One of the most frequently encountered types of data is where the response variables are measured on an ordinal scale. Although there have been substantial developments in the statistical techniques for the analysis of ordinal data, methods appropriate for repeatedly assessed ordinal data collected from field experiments are limited. A series of biennial field screening trials for evaluating cultivar resistance of potato to the disease, late blight, caused by the fungus Phytophthora infestans (Mont.) de Bary has been conducted by the New Zealand Institute of Crop and Food Research since 1983. In each trial, the progression of late blight was visually assessed several times during the planting season using a nine-point ordinal scale based on the percentage of necrotic tissues. As for many other agricultural field experiments, spatial differences between the experimental units is one of the major concerns in the analysis of data from the potato late blight trial. The aim of this thesis is to construct a statistical model which can be used to analyse the data collected from the series of potato late blight trials. We review existing methodologies for analysing ordinal data with mixed effects particularly those methods in the Bayesian framework. Using data collected from the potato late blight trials we develop a Bayesian hierarchical model for the analyses of repeatedly assessed ordinal scores with spatial effects, in particular the time dependence of the scores assessed on the same experimental units was modelled by a sigmoid logistic curve. Data collected from the potato late blight trials demonstrated the importance of spatial effects in agricultural field trials. These effects cannot be neglected when analysing such data. Although statistical methods can be refined to account for the complexity of the data, appropriate trial design still plays a central role in field experiments. / Accompanying dataset is at http://hdl.handle.net/2292/5240

The research on multi-state Markov transition model is motivated by the nature of the longitudinal data from the Nun Study (Snowdon, 1997), and similar information on the BRAiNS cohort (Salazar, 2004). Our goal is to develop a flexible methodology for handling the categorical longitudinal responses and competing risks time-to-event that characterizes the features of the data for research on dementia. To do so, we treat the survival from death as a continuous variable rather than defining death as a competing absorbing state to dementia. We assume that within each subject the survival component and the Markov process are linked by a shared latent random effect, and moreover, these two pieces are conditionally independent given the random effect and their corresponding predictor variables. The problem of the dependence among observations made on the same subject (repeated measurements) is addressed by assuming a first order Markovian dependence structure. A closed-form expression for the individual and thus overall conditional marginal likelihood function is derived, which we can evaluate numerically to produce the maximum likelihood estimates for the unknown parameters. This method can be implemented using standard statistical software such as SAS Proc Nlmixed©. We present the results of simulation studies designed to show how the model’s ability to accurately estimate the parameters can be affected by the distributional form of the survival term. Then we focus on addressing the problem by accommodating the residual life time of the subject’s confounding in the nonhomogeneous chain. The convergence status of the chain is examined and the formulation of the absorption statistics is derived. We propose using the Delta method to estimate the variance terms for construction of confidence intervals. The results are illustrated with applications to the Nun Study data in details.

One of the most frequently encountered types of data is where the response variables are measured on an ordinal scale. Although there have been substantial developments in the statistical techniques for the analysis of ordinal data, methods appropriate for repeatedly assessed ordinal data collected from field experiments are limited. A series of biennial field screening trials for evaluating cultivar resistance of potato to the disease, late blight, caused by the fungus Phytophthora infestans (Mont.) de Bary has been conducted by the New Zealand Institute of Crop and Food Research since 1983. In each trial, the progression of late blight was visually assessed several times during the planting season using a nine-point ordinal scale based on the percentage of necrotic tissues. As for many other agricultural field experiments, spatial differences between the experimental units is one of the major concerns in the analysis of data from the potato late blight trial. The aim of this thesis is to construct a statistical model which can be used to analyse the data collected from the series of potato late blight trials. We review existing methodologies for analysing ordinal data with mixed effects particularly those methods in the Bayesian framework. Using data collected from the potato late blight trials we develop a Bayesian hierarchical model for the analyses of repeatedly assessed ordinal scores with spatial effects, in particular the time dependence of the scores assessed on the same experimental units was modelled by a sigmoid logistic curve. Data collected from the potato late blight trials demonstrated the importance of spatial effects in agricultural field trials. These effects cannot be neglected when analysing such data. Although statistical methods can be refined to account for the complexity of the data, appropriate trial design still plays a central role in field experiments. / Accompanying dataset is at http://hdl.handle.net/2292/5240

One of the most frequently encountered types of data is where the response variables are measured on an ordinal scale. Although there have been substantial developments in the statistical techniques for the analysis of ordinal data, methods appropriate for repeatedly assessed ordinal data collected from field experiments are limited. A series of biennial field screening trials for evaluating cultivar resistance of potato to the disease, late blight, caused by the fungus Phytophthora infestans (Mont.) de Bary has been conducted by the New Zealand Institute of Crop and Food Research since 1983. In each trial, the progression of late blight was visually assessed several times during the planting season using a nine-point ordinal scale based on the percentage of necrotic tissues. As for many other agricultural field experiments, spatial differences between the experimental units is one of the major concerns in the analysis of data from the potato late blight trial. The aim of this thesis is to construct a statistical model which can be used to analyse the data collected from the series of potato late blight trials. We review existing methodologies for analysing ordinal data with mixed effects particularly those methods in the Bayesian framework. Using data collected from the potato late blight trials we develop a Bayesian hierarchical model for the analyses of repeatedly assessed ordinal scores with spatial effects, in particular the time dependence of the scores assessed on the same experimental units was modelled by a sigmoid logistic curve. Data collected from the potato late blight trials demonstrated the importance of spatial effects in agricultural field trials. These effects cannot be neglected when analysing such data. Although statistical methods can be refined to account for the complexity of the data, appropriate trial design still plays a central role in field experiments. / Accompanying dataset is at http://hdl.handle.net/2292/5240

One of the most frequently encountered types of data is where the response variables are measured on an ordinal scale. Although there have been substantial developments in the statistical techniques for the analysis of ordinal data, methods appropriate for repeatedly assessed ordinal data collected from field experiments are limited. A series of biennial field screening trials for evaluating cultivar resistance of potato to the disease, late blight, caused by the fungus Phytophthora infestans (Mont.) de Bary has been conducted by the New Zealand Institute of Crop and Food Research since 1983. In each trial, the progression of late blight was visually assessed several times during the planting season using a nine-point ordinal scale based on the percentage of necrotic tissues. As for many other agricultural field experiments, spatial differences between the experimental units is one of the major concerns in the analysis of data from the potato late blight trial. The aim of this thesis is to construct a statistical model which can be used to analyse the data collected from the series of potato late blight trials. We review existing methodologies for analysing ordinal data with mixed effects particularly those methods in the Bayesian framework. Using data collected from the potato late blight trials we develop a Bayesian hierarchical model for the analyses of repeatedly assessed ordinal scores with spatial effects, in particular the time dependence of the scores assessed on the same experimental units was modelled by a sigmoid logistic curve. Data collected from the potato late blight trials demonstrated the importance of spatial effects in agricultural field trials. These effects cannot be neglected when analysing such data. Although statistical methods can be refined to account for the complexity of the data, appropriate trial design still plays a central role in field experiments. / Accompanying dataset is at http://hdl.handle.net/2292/5240

One of the most frequently encountered types of data is where the response variables are measured on an ordinal scale. Although there have been substantial developments in the statistical techniques for the analysis of ordinal data, methods appropriate for repeatedly assessed ordinal data collected from field experiments are limited. A series of biennial field screening trials for evaluating cultivar resistance of potato to the disease, late blight, caused by the fungus Phytophthora infestans (Mont.) de Bary has been conducted by the New Zealand Institute of Crop and Food Research since 1983. In each trial, the progression of late blight was visually assessed several times during the planting season using a nine-point ordinal scale based on the percentage of necrotic tissues. As for many other agricultural field experiments, spatial differences between the experimental units is one of the major concerns in the analysis of data from the potato late blight trial. The aim of this thesis is to construct a statistical model which can be used to analyse the data collected from the series of potato late blight trials. We review existing methodologies for analysing ordinal data with mixed effects particularly those methods in the Bayesian framework. Using data collected from the potato late blight trials we develop a Bayesian hierarchical model for the analyses of repeatedly assessed ordinal scores with spatial effects, in particular the time dependence of the scores assessed on the same experimental units was modelled by a sigmoid logistic curve. Data collected from the potato late blight trials demonstrated the importance of spatial effects in agricultural field trials. These effects cannot be neglected when analysing such data. Although statistical methods can be refined to account for the complexity of the data, appropriate trial design still plays a central role in field experiments. / Accompanying dataset is at http://hdl.handle.net/2292/5240

Neste trabalho são apresentadas algumas extensões de modelos de sobrevivência com fração de cura, assumindo o contexto em que as observações estão agrupadas. Dois efeitos aleatórios são incorporados para cada grupo: um para explicar o efeito no tempo de sobrevida das observações suscetíveis e outro para explicar a probabilidade de cura. Apresenta-se uma abordagem clássica através dos estimadores REML e uma abordagem bayesiana através do uso de processos de Dirichlet. Discute-se alguns estudos de simulação em que avalia-se o desempenho dos estimadores propostos, além de comparar as duas abordagens. Finalmente, ilustram-se os resultados com dados reais. / In this work some extensions in survival models with cure fraction are presented, assuming the context in which the observations are grouped into clusters. Two random effects are incorporated for each group: one to explain the effect on survival time of susceptible observations and another to explain the probability of cure. A classical approach through the REML estimators is presented as well as a bayesian approach through Dirichlet Process. Besides comparing both approaches, some simulation studies which evaluates the performance of the proposed estimators are discussed. Finally, the results are illustrated with a real database.

Neste trabalho são apresentadas algumas extensões de modelos de sobrevivência com fração de cura, assumindo o contexto em que as observações estão agrupadas. Dois efeitos aleatórios são incorporados para cada grupo: um para explicar o efeito no tempo de sobrevida das observações suscetíveis e outro para explicar a probabilidade de cura. Apresenta-se uma abordagem clássica através dos estimadores REML e uma abordagem bayesiana através do uso de processos de Dirichlet. Discute-se alguns estudos de simulação em que avalia-se o desempenho dos estimadores propostos, além de comparar as duas abordagens. Finalmente, ilustram-se os resultados com dados reais. / In this work some extensions in survival models with cure fraction are presented, assuming the context in which the observations are grouped into clusters. Two random effects are incorporated for each group: one to explain the effect on survival time of susceptible observations and another to explain the probability of cure. A classical approach through the REML estimators is presented as well as a bayesian approach through Dirichlet Process. Besides comparing both approaches, some simulation studies which evaluates the performance of the proposed estimators are discussed. Finally, the results are illustrated with a real database.

長期性資料(longitudinal data)，是指對同一個觀察個體(subject)或實驗單位(experiment unit)，在不同時間點上重複觀察或測量一個或多個變數。雖然觀察個體之間互相獨立，但就同一個個體而言，不同時間的觀察或測量常常是有相關性的。且觀察的個體之間可能由於一些無法測量的環境因素造成個體之間有差異，因此在傳統橫斷面分析中，假設其有相同迴歸係數的邊際模型可能不合理。隨機效果模型可以解決長期資料分析的相關，並假設每個個體的迴歸係數不同；此模型不但可以說明橫斷面資料的cohort效果，也可直接解釋長期資料的age效果；更可以區分個體之間與個體之內的變異。 本研究以1995年至2000年台灣11個產業中的100家公司之每股盈餘與各財務比率，作為實證分析的資料；分別配適每股盈餘與時間、產業別、時間產業別交互作用及財務比率及排除每股盈餘有異常值後之邊際效果模型(一般迴歸分析)及隨機效果模型，並比較其參數估計之異同。實證結果顯示，一般迴歸分析與假設誤差不相關且等變異下的隨機效果模型參數估計相似，但後者能區分變異為個體之間(between-subjects)與個體之內(within-subject)的變異。而假設誤差不相關且不等變異與假設誤差服從AR(1)且不等變異下的隨機效果模型估計相近。實證結果並顯示，在排除異常值後的模型參數估計，一般迴歸分析不論是估計值及顯著性大多沒有很大差別；而隨機效果模型的估計在排除異常值前後較有差別。特別是現金流量比率(CFR)原本為不顯著變數，在排除異常值後的模型配適全部變顯著性變數。 / The defining characteristic of a longitudinal study is that individuals are measured repeatedly through time. Although it is independent between subjects, the set of observations on one subject tends to be inter-correlated. Because there is some natural heterogeneity due to unmeasured factors between subjects, it is not corrected to assume they have the same regression coefficients. A random effect model is a reasonable description about the different regression coefficients, and it can resolve the inter-correlation of the observations on one subject. The major advantages of the random effect model are its capacity to separate what in the context of population studies are called cohort and age effects, and it can distinguish the variations between subjects and within subjects. This study describes the marginal model and random effect model, and shows their difference by real data analysis. We apply these models to the earnings per share (EPS) and other financial ratios of one hundred companies in Taiwan, which are distributed in eleven industries. The results show that the parameter estimates of the marginal model and random effect model are similar when error structure is independent and of equal variance. Furthermore, the latter can distinguish the variations between subjects and within subjects. However, the residual analysis reveals that the error structure may not be constant. Therefore, we consider heteroscedasticity error in random effect model. We also assume that error follows an autoregressive process (e.g. AR(1) model), which leads to the optimum among our results in terms of residual analysis. There are some observations that appear to be outlying from the majority of data. The results show little difference in the marginal models no matter whether those outliers are included. However, we obtain different results in the random effect models. Especially, the variable of “cash flow ratio” becomes significant once those potential outliers have been excluded, while it is not significant when all cases are fitted in the model.

This thesis develops and evaluates statistical methods for different types of genetic analyses, including quantitative trait loci (QTL) analysis, genome-wide association study (GWAS), and genomic evaluation. The main contribution of the thesis is to provide novel insights in modeling genetic variance, especially via random effects models. In variance component QTL analysis, a full likelihood model accounting for uncertainty in the identity-by-descent (IBD) matrix was developed. It was found to be able to correctly adjust the bias in genetic variance component estimation and gain power in QTL mapping in terms of precision.  Double hierarchical generalized linear models, and a non-iterative simplified version, were implemented and applied to fit data of an entire genome. These whole genome models were shown to have good performance in both QTL mapping and genomic prediction. A re-analysis of a publicly available GWAS data set identified significant loci in Arabidopsis that control phenotypic variance instead of mean, which validated the idea of variance-controlling genes.  The works in the thesis are accompanied by R packages available online, including a general statistical tool for fitting random effects models (hglm), an efficient generalized ridge regression for high-dimensional data (bigRR), a double-layer mixed model for genomic data analysis (iQTL), a stochastic IBD matrix calculator (MCIBD), a computational interface for QTL mapping (qtl.outbred), and a GWAS analysis tool for mapping variance-controlling loci (vGWAS).