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

Submitted by Jos? Henrique Henrique (jose.neves@ufvjm.edu.br) on 2017-09-28T19:28:43Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) mariane_rodrigues_ferreira.pdf: 1446137 bytes, checksum: b0c55b008bb6208223dfeaa66f8b1e31 (MD5) / Approved for entry into archive by Rodrigo Martins Cruz (rodrigo.cruz@ufvjm.edu.br) on 2017-10-09T14:21:58Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) mariane_rodrigues_ferreira.pdf: 1446137 bytes, checksum: b0c55b008bb6208223dfeaa66f8b1e31 (MD5) / Made available in DSpace on 2017-10-09T14:21:58Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) mariane_rodrigues_ferreira.pdf: 1446137 bytes, checksum: b0c55b008bb6208223dfeaa66f8b1e31 (MD5) Previous issue date: 2017 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES) / Objetivou-se com este trabalho determinar o melhor m?todo de estima??o dos coeficientes de repetibilidade e as melhores combina??es entre cortes de acordo com a estabiliza??o genot?pica para caracter?sticas agron?micas, estimar par?metros gen?ticos e formar grupos morfofuncionais com base nas caracter?sticas morfog?nicas e estruturais por meio do agrupamento de Otimiza??o de Tocher em gen?tipos de Panicum maximum. Os coeficientes de repetibilidade para produ??o de massa seca total (MST), massa seca foliar (MSF), massa seca do colmo (MSC), porcentagem de folhas (%F), porcentagem de colmo (%C), foram estimados por meio de quatro m?todos: an?lise de vari?ncia (ANOVA), an?lise estrutural com base na m?dia dos coeficientes de correla??o (AECOR), an?lise de componentes principais com base na matriz de covari?ncia (CPCOV) e na matriz de correla??es (CPCOR). Para o estudo da estabiliza??o genot?pica, utilizaram-se os coeficientes estimados pela ANOVA e CPCOR. Para a avalia??o das caracter?sticas morfog?nicas foram estimadas: taxa de aparecimento foliar (TAPF), filocrono (FIL), taxa de alongamento foliar (TALF), taxa de senesc?ncia foliar (TSF), comprimento final da l?mina (CFL), n?mero de folhas vivas (NFV), dura??o de vida das folhas (DVF), taxa de alongamento de pseudocolmo (TALC), n?mero m?dio de perfilhos (NMP), rela??o l?mina:colmo (RLC). Para MST, foram observados coeficientes de repetibilidade variando entre 0,3500 e 0,4300 pelos m?todos da ANOVA e CPCOR, respectivamente. Altos coeficientes de repetibilidade tamb?m foram encontrados para a caracter?stica MSF. Baixos coeficientes de repetibilidade foram observados para %F e %Ce rela??o l?mina:colmo. Para estabiliza??o genot?pica da MST, os melhores coeficientes foram observados para a combina??o entre os cortes 6 a 7 e entre os cortes 5 a 8, enquanto os menores coeficientes foram observados quando se utilizaram apenas os cortes 3 a 4 e de 1 a 2, em ambos os m?todos. Para a rela??o l?mina:colmo, os melhores coeficientes foram registrados para os cortes 6 a 7 pelo m?todo da ANOVA, e 1 a 2 pelo m?todo CPCOR. De maneira geral, a combina??o entre os cortes de 6 a 7, tamb?m proporcionou maior repetibilidade e determina??o, otimizando a estabiliza??o dos gen?tipos para as massas e porcentagens de folha e de colmo. No estudo dos par?metros gen?ticos e agrupamento, foi observado que somente as caracter?sticas TALF, CFL e RLC tiveram o componente vari?ncia gen?tica significativo. Apesar disto, as caracter?sticas TALC, NFV, apresentaram coeficientes de varia??o genot?picos (CVg) superiores aos coeficientes de varia??o residual ou ambiental (CVe). As caracter?sticas TAPF, FIL, DVF e TSF apresentaram valores abaixo da unidade para a raz?o CVg/CVe. Alta raz?o CVg/CVe foi observada para as caracter?sticas RLC, NFV, TALC, TALF, CFL, sendo os maiores coeficientes foram registrados para RLC. Ap?s o agrupamento, constatou-se a forma??o de cinco grupos morfofuncionais. Os grupos que apresentaram maiores valores de TALF foram os grupos 3, 5 e 1 com valores superiores ? m?dia geral de todos os gen?tipos avaliados. Enquanto o grupo 4 obteve menor desempenho para esta caracter?stica. Para a TALC o grupo 2 se destacou, seguido pelo grupo 5. Dentre todos os grupos a maior RLC constada foi para o grupo 4 e para CFL o grupo 3. Conclui-se que os m?todos que proporcionaram os melhores coeficientes de repetibilidade de determina??o foram os dos componentes principais com base na matriz de correla??o e de covari?ncia. Para a estabiliza??o genot?pica, os melhores coeficientes de repetibilidade e determina??o s?o observados para os cortes realizados no segundo per?odo das ?guas. As caracter?sticas TALF, CFL e RLC apresentam variabilidade gen?tica significativa, e as caracter?sticas TAPF, FIL, DVF e TSF apresentam baixa raz?o CVg/CVe e necessitam de maior controle ambiental. Os grupos 3, 5 e 1, apresentam altas taxas de alongamento de folha como mecanismo de ac?mulo de forragem. J? o grupo 4 se destaca pela capacidade de perfilhamento. / Disserta??o (Mestrado) ? Programa de P?s-Gradua??o em Zootecnia, Universidade Federal dos Vales do Jequitinhonha e Mucuri, 2017. / The objective was to evaluate the coefficient of repeatability of the agronomic traits and to estimate the breeding value of morphogenic characteristics to stablish morphofunctional groups in the clustering analysis of Tocher in Panicum maximum genotypes. The repeatability coefficients were estimated by four methods: analysis of variance (ANOVA), structural analysis based on the correlation matrix (EACOR), principal component analysis based on the variance and covariance?s matrix (PCCOV) and principal component analysis based on the correlation matrix (PCCOR). To the genotypic stabilization study, the ANOVA and PCCOR were used. To the morphogenic evaluation, the characteristics were estimated: leaf appearance rate (LAR), phillochron (PHC), leaf elongation rate (LER), leaf senescence rate (LSR), number of live leaves (NLL), leaf life spam (LLS), leaf final length (LFL), stem elongation rate (SER), average number of tillers (ANT) and leaf:stem ratio (LSR). To total dry matter were observed repeatability coefficients ranging from 0.3500 to 0.4300 by the ANOVA and PCCOR methods, respectively. High coefficients of repeatability were estimated to leaf dry mass too. Low coefficients of repeatability were observed to percentage of leaves, stems and leaf:stem ratio. In the genotypic stabilization of total dry mass the higher coefficients were observed between the 6 and 7th harvest and between the 5 and 8th harvest, while the lowest coefficients were observed when the harvests 3 to 4 and 1 to 2 were considered in both methods. To leaf:stem ratio the higher coefficients were observed to harvests between 6 and 7 in the ANOVA method and 1 to 2 in the PCCOR method. In general, the combination between the 6 and 7th harvests also improves the repeatability and determination coefficients, optimizing the stabilization of the genotypes to dry mass and percentage of leaf and stems. In the study of genetic parameters and clustering, were observed significant effect to genetic variance component only to LER, LFL and LSR. In spite of this the characteristic SER and NLL had CVg higher than CVr. The characteristics LAR. PHC, LLS and LSR had CVg/CVr above the unity. High CVg/CVr ratio were observed to LSR, NLL, SER, LER and LFL, so that the highest coefficient observed to LSR. After the clustering analysis was found five morphofunctional groups. The groups with higher LER were 3, 5 and 1 with breeding values above the general mean. The group 4 had lowest LER. The groups 2 and 5 had the highest SER and the highest LSR was observed to the group 4. The group 3 showed high LFL. It was possible to conclude that the total and leaf dry mass have higher coefficient of repeatability, indicating better accuracy in the identification of the superior genotypes of P. maximum. In the genotypic stabilization, the higher coefficient and determination were observed to the harvests realized in the rainy period. The morphogenic characteristics that have the highest genetic variance have more possibility of gains with the selection and the traits with low CVg/CVr ratio need more environmental control. The groups 3, 5 and 1 have high potential to forage production duly its high leaf elongation rate.

Master of Science / Department of Statistics / Suzanne Dubnicka / In animal science, challenge model studies often produce longitudinal data. Many times the lognormal distribution is useful in modeling the data at each time point. Escherichia coli O157 (E. coli O157) studies measure and record the concentration of colonies of the bacteria. There are times when the concentration of colonies present is too low, falling below a limit of detection. In these cases a zero is recorded for the concentration. Researchers employ a method of enrichment to determine if E. coli O157 was truly not present. This enrichment process searches for bacteria colony concentrations a second time to confirm or refute the previous measurement. If enrichment comes back without evidence of any bacteria colonies present, a zero remains as the observed concentration. If enrichment comes back with presence of bacteria colonies, a minimum value is imputed for the concentration. At the conclusion of the study the data are log10-transformed. One problem with the transformation is that the log of zero is mathematically undefined, so any observed concentrations still recorded as a zero after enrichment can not be log-transformed. Current practice carries the zero value from the lognormal data to the normal data. The purpose of this report is to evaluate methods for handling missing data due to a limit of detection and to provide results for various analyses of the longitudinal data. Multiple methods of imputing a value for the missing data are compared. Each method is analyzed by fitting three different models using SAS. To determine which method is most accurately explaining the data, a simulation study was conducted.

Adjusted Wald intervals for binomial proportions in one-sample and two-sample designs have been shown to perform about as well as the best available methods. The adjusted Wald intervals are easy to compute and have been incorporated into introductory statistics courses. An adjusted Wald interval for paired binomial proportions is proposed here and is shown to perform as well as the best available methods. A sample size planning formula is presented that should be useful in an introductory statistics course.

No description available.

The purpose of the study was to investigate how the online, computer-based learner's personal learning profile (Preference), the content delivery method supplemented with visual content based on Neil Fleming's VARK (visual, aural, read/write, kinesthetic) model (Content), and the interaction of Preference and Content, influenced learner performance (Performance) and/or learner self-reported satisfaction (Satisfaction). Participants were drawn from a population of undergraduates enrolled in a large public southwestern research university during the fall 2015 semester. The 165 student participants (13.79% completion rate) were comprised of 52 (31.5%) females and 113 (68.5%) males age 18-58+ years with 126 (76.4%) age 18-24 years. For race/ethnicity, participants self-identified as 1 (0.66%) American Indian/Alaska Native, 21 (12.7%) Asian/Pacific Islander, 27 (16.4%) Black, non-Hispanic, 28 (17%) Hispanic, 78 (47.3%) White, non-Hispanic, 10 (6.1%) other. Reported socioeconomic status was 22 (13.3%) withheld, 53 (32.1%) did not know, 45 (27.3%) low, 13 (7.9%) moderately low, 16 (9.7%) middle, 8 (4.8%) upper middle, and 8 (4.8%) upper. This causal-comparative and quasi-experimental, mixed-method, longitudinal study used researcher-developed web-based modules to measure Performance and Satisfaction, and used the criterion p < .05 for statistical significance. A two-way, 4 x 3 repeated measures (Time) analysis of variance (RM-ANOVA) using Preference and Content was statistically significant on each Performance measure over Time, and at two measures on Satisfaction over Time. The RM-ANOVA was statistically significant on between-subjects main effect Performance for read/write modality Content compared to aural and kinesthetic Content. There were no statistically significant main effects observed for Satisfaction. A Pearson r correlation analysis showed that participants that were older, married, and of higher socioeconomic status performed better. The correlation analysis also showed that participants who performed better reported greater likelihood to take online courses in the future, higher motivation, sufficient time and support for studies, and sufficient funding for and access to the Internet. The study results suggested that regardless of Preference, using read/write modality Content based on the VARK model while maintaining the verbal language can yield better Performance outcomes. The study results also suggested that while maintaining the verbal language, Preference, and Content based on the VARK model do not distinguish learner Satisfaction outcomes. However, because Satisfaction has been shown to impact Performance, efficacy, and retention, it matters to educational institutions. Future research should consider more granular models and factorial research methods, because models that utilize a single representative construct score can mask effects when analyzing Performance and Satisfaction.

No presente trabalho propôs-se uma abordagem simples visando à escolha de um modelo linear misto a ser ajustado a dados com medidas repetidas. A construção do modelo envolveu a escolha dos efeitos aleatórios, dos efeitos fixos e da estrutura de covariâncias utilizando técnicas gráficas e analíticas. O uso do Teste da Razão de Verossimilhança e dos Critérios de Informação de Akaike - AIC e de Schwarz - BIC pode levar a escolhas diferentes da estrutura de covariâncias, o que pode influenciar os resultados das inferências feitas sobre os parâmetros de efeitos fixos. A abordagem foi aplicada a conjuntos de dados resultantes de estudos agropecuários utilizando o software livre R. Foram feitas comparações dos resultados obtidos de modelos implementados com o proc mixed do SAS e com a função lme() do R, observando as vantagens e restrições destes dois softwares. / In this present work was proposed a simple approach to know how to choose a linear mixed model that can be adjustable to data with repeated measures. The construction of the model involved the choice of random effects, the fixed effects and covariance structure, using graphical and analytical techniques. The use of the Likelihood Ratio Test and the Akaike Information Criteria - AIC and Schwarz - BIC can lead to different choices of the structure of covariance, which may influence the results of inferences made about the parameters of fixed effects. The approach was applied to data sets that was resulted from farming studies using the software R. Comparisons of the results of models implemented were made with the proc mixed of SAS and with the function lme() of R, noting the advantages and limitations of these two softwares.

A principal fonte de proteína na nutrição dos ruminantes é a proteína de origem microbiana, sintetizada no processo fermentativo de degradação ruminal a partir de proteína dietética ou microbiana. Logo o conhecimento deste processo é de grande importância em estudos de avaliação de alimentos para estes animais. Modelos não lineares são amplamente utilizados nestes estudos, buscando estimar os parâmetros da cinética de degradação ruminal através de métodos clássicos de análise univariada. Como estes ensaios envolvem medidas repetidas, propõem-se o uso de modelos não lineares mistos que permitem que a função de regressão não linear dependa de efeitos fixos e aleatórios, o que pode resolver os problemas de correlação entre as medidas repetidas e heterogeneidade de variâncias das respostas. Neste trabalho foram utilizadas duas alternativas comuns de análise de dados de digestibilidade, e seus resultados foram comparados com os da abordagem que utiliza modelos não lineares mistos. Utilizou-se o modelo não linear de Orskov e McDonald (1979) para explicar a cinética de degradação ruminal da matéria seca (MS) e da fibra em detergente neutro (FDN) do feno de capim-Tifton 85, em novilhos alimentados com seis rações experimentais compostas por três diferentes combinações de volumoso(Vo):concentrado(Co) (70:30, 50:50 e 30:70%). Como volumoso foram utilizados fenos de capim-Tifton 85 de diferentes qualidades (4% e 10% de proteína bruta) e como concentrado, casca de soja, milho moído e farelo de girassol. A degradabilidade foi determinada pela técnica in situ e os dez tempos de incubação foram de: 3, 6, 12, 24, 48, 60, 72, 84, 96 e 120 horas. Originalmente o experimento foi delineado em quadrado latino (6×6) com seis novilhos mestiços fistulados (linhas), seis períodos (colunas) e seis tratamentos, em que nas parcelas tem-se uma estrutura de parcelas subdivididas, sendo as subparcelas, os tempos de incubação. O uso de modelos não lineares mistos na análise de dados de digestibilidade in situ é bastante atraente principalmente quando a pesquisa tem por objetivo entender o comportamento do processo de digestibilidade ao longo dos tempos de incubação. Além disso, quanto maior a variabilidade dos dados, a abordagem mista se torna mais indicada, reduzindo os erros padrão das estimativas dos parâmetros. Mesmo não incluindo a estrutura de delineamento experimental, os modelos não lineares mistos conseguem explicar bem a variabilidade extra, provocada pelos efeitos dos fatores associados ao delineamento, com a inclusão de efeitos aleatórios nos parâmetros do modelo de Orskov e McDonald (1979). O pacote estatístico nlme do R mostrou-se ágil e eficiente no ajuste dos modelos não lineares mistos e as suas ferramentas gráficas foram importantes na avaliação da qualidade dos ajustes e na escolha de modelos. / The main source of protein in ruminant nutrition is the protein of microbial origin, synthesized in the fermentation process of ruminal degradation starting from dietetics or microbial protein. Then, the knowledge of this process is of great importance in evaluation studies of food for these animals. Nonlinear models are widely used in these studies to estimate the parameters of ruminal degradation kinetics through the classical methods of univariate analysis. As these trials involve repeated measurements, we propose the use of nonlinear mixed models which allows that the nonlinear regression function depends on fixed and random effects, which can solve the problems of correlation between the repeated measurements and heterogeneity of variances of the responses. In this work, we used two common alternatives of digestibility data analysis, and their results were compared with the approach which uses nonlinear mixed model. We used the nonlinear model of Orskov and McDonald (1979) to explain the kinetics of ruminal degradation of dry matter (MS) and neutral detergent fiber (FDN) of the hay grass-Tifton 85, in steers fed experimental with six diets composed of three different combinations of forage(Vo):concentrate(Co) (70:30, 50:50 and 30:70%). As forage, we used hay grass-Tifton 85 of different qualities (4% and 10% crude protein) and as concentrate, soybean hulls, corn and sunflower meal. The degradability was determined by the in situ technique and the incubation times were 3, 6, 12, 24, 48, 60, 72, 84, 96 and 120 hours. Originally the experiment was designed as a Latin square (6 × 6) with six fistulated crossbred steers (lines), six periods (columns) and six treatments, in which the plots have a splitplot structure where the subplots were considered the times of incubation. The use of nonlinear mixed models in the analysis of the in situ digestibility data is quite attractive especially when the research aims to understand the process behavior digestibility over the incubation times. Moreover, the higher the variability of the data, the mixed approach becomes more suitable, reducing standard errors of the estimated parameters. Even excluding the structure of experimental design, the linear mixed models can explain well the extra variability caused by the effects of the factors associated with the design, with the inclusion of random effects in the model parameters of Orskov and McDonald (1979). The R statistical package nlme proved to be agile and efficient for the adjustment of nonlinear mixed models and its graphical tools were important in evaluating the quality of the adjustments and the choice of models.

Nesse trabalho foi abordada a situação em que observações de produtividade da cana-de-açúcar (TCH) foram tomadas na mesma unidade experimental em diferentes condições de avalições (anos). Foram avaliados os perfis médios de resposta de 48 genótipos de cana-de-açúcar em dois experimentos: Experimento 1 e Experimento 2, durante três e cinco anos respectivamente, ambos com o delineamento de blocos ao acaso. Esse tipo de planejamento produz uma forma de relação entre as observações tomadas na mesma unidade experimental, portanto requer outras suposições, além das usuais, para que análise seja correta e os testes produzam resultados válidos. Para que as inferências sobre as médias de produtividade sejam válidas e seguras é necessário que o modelo da matriz de covariância dos dados seja apropriado. Diante disso, foram avalidos três alterantivas de análise para dados longitudinais (medidas repetidas no tempo ), sendo utilizados portanto, o modelo univariado, conforme o planejamento do tipo \"split-plot on time\", que impõe forte restrição quanto a matriz de variâncias-covariâncias; o modelo multivariado, que utiliza uma matriz de variâncias-covariâncias não-estruturada e o modelo mistos, que possibilita a seleção de uma matriz que melhor representa os dados. Contudo, verificou-se que não houve diferença entre os resultados dos testes para as diferentes metodologias. Porém, é interessante a continuidade do estudo em relação ao modelo misto, pois devido a sua flexibilidade e precisão é possível obter estimativas mais seguras dos componentes de variância e predizer os valores genotípicos, que por fim poderá proporcionar a predição de produção de uma futura colheita para um determinado genótipo. / This work has been dealt with situation in which observations of productivity of sugar of cane (TCH) were taken in the same unit experimental in different condition of assessments (years). The response profiles average of 48 genotypes of sugar of cane were evaluated in two experiments: Experiment 1 and Experiment 2, for three and five years respectively, both with the randomized complete block design. This type of planning produces a form of relationship between the observations made in the same unit experimental therefore requires other assumptions, in addition to the usual, so that analysis is correct and the test results valid. To that inferences on the means of productivity are valid and safe it is necessary that the model of covariance matrix of the data is appropriate. Therefore, were evaluated three alternatives for analysis of longitudinal data (repeated measures over time), the univariate model as the planning of the split-plot on time which imposes strong restrictions on variances - covariances matrix, the multivariate model, which uses a non-structured variances - covariances matrix and mixed model, which they are enable the selection of a matrix that best represents the data. However, it was found that there was no difference between the results of tests for the different methodologies. But it is interesting the continuity of the study in relation to mixed model, because due to its flexibility and accuracy will be possible to obtain more reliable estimates of the variance components and predict the genotypic values, which ultimately could provide a prediction of production of a future harvest for a given genotype.