification of risks in individual patients. However, the development of these indices is challenged; and primarily based on heuristic arguments. Statistically, most medical indices can be expressed as a function of a linear combination of individual variables and fitted by single-index model. Single-index model represents a way to retain latent nonlinear features of the data without the usual complications that come with increased dimensionality. In my dissertation, I propose a single-index model approach to analytically derive indices from observed data; the resulted index inherently correlates with specific health outcomes of interest. The first part of this dissertation discusses the derivation of an index function for the prediction of one outcome using longitudinal data. A cubic-spline estimation scheme for partially linear single-index mixed effect model is proposed to incorporate the within-subject correlations among outcome measures contributed by the same subject. A recursive algorithm based on the optimization of penalized least square estimation equation is derived and is shown to work well in both simulated data and derivation of a new body mass measure for the assessment of hypertension risk in children. The second part of this dissertation extends the single-index model to a multivariate setting. Specifically, a multivariate version of single-index model for longitudinal data is presented. An important feature of the proposed model is the accommodation of both correlations among multivariate outcomes and among the repeated measurements from the same subject via random effects that link the outcomes in a unified modeling structure. A new body mass index measure that simultaneously predicts systolic and diastolic blood pressure in children is illustrated. The final part of this dissertation shows existence, root-n strong consistency and asymptotic normality of the estimators in multivariate single-index model under suitable conditions. These asymptotic results are assessed in finite sample simulation and permit joint inference for all parameters.

The Mississippi River Valley Alluvial Aquifer (MRVAA) is one of the most productive agricultural regions in the United States. The main objectives of this research are to identify long term trends and change points in hydrological variables (streamflow and rainfall), to assess the relationship between hydrological variables, and to evaluate the influence of global climate indices on hydrological variables. Non-parametric tests, MMK and Pettitt’s tests were used to analyze trend and change points. PCC and Streamflow elasticity analysis were used to analyze the relationship between streamflow and rainfall and the sensitivity of streamflow to rainfall changes. PCC and MLR analysis were used to evaluate the relationship between climate indices and hydrological variables and the combined effect of climate indices with hydrological variables. The results of the trend analysis indicated spatial variability within the aquifer, increase in streamflow and rainfall in the Northern region of the aquifer, while a decrease was observed in the southern region of the aquifer. Change point analysis of annual maximum, annual mean streamflow and annual precipitation revealed that statistically decreasing shifts occurred in 2001, 1998 and 1995, respectively. Results of PCC analysis indicated that streamflow and rainfall has a strong positive relationship between them with PCC values more than 0.6 in most of the locations within the basin. Results of the streamflow elasticity for the locations ranged from 0.987 to 2.33 for the various locations in the basin. Results of the PCC analysis for monthly maximum and mean streamflow showed significant maximum positive correlation coefficient for Nino 3.4. Monthly maximum rainfall showed a maximum significant positive correlation coefficient for PNA and Nino3.4 and the monthly mean rainfall showed a maximum significant positive correlation coefficient of 0.18 for Nino3.4. Results of the MLR analysis showed a maximum significant positive correlation coefficient of 0.31 for monthly maximum and mean streamflow of 0.21 and 0.23 for monthly maximum and mean rainfall, respectively. Overall, results from this research will help in understanding the impacts of global climate indices on rainfall and subsequently on streamflow discharge, so as to mitigate and manage water resource availability in the MRVAA underlying the LMRB.

Vor dem Hintergrund der Fragen, wer bereit ist eine enge Beziehung zu einer Person mit hohem Narzissmus einzugehen und wie Personen mit hohem Narzissmus ihre Freundschaften wahrnehmen, war das Ziel dieser Arbeit die wahrgenommene Beziehungsqualität in langfristigen Freundschaften in Abhängigkeit von Narzissmus zu untersuchen. In der ersten Studie wurde eine dyadische Perspektive eingenommen und beobachtet, ob sich die Qualität der Freundschaft in Abhängigkeit von dem Narzissmuslevel zweier Freunde unterscheidet. Wie angenommen, schätzten Personen in Dyaden mit höherem Narzissmus die Qualität ihrer Freundschaft geringer ein als Personen in Dyaden mit niedrigerem Narzissmus. Über alle Narzissmusaspekte hinweg wurden mehr Konflikte wahrgenommen. Dyaden mit hohem antagonistischem Narzissmus empfanden zudem weniger Wertschätzung und Intimität. Die Befunde wurden zugunsten der Annahme interpretiert, dass narzisstisches Verhalten von denjenigen toleriert wird, die selbst narzisstische Züge besitzen. In der zweiten Studie wurde eine längsschnittliche Perspektive eingenommen, um die Interaktionseffekte von Narzissmus und wahrgenommener Freundschaftsqualität in 4 Messzeitpunkten zu untersuchen. Innerhalb von Personen zeigte sich, dass diejenigen, die ihren Narzissmus niedriger als üblich einschätzten, in der Folge höhere Wertschätzung empfanden, und dass diejenigen, die eine niedrigere Wertschätzung als üblich empfanden ihr Verhalten als antagonistischer einschätzten. Die zu Beginn von Freundschaften gefundenen Effekte scheinen daher übertragbar auf die Phase der Aufrechterhaltung von Freundschaften, wobei besonders der antagonistische Narzissmus die negativen Auswirkungen von Narzissmus zu treiben scheint. Insgesamt wurde in dieser Arbeit die bisherige Forschung zu Narzissmus und sozialen Beziehungen durch die Beobachtung der Beziehungsqualität in langfristigen Freundschaften erweitert, indem sowohl eine dyadische als auch eine längsschnittliche Perspektive einbezogen wurde. / Who is willing to be in a close relationship to an individual with high narcissism, and how do individuals with high narcissism perceive their friendships? Three aspects of narcissism were distinguished (agentic, antagonistic, neurotic) to determine their association with four aspects of friendship quality (appreciation, intimacy, conflict, dominance). In the first study, a dyadic perspective was taken to observe whether friendship quality differs depending on the dyadic narcissism level of friends. As hypothesized, individuals in dyads with higher narcissism perceived their friendship quality as lower, compared to individuals in dyads with lower narcissism. More conflicts were perceived across narcissism aspects. Dyads with high antagonistic narcissism also perceived lower appreciation and intimacy. Results were interpreted in favor of the assumption that maladaptive traits are tolerated by those who possess these traits themselves. In the second study, a longitudinal perspective was taken to examine interactional effects of narcissism and friendship quality across 4 measurement occasions. On a within-person level, individuals scoring lower than usual on narcissism were found to subsequently perceive higher appreciation, and those perceiving lower appreciation than usual subsequently increased in antagonistic narcissism. Results suggested that the effects found in relationship formation tend to generalize to relationship maintenance. Overall, this work expanded previous research on narcissism and social relationships by observing relationship quality in long-term friendships including a dyadic as well as a longitudinal perspective. To answer the question of who is willing to be friends with someone high in narcissism, results suggest that it would be individuals who also score high on narcissism. In regard to the question of how individuals with high narcissism perceive their friendships it was found that they tend to be willing to accept lower friendship quality.

長期性資料(longitudinal data)的最主要特徵是為對多個被觀測個體在不同的時間點上重複測量一個或多個反應變數。而在分析長期性資料的方法中，Laird & Ware(1982)建議以線性混合效果模型(linear mixed effects model，LME)來進行估計分析，此模型方法中，資料可以允許遺失值，並可將受測個體間與個體內的變異分開說明。 另在配適最小平方法(OLS)的迴歸模型中，係數估計經常會受到異常值的影響，而Rousseeuw & Leroy(1987)提出最小消去平方法(least trimmed squares，LTS)的穩健迴歸模型，即是解決最小平方法中對於異常值敏感的問題。 本研究主要針對台灣股票預期報酬之三種模型：資本資產定價模型、特徵模型、因子模型分別以OLS、LTS、LME三種估計方法做配適，並比較配適模型之適當與否，樣本資料為民國七十年七月至九十年六月共252個月516家上市公司股票報酬。實證結果顯示，不論是採用OLS、LTS、LME的估計方法，股票報酬解釋變數：系統風險、公司規模、帳面權益對市值比、SMB、HML皆為股票報酬的顯著解釋因子；而在模型比較方面，不論是配適資本資產定價模型、特徵模型或因子模型，LME都較OLS為較適當配適模型。這顯示了在分析長期性資料時，LME的確是一個較佳的統計分析模型。

資本資產定價模型 (CAPM) 由Sharp (1964)、Lintner (1965)及Black (1972)發展出後，近年來已被廣泛的應用於衡量證券之預期報酬率與風險間之關係。一般而言，衡量結果之估計有兩個階段，首先由時間序列分析估計出貝它(beta)係數，然後再檢定廠商或投資組合之平均報酬率與貝它係數之關係。 Fama與MacBeth (1973)利用最小平方法估計貝它係數，再將由橫斷面迴歸方法所得出之斜率係數加以平均後，以統計t-test檢定之。然而以最小平方法估計係數，其估計值很容易受離群值之影響，因此本研究考慮以穩健估計 (robust estimator)來避免此一問題。另外，本研究亦將長期資料分析 (longitudinal data analysis) 引入CAPM裡，期望能檢定貝它係數是否能確實有效地衡量出系統性風險。 論文中以台灣股票市場電子業之實證分析來比較上述不同方法對CAPM的結果，資料蒐集期間為1998年9月至2001年12月之月資料。研究結果顯示出，穩健估計相對於最小平方法就CAPM有較佳的解釋力。而長期資料分析模型更用來衡量債券之超額報酬部分，是否會依上、中、下游或公司之不同而不同。 / The Capital Asset Pricing Model (CAPM) of Sharp (1964), Lintner (1965) and Black (1972) has been widely used in measuring the relationship between the expected return on a security and its risk in the recent years. It consists of two stages to estimate the relationship between risk and expected return. The first one is that betas are estimated from time series regressions, and the second is that the relationship between mean returns and betas is tested across firms or portfolios. Fama and MacBeth (1973) first used ordinary least squares (OLS) to estimate beta and took time series averages of the slope coefficients from monthly cross-sectional regressions in such studies. However it is well known that OLS is sensitive to outliers. Therefore, robust estimators are employed to avoid the problems. Furthermore, the longitudinal data analysis is applied to examine whether betas over time and securities are the valid measure of risk in the CAPM. An empirical study is carried out to present the different approaches. We use the data about the Information and Electronic industry in Taiwan stock market during the period from September 1998 to December 2001. For the time series regression analysis, the robust methods lead to more explanatory power than the OLS results. The linear mixed-effect model is used to examine the effects of different streams and companies for the security excess returns in these data.

In this paper, I analyze the effectiveness of state level Earned Income Tax Credit programs on improving of poverty levels. I conducted this analysis for the years 1991 through 2011 using a panel data model with fixed effects. The main independent variables of interest were the state and federal EITC rates, minimum wage, gross state product, population, and unemployment all by state. I determined increases to the state EITC rates provided only a slight decrease to both the overall white below-poverty population and the corresponding white childhood population under 18, while both the overall and the under-18 black population for this category realized moderate decreases in their poverty rates for the same time period. I also provide a comparison of the effectiveness of the state level EITCs and minimum wage at the state level over the same time period on these select demographic groups.

Les analyses effectuées dans le cadre de ce mémoire ont été réalisées à l'aide du module MatchIt disponible sous l’environnent d'analyse statistique R. / Statistical analyzes of this thesis were performed using the MatchIt package available in the statistical analysis environment R. / L’estimation sans biais de l’effet causal d’une intervention nécessite la comparaison de deux groupes homogènes. Il est rare qu’une étude observationnelle dispose de groupes comparables et même une étude expérimentale peut se retrouver avec des groupes non comparables. Les chercheurs ont alors recours à des techniques de correction afin de rendre les deux groupes aussi semblables que possible. Le problème consiste alors à choisir la méthode de correction appropriée. En ce qui nous concerne, nous limiterons nos recherches à une famille de méthodes dites d’appariement. Il est reconnu que ce qui importe lors d’un appariement est l’équilibre des deux groupes sur les caractéristiques retenues. Autrement dit, il faut que les variables soient distribuées de façon similaire dans les deux groupes. Avant même de considérer la distribution des variables entre les deux groupes, il est nécessaire de savoir si les données en question permettent une inférence causale. Afin de présenter le problème de façon rigoureuse, le modèle causal contrefactuel sera exposé. Par la suite, les propriétés formelles de trois méthodes d’appariement seront présentées. Ces méthodes sont l’appariement par la distance de Mahalanobis, de l’appariement par le score de propension et de l’appariement génétique. Le choix de la technique d’appariement appropriée reposera sur quatre critères empiriques dont le plus important est la différence des moyennes standardisées. Les résultats obtenus à l’aide des données de l’Enquête longitudinale et expérimentale de Montréal (ÉLEM) indiquent que des trois techniques d’appariement, l’appariement génétique est celui qui équilibre mieux les variables entre les groupes sur tous les critères retenus. L’estimation de l’effet de l’intervention varie sensiblement d’une technique à l’autre, bien que dans tous les cas cet effet est non significatif. Ainsi, le choix d’une technique d’appariement influence l’estimation de l’effet d’une intervention. Il est donc impérieux de choisir la technique qui permet d’obtenir un équilibre optimal des variables selon les données à la disposition du chercheur. / The unbiased estimate of the causal effect of an intervention requires the comparison of two homogeneous groups. It is rare that an observational study has comparable groups and even an experiment may end up with non-comparable groups. The researchers then used correction techniques to make the two groups as similar as possible. The problem then is to choose the appropriate correction method. In our case, we will restrict our research to a family of so-called matching methods. It is recognized that what matters in a match is the balance between the two groups on selected characteristics. In other words, it is necessary that the variables are distributed similarly in both groups. Even before considering the distribution of variables between the two groups, it is necessary to know whether the data in question allow for causal inference. To present the problem rigorously, the counterfactual causal model will be exposed. Thereafter, the formal properties of three matching methods will be presented. Those methods are the Mahalanobis matching, the propensity score matching and genetic matching. The choice of the appropriate matching technique is based on four empirical criteria which the most important is the standardized mean difference. Results obtained using data from the Montréal Longitudinal and Experimental Study indicate that of the three matching techniques, genetic matching is the one that better balance the variables between groups on all criteria. The estimate of the effect of intervention varies substantially from one technique to another, although in all cases this effect is non significant. Thus, the selection of a matching technique influences the estimation of the effect of an intervention. Therefore, it is imperative to choose the technique that provides an optimal balance of the variables based on data available to the researcher.

Diabetes is a major risk factor for the development of cataract [3,14,20,22]. In this thesis, we create a model that allows us to understand the incidence of one disease in the context of another; in particular, cataract in the presence of diabetes. The World Health Organization's Vision 2020 blindness-prevention initiative administers surgeries to remove cataracts, the leading cause of blindness worldwide [24]. One of the geographic areas most impacted by cataract-related blindness is Sub-Saharan Africa. In order to plan the number of surgeries to administer, the World Health Organization uses data on cataract prevalence. However, an estimation of the incidence of cataract is more useful than prevalence data for the purpose of resource planning. In 2012, Dray and Williams developed a method for estimating incidence based on prevalence data [5]. Incidence estimates can be further refined by considering associated risk factors such as diabetes. We therefore extend the Dray and Williams model to include diabetes prevalence when calculating cataract incidence estimates. We explore two possible approaches to our model construction, one a detailed extension, and the other, a simplification of that extension. We provide a discussion comparing the two approaches.

Researchers use natural phenomena in a number of disciplines to help explain human behavioral outcomes. Research regarding the potential effects of magnetic fields on animal and human behavior indicates that fields could influence outcomes of interest to social scientists. Tests so far have been limited in scope. This work is a preliminary evaluation of whether the earth’s magnetic field influences human behavior it examines the baseline relationship exhibited between geomagnetic readings and a host of social and political outcomes. The emphasis on breadth of topical coverage in these statistical trials, rather than on depth of development for any one model, means that evidence is only suggestive – but geomagnetic readings frequently covary with social and political variables in a fashion that seems inexplicable in the absence of a causal relationship. The pattern often holds up in more-elaborate statistical models. Analysis provides compelling evidence that geomagnetic variables furnish valuable information to models. Many researchers are already aware of potential causal mechanisms that link human behavior to geomagnetic levels and this evidence provides a compelling case for continuing to develop the line of research with in-depth, focused analysis.