Anticipated climate change and increasing wood demand require dependable diameter growth models for adaptive forest management. We used a mixed-effects modeling approach with Forest Inventory and Analysis (FIA) data to fit diameter growth models for loblolly pine, other softwood species (slash pine, shortleaf pine, and longleaf pine), sweetgum, and other hardwood (southern red oak, red maple, and water oak) species. Climatic variables coupled with individual tree attributes and competition factors improved climate insensitive models. Growth of loblolly pine and sweetgum was positively correlated with mean temperature of the coldest month. Mean temperature of the warmest month negatively influenced diameter growth of loblolly pine and other hardwood species. Growing season precipitation and summer precipitation balance had negative effects on the growth of softwood and hardwood species, respectively. Inclusion of FIA plot as random effect improved model fit statistics and residual distribution of climate sensitive models. These findings will be useful to managers for recalibrating diameter growth models resulting in improved biomass yield and volume estimates that will better inform decisions.

No description available.

<p>Hypercholesterolemia is the presence of high levels of cholesterol in the blood, and it is one of the major factors for the development of long-term complications in T1D patients.</p> <p>In the thesis, we studied 1303 Caucasians with type 1 diabetes in the Diabetes Control and Complications Trial (DCCT). With the experience of diabetes study, many factors are associated with diabetes complications, they are age, gender, cohort, treatment, diabetes duration, body mass index (BMI), exercise, insulin dose, etc. We mainly focus on which factors are associated with total cholesterol (CHL) analysis in the thesis.</p> <p>Many measures were collected monthly, quarterly or yearly for average 6.5 years from 1983 to 1993. We used annually lipid measures of DCCT because of their values are sufficient and complete, and they belong to longitudinal data.</p> <p>Different methods are discussed in the study, and linear mixed effect models are the appropriate approach to the study. The details of model selection with CHL model analysis are shown, which includes fixed effect selection, random effects selection, and residual correlation structure selection. Then the SNPs were added on three models individually in GWAS. We found locus (rs7412) is not only genome-wide associated with CHL, but also genome-wide associated with LDL.</p> <p>We will assess whether these SNPs are diabetes-specific in the future, and we will add dietary data in the three models to identify locus are associated with the interaction of diet and SNPs.</p> / Master of Science (MSc)

In this dissertation, we focus on two research topics related to mixture models. The first topic is Adaptive Rejection Metropolis Simulated Annealing for Detecting Global Maximum Regions, and the second topic is Bayesian Model Selection for Nonlinear Mixed Effects Model. In the first topic, we consider a finite mixture model, which is used to fit the data from heterogeneous populations for many applications. An Expectation Maximization (EM) algorithm and Markov Chain Monte Carlo (MCMC) are two popular methods to estimate parameters in a finite mixture model. However, both of the methods may converge to local maximum regions rather than the global maximum when multiple local maxima exist. In this dissertation, we propose a new approach, Adaptive Rejection Metropolis Simulated Annealing (ARMS annealing), to improve the EM algorithm and MCMC methods. Combining simulated annealing (SA) and adaptive rejection metropolis sampling (ARMS), ARMS annealing generate a set of proper starting points which help to reach all possible modes. ARMS uses a piecewise linear envelope function for a proposal distribution. Under the SA framework, we start with a set of proposal distributions, which are constructed by ARMS, and this method finds a set of proper starting points, which help to detect separate modes. We refer to this approach as ARMS annealing. By combining together ARMS annealing with the EM algorithm and with the Bayesian approach, respectively, we have proposed two approaches: an EM ARMS annealing algorithm and a Bayesian ARMS annealing approach. EM ARMS annealing implement the EM algorithm by using a set of starting points proposed by ARMS annealing. ARMS annealing also helps MCMC approaches determine starting points. Both approaches capture the global maximum region and estimate the parameters accurately. An illustrative example uses a survey data on the number of charitable donations. The second topic is related to the nonlinear mixed effects model (NLME). Typically a parametric NLME model requires strong assumptions which make the model less flexible and often are not satisfied in real applications. To allow the NLME model to have more flexible assumptions, we present three semiparametric Bayesian NLME models, constructed with Dirichlet process (DP) priors. Dirichlet process models often refer to an infinite mixture model. We propose a unified approach, the penalized posterior Bayes factor, for the purpose of model comparison. Using simulation studies, we compare the performance of two of the three semiparametric hierarchical Bayesian approaches with that of the parametric Bayesian approach. Simulation results suggest that our penalized posterior Bayes factor is a robust method for comparing hierarchical parametric and semiparametric models. An application to gastric emptying studies is used to demonstrate the advantage of our estimation and evaluation approaches. / Ph. D.

The Forest Vegetation Simulator (FVS) is a growth and yield modeling system widely-used for predicting stand and tree-level attributes for management and planning applications in North American forests. The accuracy of FVS predictions for a range of tree and stand level attributes depends a great deal on the performance of the diameter increment model and its predictions of change in diameter at breast height (DBH) over time. To address the challenge of predicting growth in highly variable and geographically expansive forest systems, FVS was designed to include an internal calibration algorithm that makes use of growth observations, when available, from permanent inventory plots. The basic idea is that observed growth rates on a collection of remeasured trees are used to adjust or "calibrate" FVS diameter growth predictions. Therefore, DBH modeling was the focus of this investigation. Five methods were proposed for local calibration of individual tree DBH growth predictions and compared to two sets of results generated without calibration. Data from the US Forest Service's Forest Inventory and Analysis (FIA) program were used to test the methods for eleven widely-distributed forest tree species in Virginia. Two calibration approaches were based on median prediction errors from locally-observed DBH increments spanning a five year average time interval. Two were based on simple linear regression models fitted to the locally-observed prediction errors, and one method employed a mixed effects regression model with a random intercept term estimated from locally-observed DBH increments. Data witholding, specifically a leave-one-out cross-validation was used to compare results of the methods tested. Results showed that any of the calibration approaches tested in general led to improved accuracy of DBH growth predictions, with either of the median-based methods or regression based methods performing better than the random-effects-based approach. Equivalence testing showed that median or regression-based local calibration methods met error tolerances within ± 12% of observed DBH increments for all species with the random effects approach meeting a larger tolerance of ± 17%. These results showed improvement over uncalibrated models, which failed to meet tolerances as high as ± 30% for some species in a newly-fitted DBH growth model for Virginia, and as high as ± 170% for an existing model fitted to data from a much larger region of the Southeastern United States. Local calibration of regional DBH increment models provides an effective means of substantially reducing prediction errors when a relatively small set of observations are available from local sources such as permanent forest inventory plots, or the FIA database. / MS / The Forest Vegetation Simulator (FVS) is a growth and yield model widely-used for predicting stand dynamics, management and decision support in North American forests. Diameter increment is a major component in modeling tree growth. The system of integrated analytical tools in FVS is primarily based on the performance of the diameter increment model and the subsequent use of predicted in diameter at breast height (DBH) over time in forecasting tree attributes. To address the challenge of predicting growth in highly variable and geographically expansive forest systems, FVS was designed to include an internal calibration algorithm that makes use of growth observations, when available, from permanent inventory plots. The basic idea was that observed growth rates on a small set of remeasured trees are used to adjust or “calibrate” FVS growth predictions. The FVS internal calibration was the subject being investigated here. Five alternative methods were proposed attributed to a specific site or stand of interest and compared to two sets of results, which were based on median prediction errors, generated without calibration. Results illustrated that median-based methods or regression based methods performed better than the random-effects-based approach using independently observed growth data from Forest Service FIA re-measurements in Virginia. Local calibration of regional DBH increment models provides an effective means of substantially reducing prediction errors. The results of this study should also provide information to evaluate the efficiency of FVS calibration alternatives and a possible method for future implementation.

Os experimentos agronômicos que envolvem somente um fator longitudinal são bastante comuns. No entanto, existem casos em que as observações são tomadas considerando dois ou mais desses fatores, como nos casos em que são feitas medidas de uma variável resposta em profundidades diferentes ao longo do tempo, por exemplo. Admite-se que essas observações, tomadas de modo sistemático em cada unidade experimental, sejam correlacionadas e as variâncias nos diferentes níveis do fator longitudinal sejam heterogêneas. Com o uso de modelos mistos, essa correlação entre medidas repetidas e a heterogeneidade de variâncias podem ser modeladas convenientemente. Para que esses modelos sejam ajustados a um conjunto de dados envolvendo presença de dois fatores longitudinais, existe a necessidade de se adaptarem algumas estruturas de variâncias e covariâncias que são comuns em experimentos com somente um fator longitudinal. O objetivo do presente trabalho é utilizar a classe dos modelos lineares mistos para estudar a massa seca de raiz no solo de uma plantação de cana-de-açúcar. O experimento foi casualizado em blocos e as parcelas receberam quatro doses de nitrogênio. Foram feitas medidas repetidas ao longo de dois fatores longitudinais, sendo um qualitativo ordinal (profundidades) e um quantitativo (distâncias da linha de plantio). Por meio dos testes de razão de verossimilhanças, de Wald e utilizando os critérios de informação AIC e BIC, selecionou-se uma estrutura de covariâncias parcimoniosa e outra estrutura para explicar o comportamento médio das respostas. A verificação do ajuste foi feita por meio de gráficos de diagnósticos de resíduos. / Agronomic experiments involving only one longitudinal factor are quite common. However, there are cases that the observations are made by considering two or more of these factors such as where measurements are made in a response variable at different depths along the time, for example. It is admitted that these observations, taken in a systematic way in each experimental unit are correlated and variances are heterogeneous in different levels of longitudinal factor. Using mixed models, this correlation between repeated measures and heterogeneity of variances can be modeled conveniently. To fit these models to data set involving presence of two longitudinal factors, there is need to adapt some variance and covariance structures that are common in experiments with only one longitudinal factor. The objective of this work is to use the class of linear mixed models to study the dry root mass in the soil of a plantation of cane sugar. The experiment was the randomized complete blocks design and parcels received four doses of nitrogen. Repeated measurements were made along two longitudinal factors being one ordinal qualitative (depths) and one quantitative (distances from the row). With the aid of likelihood ratio, Wald tests and using the AIC and BIC information criteria, we selected a parsimonious covariance structure and another structure to explain the average behavior of the responses. Checking the fit was made using diagnostic graphics of residuals.

Des écoulements matriciels et des flux préférentiels peuvent se produire concurremment dans le même sol. Ces deux régimes d’écoulements se manifestent par des empreintes de flux caractéristiques qu’on peut visualiser par des essais de traçage. Afin d’extraire l’information quantitative des essais de traçage un grand nombre de méthodes existe. On peut, entre autre, décrire les empreintes de traceur par ce qu’on appelle la fonction de couverture, c’est à dire le pourcentage de région teintée par un traceur coloré en fonction de la profondeur du sol. En utilisant la statistique des valeurs extrêmes cette fonction peut être réinterprétée comme une fonction exprimant la probabilité de trouver le traceur à une profondeur donnée. Ainsi, la fonction de probabilité à deux paramètres 1 – H, H étant la distribution de Pareto généralisée, peut être ajustée. Le paramètre de forme de cette fonction est utilisé comme indice de risque de propagation verticale des solutés. Nous avons effectué des essais de traçage au Bleu Brillant FCF sur trois sites différents : dans une forêt d’épicéa dans le sud-est de l’Allemagne, dans une forêt tropicale humide montagnarde en Équateur et sur un champ agricole au sud de la France. Nous avons examiné la capacité de l’indice de risque à rassembler l’information principale des essais de traçage et à caractériser les empreintes de flux dans des sols différents, sous conditions aux limites diverses. Nos résultats indiquent que l’indice de risque est, dans une certaine mesure insensible aux changements des conditions aux limites (comme l’intensité d’irrigation). Par contre, l’humidité initiale du sol semble influencer cet indice de façon importante. L’ajustement des paramètres de la fonction Pareto généralisée s’avère difficile si la fonction de couverture fluctue ou ne décroît pas de manière monotone. Ceci peut être dû à la tortuosité des chemins d’écoulement, à la variation des mécanismes de flux ou aux changements de propriétés physiques du sol (stratification). Ainsi, dans des sols stratifiés nous avons restreint l’analyse à la partie inférieure du profil de sol. En effet, étant donné que la théorie de l’indice de risque est basée sur les valeurs extrêmes de propagation verticale de solutés c’est la partie inférieure qui est la plus intéressante. Nous proposons de combiner les deux paramètres de la fonction Pareto généralisée et d’utiliser la distribution 1 – H complète afin d’estimer le risque de propagation verticale des solutés dans le sol. Bien que l’indice de risque montre une certaine invariance vis-à-vis du changement des conditions aux limites il n’est pas un paramètre intrinsèque de sol. Comme le régime d’écoulement dans un même sol peut être dominé soit par le flux matriciel soit par le flux préférentiel le risque de propagation verticale des solutés change. Ceci est une réalité physique et non un défaut dans la théorie de l’indice de risque. Les paramètres de la fonction de Pareto généralisée capturent le régime d’écoulement dominant représenté par les empreintes du traceur. En prenant en compte les conditions aux limites de l’essai de traçage comme l’intensité d’irrigation, le traceur utilisé, l’humidité initiale du sol ou la nature de la végétation (pérenne ou saisonnière, type d’enracinement) il est ainsi possible de comparer des sites différents ou des résultats obtenus sur le même site sous conditions aux limites différentes et d’estimer le risque de propagation verticale de solutés. L’analyse d’image d’empreintes de flux basée sur le risque de propagation verticale de solutés a révélé l’existence d’écoulements préférentiels sur le site allemand. Afin de comprendre les mécanismes de flux ainsi que les impacts éventuels des flux préférentiels sur la chimie du sol nous avons analysé la texture du sol, la densité racinaire, la densité du sol, la concentration des cations échangeables, le pH, et les teneurs en C et N total dans les chemins préférentiels et la matrice du sol. Les résultats de la modélisation indiquent que sur ce site les racines constituent les chemins préférentiels et créent les écoulements le long des macropores, surtout dans la partie supérieure du sol. Dans la partie inférieure la densité racinaire diminue et l’infiltration hétérogène à partir des chemins préférentiels dans la matrice provoque un écoulement non-uniforme. Nous n’avons constaté aucune différence significative de texture, mais des différences de densité du sol dans les chemins préférentiels par rapport à celle de la matrice. Ceci est probablement dû à la quantité de matière organique plus élevée dans les chemins préférentiels. Nous avons également trouvé des pH plus acides, plus de Ca, plus de Mg, et plus de C et de N dans les chemins préférentiels. Comparé à la matrice, des quantités plus importantes d’Al et de Fe (mais de petites quantités absolues) ont été trouvés dans la partie inférieure du sol où l’écoulement préférentiel le long des macropores créés par les racines diminue et le flux matriciel hétérogène domine. Ces propriétés chimiques distinctes peuvent s’expliquer par l’activité racinaire et la translocation de solutés et du carbone organique dissous (COD) le long des chemins préférentiels. Le temps de contact entre le COD et le sol étant réduit il est transporté plus bas dans le profil où il peut potentiellement créer des complexes organo-minéraux. Ainsi, l’écoulement préférentiel est un mécanisme qui peut promouvoir la séquestration de C en sous-sol et n’influence pas uniquement son environnent immédiat, mais aussi les horizons sous-jacents. Un des acquis majeurs de cette thèse est le nombre important d’images d’empreintes de flux issues des sols différents. Dans les études qui suivront les méthodes récentes de réduction de dimensionnalité peuvent être employées afin de trouver d’éventuelles structures de basse dimensionnalité dans ces images / Matrix flow and preferential flow can occur concurrently in the same soil. Both flow regimes produce typical flow patterns that can be visualised in dye tracer experiments. To extract quantitative information from dye tracer studies a vast variability of approaches exists. One of them is to describe dye patterns by the so called dye coverage function, i.e. the percentage of stained area per soil depth. Based on extreme value statistics the dye coverage function can be reinterpreted as a probability function to find the tracer in a certain depth. Therefore, the two-parametric probability distribution 1 – H, H being the generalised Pareto distribution, can be fitted to the dye coverage function. The form parameter of this distribution serves as a risk index for vertical solute propagation. We did tracer experiments with Brilliant Blue FCF at three different study sites: in a Norway spruce forest in southeast Germany, in a tropical mountain rainforest in southern Ecuador and on an agricultural field in southern France. We tested the ability of the risk index to summarise main information obtained in dye tracer studies and characterise flow patterns in different soils under varying boundary conditions. Our results suggest that the risk index is to some degree invariant to changing experimental conditions (such as irrigation rate). The initial soil moisture, however, seems to have a large influence on the risk index. It is difficult to adjust the parameters of the generalised Pareto distribution when the dye coverage function fluctuates or does not decrease monotonically. This might be due to tortuosity of paths, varying flow mechanism or changing soil physical properties (stratification). Thus, in stratified soil, we restricted the analysis to the lowest part of the profile. Since the theory of the risk index is based on extreme values of vertical solute propagation it is the lowest part of the profile that is the most interesting. We propose to combine the two parameters of the generalized Pareto distribution and to use the complete distribution 1 - H to estimate the risk of vertical solute propagation in soils. Despite a certain resistance to changes of experimental conditions, the risk index is not an intrinsic soil parameter. Since the flow regime in the same soil can be dominated either by preferential flow or by uniform matrix flow, the risk of vertical solute propagation will change. It is a physical reality and not a default in the risk index theory. The adjusted parameters of the generalised Pareto distribution will capture the dominant flow regime as reflected by tracer flow patterns. Bearing in mind the boundary conditions of the tracer experiment like irrigation rate, the tracer employed, soil initial moisture or type of vegetation (permanent or seasonal, deep rooted or shallow rooted) it is possible to compare different study sites or to consider the same site at different boundary conditions and to access the risk of vertical solute propagation. Pattern analysis based on the risk index for vertical solute propagation revealed the occurrence of preferential flow at the German study site. To gain insight in flow mechanisms and possible impacts of preferential flow on soil chemistry we analysed soil texture, fine root density, soil bulk density, exchangeable cations, pH and total C and N contents in preferential flow paths and soil matrix. Results from linear mixed-effects models suggested that at this study site roots constituted main preferential flow paths and induced macropore flow, especially in the topsoil. In the subsoil root density decreased and inhomogeneous infiltration from preferential flow paths into the soil matrix caused non-uniform flow. There were no textural differences between the flow domains, but smaller bulk densities in preferential flow paths. This is probably due to a higher soil organic matter content in preferential flow paths. We found smaller pH values, more Ca, more Mg, more C and more N in preferential flow paths. Compared to the adjacent soil matrix, more Al and more Fe (but small absolute amounts) were found in the subsoil where macropore flow along root channels decreases and heterogeneous matrix flow dominates. These distinct chemical properties can be explained by root activity and translocation of solutes and DOC (dissolved organic carbon) via preferential flow paths. During transport along preferential flow paths contact time between DOC and soil is reduced so that DOC is transported to greater depth where it potentially forms organo-mineral associations. If this holds true, preferential flow is a mechanism that promotes C sequestration in subsoil and does not only influence its immediate environment around paths, but also underlying subsoil horizons. A major outcome of this thesis is the large number of images of flow patterns from different soils. Further studies could employ recent dimensionality reduction techniques to investigate whether there is a low dimensional structure underlying these images / Matrixfluss und präferentieller Fluss können in ein und demselben Boden gleichzeitig auftreten. Beide Fließregime erzeugen charakteristische Fließmuster, die in Versuchen mit Farbtracern sichtbar gemacht werden können. Es existiert eine Reihe von Methoden, um Tracerversuche quantitativ auszuwerten. Eine davon ist die Beschreibung der Fließmuster durch die so genannte Deckungsgradfunktion, den Anteil der gefärbten Fläche pro Tiefe. Die Methoden der Extremwertstatistik erlauben eine Neuinterpretation der Deckungsgradfunktion als eine Wahrscheinlichkeitsfunktion, den Tracer in einer bestimmten Tiefe anzutreffen. Demzufolge kann die zweiparametrige Wahrscheinlichkeitsfunktion 1 – H (H: verallgemeinerte Paretoverteilung) an die Deckungsgradfunktion angepasst werden. Der Formparameter dieser Verteilung dient als Risikoindex für vertikale Ausbreitung von gelösten Substanzen. Tracerversuche mit Brilliant Blue FCF wurden an drei unterschiedlichen Standorten durchgeführt: in einem Fichtenwald in Südostdeutschland, einem Bergregenwald in Südostecuador und an einem landwirtschaftlichen Standort in Südfrankreich. Es wurde überprüft, ob die wichtigsten Ergebnisse aus Tracerversuchen auf unterschiedlichen Böden und bei verschiedenen Randbedingungen mithilfe des Risikoindex beschrieben werden können. Die Ergebnisse zeigen eine gewisse Unabhängigkeit des Risikoindex von experimentellen Randbedingungen (wie z. B. Beregnungsintensität). Dagegen scheint die Bodenfeuchte eine zentrale Rolle zu spielen. Schwierigkeiten bei der Anpassung der Parameter der verallgemeinerten Paretoverteilung ergeben sich, wenn die Deckungsfunktion fluktuiert oder nicht monoton fallend ist. Dies kann möglicherweise auf die Tortuosität von Fließpfaden, variierenden Fließmechanismen oder sich verändernden bodenphysikalischen Eigenschaften (Stratifikation) zurückgeführt werden. Daher wurde die Musteranalyse in stratifizierten Böden auf den Unterboden begrenzt. Da die dem Risikoindex zugrunde liegende Theorie auf den Extremwerten der vertikalen Ausbreitung von gelösten Stoffen basiert, gilt das Hauptinteresse dem untersten Teil des Bodenprofils. Wir schlagen vor, die beiden Parameter der verallgemeinerten Wahrscheinlichkeitsverteilung zu nutzen, um das Risiko der vertikalen Ausbreitung von gelösten Stoffen in Böden abzuschätzen. Obwohl der Risikoindex eine gewisse Toleranz gegenüber sich ändernden Randbedingungen zeigt, ist er kein intrinsischer Bodenparameter. Da das Fließgeschehen in ein und demselben Boden sowohl vom Matrix- als auch vom präferentiellen Fluss dominiert werden kann, ändert sich das Risiko der vertikalen Ausbreitung von gelösten Stoffen. Dies ist physikalische Realität und kein Fehler in der Theorie des Risikoindex. Die angepassten Parameter der verallgemeinerten Paretoverteilung erfassen das durch den Tracer sichtbar gemachte dominante Fließregime. Unter der Berücksichtigung der Randbedingungen des Tracerexperiments wie Beregnungsintensität, des verwendeten Tracers, Bodenfeuchte oder Art der Vegetation (einjährig, mehrjährig oder perennierend, tiefwurzelnd oder flachwurzelnd) ist es möglich, unterschiedliche Standorte zu vergleichen oder denselben Standort unter verschiedenen Randbedingungen zu betrachten und das Risiko der vertikalen Ausbreitung von gelösten Stoffen abzuschätzen. Extremwertstatistikgestützte Musteranalyse zeigte das Auftreten von präferentiellem Fluss auf dem Standort in Südostdeutschland. Um die Fließmechanismen und mögliche Auswirkungen des präferentiellen Flusses auf die Bodenchemie aufzudecken, wurden Textur, Feinwurzeldichte, Trockenraumdichte, austauschbare Kationen, pH, Gehalt an totalem C und N in präferentiellen Fließwegen und Bodenmatrix analysiert. Ergebnisse aus gemischten Modellen zeigen, dass auf diesem Standort präferentielle Fließwege durch Wurzeln gebildet werden, und zwar hauptsächlich im Oberboden. Im Unterboden nimmt die Durchwurzelung ab, und heterogene Infiltration aus den präferentiellen Fließpfaden in die Bodenmatrix führt zu ungleichmäßigem Matrixfluss. Es wurden keine signifikanten Unterschiede in der Textur gefunden. Allerdings ist die Trockenraumdichte in den präferentiellen Fließwegen geringer als in der Bodenmatrix, wahrscheinlich bedingt durch den erhöhten Gehalt an organischer Materie. Weiterhin wurden in den präferentiellen Fließwegen niedrigere pH-Werte, höherer Gehalt an Ca, Mg, C und N gemessen. Im Vergleich zur umgebenden Bodenmatrix wurde im weniger durchwurzelten und von heterogenem Matrixfluss dominierten Unterboden höherer Gehalt an Al und Fe (allerdings kleine absolute Mengen) festgestellt. Diese klar unterschiedlichen chemischen Eigenschaften lassen sich durch Wurzelaktivitäten und den Transport von gelösten Substanzen (darunter auch DOC: gelöster organischer Kohlenstoff) durch präferentielle Fließwege erklären. Während des Transports ist die Kontaktzeit zwischen dem DOC und dem Boden verkürzt, so dass der Kohlenstoff in tiefere Bodenhorizonte transportiert wird, in denen er eventuell organo-mineralische Komplexe bilden kann. Dies würde bedeuten, dass präferentieller Fluss unter Umständen die Kohlenstoff-Sequestration im Unterboden begünstigen könnte, und nicht nur seine unmittelbare Umgebung, sondern auch die tiefer liegenden Bodenhorizonte beeinflusst. Ein wichtiges Ergebnis dieser Untersuchungen ist die große Anzahl an Bildern der Fließmuster in verschiedenen Böden. In nachfolgenden Arbeiten könnte mit den neuesten Methoden der Reduktion der Dimension untersucht werden, ob diesen Bildern eine niedrigdimensionale Struktur zugrunde liegt

Os experimentos agronômicos que envolvem somente um fator longitudinal são bastante comuns. No entanto, existem casos em que as observações são tomadas considerando dois ou mais desses fatores, como nos casos em que são feitas medidas de uma variável resposta em profundidades diferentes ao longo do tempo, por exemplo. Admite-se que essas observações, tomadas de modo sistemático em cada unidade experimental, sejam correlacionadas e as variâncias nos diferentes níveis do fator longitudinal sejam heterogêneas. Com o uso de modelos mistos, essa correlação entre medidas repetidas e a heterogeneidade de variâncias podem ser modeladas convenientemente. Para que esses modelos sejam ajustados a um conjunto de dados envolvendo presença de dois fatores longitudinais, existe a necessidade de se adaptarem algumas estruturas de variâncias e covariâncias que são comuns em experimentos com somente um fator longitudinal. O objetivo do presente trabalho é utilizar a classe dos modelos lineares mistos para estudar a massa seca de raiz no solo de uma plantação de cana-de-açúcar. O experimento foi casualizado em blocos e as parcelas receberam quatro doses de nitrogênio. Foram feitas medidas repetidas ao longo de dois fatores longitudinais, sendo um qualitativo ordinal (profundidades) e um quantitativo (distâncias da linha de plantio). Por meio dos testes de razão de verossimilhanças, de Wald e utilizando os critérios de informação AIC e BIC, selecionou-se uma estrutura de covariâncias parcimoniosa e outra estrutura para explicar o comportamento médio das respostas. A verificação do ajuste foi feita por meio de gráficos de diagnósticos de resíduos. / Agronomic experiments involving only one longitudinal factor are quite common. However, there are cases that the observations are made by considering two or more of these factors such as where measurements are made in a response variable at different depths along the time, for example. It is admitted that these observations, taken in a systematic way in each experimental unit are correlated and variances are heterogeneous in different levels of longitudinal factor. Using mixed models, this correlation between repeated measures and heterogeneity of variances can be modeled conveniently. To fit these models to data set involving presence of two longitudinal factors, there is need to adapt some variance and covariance structures that are common in experiments with only one longitudinal factor. The objective of this work is to use the class of linear mixed models to study the dry root mass in the soil of a plantation of cane sugar. The experiment was the randomized complete blocks design and parcels received four doses of nitrogen. Repeated measurements were made along two longitudinal factors being one ordinal qualitative (depths) and one quantitative (distances from the row). With the aid of likelihood ratio, Wald tests and using the AIC and BIC information criteria, we selected a parsimonious covariance structure and another structure to explain the average behavior of the responses. Checking the fit was made using diagnostic graphics of residuals.

Title: Joint Models for Longitudinal and Time-to-Event Data Author: Jana Vorlíčková Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Arnošt Komárek, Ph.D., Department of Probability and Mathematical Statistics Abstract: The joint model of longitudinal data and time-to-event data creates a framework to analyze longitudinal and survival outcomes simultaneously. A commonly used approach is an interconnection of the linear mixed effects model and the Cox model through a latent variable. Two special examples of this model are presented, namely, a joint model with shared random effects and a joint latent class model. In the thesis we focus on the joint latent class model. This model assumes an existence of latent classes in the population that we are not able to observe. Consequently, it is assumed that the longitudinal part and the survival part of the model are independent within one class. The main intention of this work is to transfer the model to the Bayesian framework and to discuss an estimation procedure of parameters using a Bayesian statistic. It consists of a definition of the model in the Bayesian framework, a discussion of prior distributions and the derivation of the full conditional distributions for all parameters of the model. The model's ability to...

1 AbstraktEN The diploma thesis deals with linear mixed effects models. In the first chap- ter, we discuss parameter estimation and hypothesis testing in the linear mixed effects models. The second chapter is dedicated to graphical diagnostics. We look at the suitable diagnostic plots for residuals and random effects estimates. It is closely described, how the violations of assumptions affect the diagnostic plots. In the third chapter we have consequences of the violations of assumptions on the parameter estimates and results of hypothesis testing for fixed effects. 1