abstract: Though the likelihood is a useful tool for obtaining estimates of regression parameters, it is not readily available in the fit of hierarchical binary data models. The correlated observations negate the opportunity to have a joint likelihood when fitting hierarchical logistic regression models. Through conditional likelihood, inferences for the regression and covariance parameters as well as the intraclass correlation coefficients are usually obtained. In those cases, I have resorted to use of Laplace approximation and large sample theory approach for point and interval estimates such as Wald-type confidence intervals and profile likelihood confidence intervals. These methods rely on distributional assumptions and large sample theory. However, when dealing with small hierarchical datasets they often result in severe bias or non-convergence. I present a generalized quasi-likelihood approach and a generalized method of moments approach; both do not rely on any distributional assumptions but only moments of response. As an alternative to the typical large sample theory approach, I present bootstrapping hierarchical logistic regression models which provides more accurate interval estimates for small binary hierarchical data. These models substitute computations as an alternative to the traditional Wald-type and profile likelihood confidence intervals. I use a latent variable approach with a new split bootstrap method for estimating intraclass correlation coefficients when analyzing binary data obtained from a three-level hierarchical structure. It is especially useful with small sample size and easily expanded to multilevel. Comparisons are made to existing approaches through both theoretical justification and simulation studies. Further, I demonstrate my findings through an analysis of three numerical examples, one based on cancer in remission data, one related to the China’s antibiotic abuse study, and a third related to teacher effectiveness in schools from a state of southwest US. / Dissertation/Thesis / Doctoral Dissertation Statistics 2017

Orientador: Luiza Aparecida Trinca / Banca: Liciana Vaz da Arruda / Banca: Osmar Delmanto Junior / Banca: Célia Regina Lopes Zimback / Banca: Marli Teixeira de A. Minhoni / Resumo: É bastante comum na área agrícola, experimentos cujas variáveis respostas são contagens ou proporções. Para esse tipo de dados, utiliza-se a metodologia de modelos lineares generalizados quando as respostas são independentes. Por outro lado, quando as respostas são dependentes, há uma correlação entre as observações e isso tem que ser levado em consideração na análise, para evitar inferências incorretas sobre os coeficientes de regressão. Na literatura há técnicas disponíveis para a modelagem e análise desses dados, sendo os modelos disponíveis extensões dos modelos lineares generalizados. No presente trabalho, utiliza-se a metodologia de equação de estimação generalizada, que inclui no modelo uma matriz de correlação para a obtenção de um melhor ajuste. Outra alternativa, também abordada neste trabalho, é a utilização de um modelo linear generalizado misto, no qual o uso de efeitos aleatórios também introduz uma correlação entre observações que tenham algum efeito em comum. Essas duas metodologias são aplicadas a um conjunto de dados obtidos de um experimento para avaliar certas condições na germinação de sementes de mamona da cultivar AL Guarany 2002, com o objetivo de se verificar qual o melhor modelo de estimação para esses dados / Abstract: Experiments whose response variables are counts or proportions are very common in agriculture. For this type of data, if the observational units are independent, the methodology of generalized linear models can be appropriate. On the other hand, when responses are dependent or clustered, there is a correlation between the observations and that has to be taken into consideration in the analysis to avoid incorrect inferences about the regression coefficients. In the literature there are techniques available for modeling and analyzing such type data, the models being extensions of generalized linear models. The present study explores the use of: 1) generalized estimation equations, that includes a correlation matrix to obtain a better fit; 2) generalized linear mixed models, that introduce a correlation between clustered observations though the addition of random effects in the model. These two methodologies are applied to a data set obtained from an experiment to evaluate certain conditions on the germination of seeds of castor bean cultivar AL Guarany 2002 with the objective of determining the best estimation model for such data / Doutor

Resumo: Foram instalados três testes clonais de Eucalyptus spp em delineamentos de blocos completos ao acaso em diferentes tamanhos de parcelas experimentais, com 18 tratamentos (18 clones) repetidos em cada experimento. Experimento 1:-Teste clonal em delineamento de blocos ao acaso, com 6 repetições de parcelas retangulares com 42 plantas (6 linhas x 7 plantas); Experimento 2:-Teste clonal em delineamento de blocos ao acaso, com 6 repetições de parcelas lineares de 10 plantas; Experimento 3:-Teste clonal em delineamento de blocos ao acaso, com uma planta por parcela (single tree plot - STP), com 20 repetições (blocos). Aos três anos de idade foi calculado o IMA (incremento médio anual de volume). Os dados do IMA foram avaliados para os valores genotípicos e os componentes de variância para os três delineamentos através de duas metodologias de análise: a) tradicional (ANOVA) e b) modelo misto (REML/BLUP). As estimativas de interesse foram obtidas utilizando os procedimentos GLM e MIXED do software estatístico SAS (2004). Foi efetuada análise de covariância para correção do efeito de competição testando três covariáveis: índice de Heigy, Falha, Média, para os três experimentos e nas duas metodologias de análise. A metodologia REML/BLUP, foi ligeiramente superior à metodologia GLM, em todas as análises. O índice de HEIGY não foi eficiente em nenhuma metodologia de análise para os três experimentos estudados para a característica IMA aos 3 anos de idade. As covariáveis Falha e Média não melhoraram as análises no experimento de parcelas retangulares, mas contribuíram para uma melhora sutil nos experimentos em linha e de planta única. Houve alteração no ordenamento dos genótipos de um delineamento para outro em todas as metodologias de análise. A alocompetição foi a grande causadora de erro experimental entre parcelas ...(Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Three Eucalyptus spp cloning tests were designed in plots at randomized blocks, under different arrays and experimental parcels size, having 18 treatments (18 clones), replicated in each experiment. Experiment 1: Clonal test in randomized blocks with 6 replications in rectangular parcels with 42 plants (6 lines x 7 plants); Experiment 2: Clonal test in randomized blocks, with 6 replications in linear parcels having 10 plants; Experiment 3: Clonal test in randomized blocks in Single Tree Plot - STP, having 20 replications (blocks). After three years, the average of volume annual increment - IMA was calculated. IMA data were evaluated to genotypes value and the variance components to the three designs trough two analysis methodologies: a) Traditional (ANOVA) and b) mixed model (REML/BLUP). Interested estimative were obtained using GLM and MIXED procedures from SAS (2004). Covariance analysis was done to correct the competition effect testing three covaries: Heigy index, Falha, Mean, to the three experiments and in the two analysis methodology. The REML/BLUP methodology was slightly better than GLM methodology in all analysis. The HEIGH index was not apply to none of the three evaluated methodology to IMA characteristic after three years. The Falha 8 and Mean 8 covaries did not improve the design analysis of rectangular parcels, but they contributed to a subtle improve in the line and only plant designs. There was alteration from a design genotype order to other in all analysis methodology. The alocompetition was the main responsible of experimental error between parcels. The rectangular experiment was more efficient than STP, being this one more efficient than the linear parcels to the actual commercial crop system (mono clonal planting). The STP experiment presented higher medium experimental productivity as well higher averages predicted in almost all genotypes tested ...(Complete abstract, click electronic access below) / Orientador: Dilermando Perecin / Coorientador: Rinaldo Cesar de Paula / Banca: João Ademir de Oliveira / Banca: Mário Luiz Teixeira de Moraes / Mestre

O objetivo do presente trabalho é analisar a presença da restrição financeira nas decisões de investimentos em condições de incerteza de um conjunto de 1223 empresas brasileiras no período de 1986 a 2006. A incerteza é incorporada no modelo de investimento considerando o comportamento das variáveis vendas e fluxo de caixa como um movimento browniano com drift. Além disso, a variável fluxo de caixa é analisada em baixa e alta incerteza, considerando três diferentes medidas para a incerteza: a variação anual do índice Ibovespa, o desvio-padrão de vendas e de fluxo de caixa. Já para considerar o efeito da restrição financeira sobre as decisões de investimento as firmas são agrupadas de acordo com o grau de intensidade de capital, tamanho da firma e grau tecnológico. A estimação dos parâmetros da equação do investimento é realizada considerando-se o modelo misto. O modelo misto, ainda não utilizado em estudos brasileiros na análise do comportamento das decisões de investimento, permite considerar a heterogeneidade nos coeficientes das variáveis independentes, o que evita o viés introduzido pela suposição de homogeneidade. Os resultados obtidos neste estudo mostraram uma maior sensibilidade do investimento ao fluxo de caixa para as firmas mais intensivas em capital, firmas de médio porte e firmas com alto grau tecnológico. Esses resultados se mantêm quando a variável fluxo de caixa é analisada em alta incerteza, ou seja, o investimento das firmas com alta intensidade de capital, médio porte e com alto grau tecnológico é mais sensível ao fluxo de caixa em condições de alta incerteza. / The aim of this research is to analyze the presence of financial constraints on investments decisions under uncertainty using data from 1223 Brazilian firms over the 1986 to 2006 period. Uncertainty is incorporated in the model of investment decisions considering the sales and cash flow variables, which are estimated by a stochastic equation of Brownian motion. In addition, the variable cash flow is grouped by high and low uncertainty according to annual rate of the Ibovespa index, the standard deviation of sales and cash flow. To consider the effects of financial constraints on firms investment decisions, this study used the degree of capital intensity, size, and the technological degree to classify firms. The investment equation parameters are estimated considering the mixed model. The mixed model, it has not yet been used in analysis of Brazilian firms, allows considering the heterogeneity on explanatory variables, which avoids the bias introduced by assumption of homogeneity. The results show greater sensitivity of investment to cash flow for more capital-intensive firms, medium and high-tech ones. These results keep when cash-flow variable is analyzed by high uncertainty, i.e, for these firms the investment is more sensitive to cash flow under higher uncertainty.

O milho é uma espécie alógama cujo produto comercial são os híbridos, os quais originam-se do cruzamento de duas linhagens endogâmicas. Uma forma para obtenção de tais linhagens é por meio das técnicas de indução de haploidia e posterior obtenção dos duplo-haploides, permitindo até 100% de homozigose. Essas técnicas retornam resultados importantes no melhoramento de milho. Uma variável de interesse importante, obtida a partir dessas técnicas é a taxa de indução de haploidia, a qual trata-se de uma proporção entre o número de sementes haploides e o número total de sementes. O conjunto de dados foi obtido pelo cruzamento da linhagem indutora LI- ESALQ, com cinco genótipos comerciais de milho (2B587PW, 30F53H, BM820, DKB390 e STATUS VIPTERA), em duas gerações F1 e F2, por meio de um delineamento em blocos ao acaso, na área experimental do Departamento de Genética da ESALQ/USP. A teoria dos modelos lineares generalizados (MLGs) possibilita mais opções para a distribuição da variável resposta, exigindo somente que a mesma pertença à família exponencial sob a forma canônica. Tal classe de distribuições pode ser ainda expandida para modelos que permitem efeitos aleatórios no preditor linear, caracterizando a classe dos modelos lineares generalizados mistos (MLGMs). O objetivo deste trabalho foi analisar a taxa de indução de haploidia em milho tropical, utilizando um modelo binomial misto, com efeito aleatório em nível de indivíduo. O método de estimação foi o de máxima verossimilhança. Com base em tal modelagem, verificou-se que o genótipo 30F53H, destacou-se em relação aos demais quanto à eficiência da taxa de indução de haploidia. Todas as análises foram implementadas no software R. / The maize is an allogeneic species whose commercial product are the hybrids, which are gerated by the crossing of two endogenous lines. An alternative to obtain these lines is using the haploid induction techniques and subsequent doubled haploid production, that allows up to 100% homozygous. Artificial production of doubled haploids is important in plant breeding. An important variable, that results from these techniques, is the haploid induction rate, which is a proportion between the number of haploid seeds and the total number of seeds. The data set was obtained by crossing the inductive line LI-ESALQ, with five commercial genotypes of corn (2B587PW, 30F53H, BM820, DKB390 and STATUS VIPTERA), in two generations F1 e F2, in a randomized block design, in the experimental area of Department of Genetics, ESALQ/USP. The generalized linear models (GLMs) allow more options for the variable response distribution, requiring only that it belongs to the exponential family in canonical form. The GLM class can be expanded to models that allow random effects in the linear predictor, the mixed generalized linear models (MGLM) class. This work aimed to analyze the haploid induction rate in the tropical maize. The binomial mixed model, that included random effects in individual level, was proposed. The maximum likelihood method was used to estimate the parameters. The result revealed that the genotype 30F53H stands out in relation to the others regarding the efficiency in the haploid induction rate. All the analyzes were implemented in the software R.

In variety testing as well as in psychological assessment, the situation occurs that in a two-way ANOVA-type model with only one replication per cell, analysis is done under the assumption of no interaction between the two factors. Tests for this situation are known only for fixed factors and normally distributed outcomes. In the following we will present five additivity tests and apply them to fixed and mixed models and to quantitative as well as to Bernoulli distributed data. We consider their performance via simulation studies with respect to the type-I-risk and power. Furthermore, two new approaches will be presented, one being a modification of Tukey's test and the other being a new experimental design to test for interactions.

abstract: Spatial regression is one of the central topics in spatial statistics. Based on the goals, interpretation or prediction, spatial regression models can be classified into two categories, linear mixed regression models and nonlinear regression models. This dissertation explored these models and their real world applications. New methods and models were proposed to overcome the challenges in practice. There are three major parts in the dissertation. In the first part, nonlinear regression models were embedded into a multistage workflow to predict the spatial abundance of reef fish species in the Gulf of Mexico. There were two challenges, zero-inflated data and out of sample prediction. The methods and models in the workflow could effectively handle the zero-inflated sampling data without strong assumptions. Three strategies were proposed to solve the out of sample prediction problem. The results and discussions showed that the nonlinear prediction had the advantages of high accuracy, low bias and well-performed in multi-resolution. In the second part, a two-stage spatial regression model was proposed for analyzing soil carbon stock (SOC) data. In the first stage, there was a spatial linear mixed model that captured the linear and stationary effects. In the second stage, a generalized additive model was used to explain the nonlinear and nonstationary effects. The results illustrated that the two-stage model had good interpretability in understanding the effect of covariates, meanwhile, it kept high prediction accuracy which is competitive to the popular machine learning models, like, random forest, xgboost and support vector machine. A new nonlinear regression model, Gaussian process BART (Bayesian additive regression tree), was proposed in the third part. Combining advantages in both BART and Gaussian process, the model could capture the nonlinear effects of both observed and latent covariates. To develop the model, first, the traditional BART was generalized to accommodate correlated errors. Then, the failure of likelihood based Markov chain Monte Carlo (MCMC) in parameter estimating was discussed. Based on the idea of analysis of variation, back comparing and tuning range, were proposed to tackle this failure. Finally, effectiveness of the new model was examined by experiments on both simulation and real data. / Dissertation/Thesis / Doctoral Dissertation Statistics 2020

This thesis presents research focused on developing statistical methods with emphasis on techniques that can be used for the analysis of data in imaging studies and sparse estimations for applications in high-dimensional data. The first contribution addresses the pixel/voxel-labeling problem for spatial hidden Markov models in image analysis. We formulate a Gaussian spatial mixture model with Potts model used as a prior for mixture allocations for the latent states in the model. Jointly estimating the model parameters, the discrete state variables and the number of states (number of mixture components) is recognized as a difficult combinatorial optimization. To overcome drawbacks associated with local algorithms, we implement and make comparisons between iterated conditional modes (ICM), simulated annealing (SA) and hybrid ICM with ant colony system (ACS-ICM) optimization for pixel labelling, parameter estimation and mixture component estimation. In the second contribution, we develop ACS-ICM algorithm for spatiotemporal modeling of combined MEG/EEG data for computing estimates of the neural source activity. We consider a Bayesian finite spatial mixture model with a Potts model as a spatial prior and implement the ACS-ICM for simultaneous point estimation and model selection for the number of mixture components. Our approach is evaluated using simulation studies and an application examining the visual response to scrambled faces. In addition, we develop a nonparametric bootstrap for interval estimation to account for uncertainty in the point estimates. In the third contribution, we present sparse estimation strategies in linear mixed model (LMM) for longitudinal data. We address the problem of estimating the fixed effects parameters of the LMM when the model is sparse and predictors are correlated. We propose and derive the asymptotic properties of the pretest and shrinkage estimation strategies. Simulation studies is performed to compare the numerical performance of the Lasso and adaptive Lasso estimators with the pretest and shrinkage ridge estimators. The methodology is evaluated through an application of a high-dimensional data examining effective brain connectivity and genetics. In the fourth and final contribution, we conduct an imaging genetics study to explore how effective brain connectivity in the default mode network (DMN) may be related to genetics within the context of Alzheimer’s disease. We develop an analysis of longitudinal resting-state functional magnetic resonance imaging (rs-fMRI) and genetic data obtained from a sample of 111 subjects with a total of 319 rs-fMRI scans from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database. A Dynamic Causal Model (DCM) is fit to the rs-fMRI scans to estimate effective brain connectivity within the DMN and related to a set of single nucleotide polymorphisms (SNPs) contained in an empirical disease-constrained set. We relate longitudinal effective brain connectivity estimated using spectral DCM to SNPs using both linear mixed effect (LME) models as well as function-on-scalar regression (FSR). / Graduate

This work deals with the way of balancing production-assembly line, which would minimalize set up costs. The production-assembly line shall allow assembling more mutually similar variants of the same product. The time of duration of each operation is constant, but can differs between individual variants of the product. Cycle time is related to the variant of the product.

Arbuscular mycorrhizal (AM) fungi are key soil symbiotic microorganisms, intensively studied for their roles in improving plant fitness and their ubiquity in terrestrial ecosystems. Research on AM fungi is difficult because their obligate biotrophic nature makes it impossible to culture them in the absence of a host. Over the last three decades, Ri T-DNA transformed roots have been the gold standard to study AM fungi under in vitro conditions. However, only two host plant species (Daucus carota and Cichorium intybus) have been routinely used to in vitro propagate less than 5% of the known AM fungal species. There is much evidence that host identity can significantly affect AM symbioses, therefore, we investigated any potential host-specific effects of two novel Ri T-DNA transformed root species, Medicago truncatula and Nicotiana benthamiana, by associating them with seven AM fungal species selected based on their contrasting behaviors when grown with Ri T-DNA transformed D. carota roots. To evaluate the performance of new Ri T-DNA transformed roots to host and propagate AM fungal species, a factorial set-up was used to generate nine unique pairs of hosts (M. truncatula, N. benthamiana, D. carota) and AM fungi (Rhizophagus irregularis, R. clarus, Glomus sp.). Using statistical modeling, all pairs of hosts and AM fungi were compared by their symbiosis development (SD) and sporulation patterns in the hyphal compartments (HCs) of two-compartment Petri dishes. Our results show that 1) most of the variation between host and AM fungus pairs relating to SD or HC sporulation was explained by an interaction between host and AM fungal identity, i.e., host identity alone was not sufficient to explain AM fungal behaviour, 2) AM symbioses involving different combinations of symbiont identities trigger heterogenous fungal behaviours. This work provides a robust framework to develop and evaluate new Ri T-DNA roots for the in vitro propagation of AM fungi, an important asset for germplasm collections and biodiversity preservation.