Often the basic assumptions of the ANOVA for an experimental design are not met or the statistical model is incorrectly specified. Randomization of treatments to experimental units is expected to protect against such shortcomings. This paper uses randomization theory to examine the impact on the expectations of mean squares, treatment means, and treatment differences for two model mis·specifications: Systematic response shifts and correlated experimental units. Systematic response shifts are presented in the context of the randomized complete block design (RCBD). In particular fixed shifts are added to the responses of experimental units in the initial and final positions of each block. The fixed shifts are called border shifts. It is shown that the RCBD is an unbiased design under randomization theory when border shifts are present. Treatment means are biased but treatment differences are unbiased. However the estimate of error is biased upwards and the power of the F test is reduced. Alternative designs to the RCBD under border shifts are the Latin square, semi-Latin square, and two-column designs. Randomization analysis demonstrates that the Latin square is an unbiased design with an unbiased estimate of error and of treatment differences. The semi-Latin square has each of the t treatments occurring only once per row and column, but t is a multiple of the number of rows or columns. Thus each row-column combination contains more than one experimental unit. The semi-Latin square is a biased design with a biased estimate of error even when no border shifts are present. Row-column interaction is responsible for the bias. Border shifts do not contaminate the expected mean squares or treatment differences, and thus the semi-Latin square is a viable alternative when the border shift overwhelms the row-column interaction. The two columns of the two-column design correspond to the border and interior experimental units respectively. Results similar to that for the semi-Latin square are obtained. Simulation studies for the RCBD and its alternatives indicate that the power of the F test is reduced for the RCBD when border shifts are present. When no row-column interaction is present, the semi-Latin square and two-column designs provide good alternatives to the RCBD. Similar results are found for the split plot design when border shifts occur in the sub plots. A main effects plan is presented for situations when the number of whole plot units equals the number of sub plot units per whole plot. The analysis of designs in which the experimental units occur in a sequence and exhibit correlation is considered next. The Williams Type Il(a) design is examined in conjunction with the usual ANOVA and with the method of first differencing. Expected mean squares, treatment means, and treatment differences are obtained under randomization theory for each analysis. When only adjacent experimental units have non negligible correlation, the Type Il(a) design provides an unbiased error estimate for the usual ANOVA. However the expectation of the treatment mean square is biased downwards for a positive correlation. First differencing results in a biased test and a biased error estimate. The test is approximately unbiased if the correlation between units is close to a half. / Ph. D.

Theory often indicates that a given response variable should be a function of certain explanatory variables yet fails to provide meaningful information as to the specific form of this function. To test the validity of a given functional form with sensitivity toward the feasible alternatives, a procedure is needed for comparing non-nested families of hypotheses. Two hypothesized models are said to be non-nested when one model is neither a restricted case nor a limiting approximation of the other. These non-nested hypotheses cannot be tested using conventional likelihood ratio procedures. In recent years, however, several new approaches have been developed for testing non-nested regression models. A comprehensive review of the procedures for the case of two linear regression models was presented. Comparisons between these procedures were made on the basis of asymptotic distributional properties, simulated finite sample performance and computational ease. A modification to the Fisher and McAleer JA-test was proposed and its properties investigated. As a compromise between the JA-test and the Orthodox F-test, it was shown to have an exact non-null distribution. Its properties, both analytically and empirically derived, exhibited the practical worth of such an adjustment. A Monte Carlo study of the testing procedures involving non-nested linear regression models in small sample situations (n ≤ 40) provided information necessary for the formulation of practical guidelines. It was evident that the modified Cox procedure, N̄ , was most powerful for providing correct inferences. In addition, there was strong evidence to support the use of the adjusted J-test (AJ) (Davidson and MacKinnon's test with small-sample modifications due to Godfrey and Pesaran), the modified JA-test (NJ) and the Orthodox F-test for supplemental information. Under non normal disturbances, similar results were yielded. An empirical study of spending patterns for household food consumption provided a practical application of the non-nested procedures in a large sample setting. The study provided not only an example of non-nested testing situations but also the opportunity to draw sound inferences from the test results. / Ph. D.

Thesis (Ph.D.)--Mississippi State University. Department of Mathematics and Statistics. / Title from title screen. Includes bibliographical references.

Made available in DSpace on 2014-06-11T19:27:42Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-01-30Bitstream added on 2014-06-13T19:35:45Z : No. of bitstreams: 1 haddad_sr_me_botfmvz.pdf: 305893 bytes, checksum: 02ff7e2de8b8a9ad8c10e7f22f207754 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Universidade Estadual Paulista (UNESP) / O presente trabalho objetivou comparar, utilizando dados de um experimento de Microarray com um delineamento simples, os resultados de diferentes testes estatísticos a fim de verificar suas características na detecção de diferenças no nível de expressão dos genes. Os dados foram provenientes da South Dakota State University-EUA, do Department of Biology and Microbiology, Department of Animal Science, onde toda a parte experimental foi realizada. O material biológico envolveu quatro aves infectadas e quatro não infectadas com o vírus de bronquite infecciosa (IBV). O RNA utilizado foi extraído da camada epitelial da traquéia de animais controle e infectados com o vírus da IBV e, após a transcrição reversa foi marcado com os corantes fluorescentes (Cy3 e Cy5) e hibridizados com o microarray 13k cDNA de aves (FHCRC, Seattle, WA). A análise de dados dos resultados do experimento de microarray englobou dois estágios, sendo o primeiro denominado de Normalização, em que os dados foram pré-processados utilizando o procedimento Loess. A seguir foram realizadas as análises estatísticas propriamente ditas com testes de significância. Utilizou-se um modelo simples de ANOVA e aplicaram-se diferentes metodologias de análise. A análise das imagens revelou que dos 16192 spots em cada slide, apenas 10.926 puderam ser lidos sem defeitos no primeiro slide, 11.633 no segundo slide, 12577 no terceiro e 13.154 no quarto slide. A grande maioria dos spots em branco e controles negativos apresentou defeitos que determinaram sua eliminação. Um total de 13.597 spots foi lido no conjunto dos quatro slides, mas apenas 9.853 spots estavam representados em todos os slides. Concluiu-se que os experimentos de microarray, por tratarem de um conjunto muito grande de observações a serem analisados requerem análises estatísticas específicas. O método de Cui et al. (2005) reduziu... / The aim of this research was to compare, using real data of an experiment of Microarray with a simple design, the results of different statistical tests in order to verify their characteristics in the detection of differences in the level of expression of the genes. The data were coming of South Dakota State University-EUA, of the Department of Biology and Microbiology, Department Animal of Science, where the whole experimental part was accomplished. The biological material involved four infected animals and four no infected with the virus of infectious bronchitis (IBV). Used RNA was extracted of the layer epitelial of the windpipe of animals control and infected with the virus of IBV and, after the reverse transcription it was marked with the fluorescent colors (Cy3 and Cy5) and hybridization with the microarray 13k cDNA of birds (FHCRC, Seattle, WA). The analysis of data of the results of the microarray experiment included two apprenticeships, being the first denominated of Normalization, in that the data were pre-processed using the procedure Loess. To follow the statistical analyses they were accomplished properly said through real data with significant tests. A simple model of ANOVA was used and different analysis methodologies were applied. The analysis of the images revealed that of the 16192 spots in each slide, only 10.926 could be read without defects in the first slide, 11.633 in the second slide, 12577 in the third slide and 13.154 in the fourth slide. The great majority of the spots in white and negative controls presented defects that determined it elimination. A total of 13.597 spots was read in the group of the four slides, but only 9.853 spots were represented in all of the slides. It was ended that the microarray experiments, for they treat of a very big group of observations to be analyzed request specific statistical analyses. The method of Cui et al. (2005) it reduced... (Complete abstract click electronic access below)

Orientador: Víctor Hugo Lachos Dávila / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-20T06:44:43Z (GMT). No. of bitstreams: 1 Matos_LarissaAvila_M.pdf: 2008810 bytes, checksum: 0aee0c4f4bbf58ba67490d26cdd300ba (MD5) Previous issue date: 2012 / Resumo: Modelos mistos são geralmente usados para representar dados longitudinais ou de medidas repetidas. Uma complicação adicional surge quando a resposta é censurada, por exemplo, devido aos limites de quantificação do ensaio utilizado. Distribuições normais para os efeitos aleatórios e os erros residuais são geralmente assumidas, mas tais pressupostos fazem as inferências vulneráveis, 'a presença de outliers. Motivados por uma preocupação da sensibilidade para potenciais outliers ou dados com caudas mais pesadas do que a normal, pretendemos desenvolver nessa dissertação, inferência para modelos lineares e não lineares de efeito misto censurados (NLMEC / LMEC) com base na distribui ção t- Student multivariada, sendo uma alternativa flexível ao uso da distribuição normal correspondente. Propomos um algoritmo ECM para computar as estimativas de máxima verossimilhança para os NLMEC / LMEC. Este algoritmo utiliza expressões fechadas no passo-E, que se baseia em fórmulas para a média e a variância de uma distribui ção t-multivariada truncada. O algoritmo proposto é implementado, pacote tlmec do R. Também propomos aqui um algoritmo ECM exato para os modelos lineares e não lineares de efeito misto censurados, com base na distribuição normal multivariada, que nos permite desenvolver análise de influência local para modelos de efeito misto com base na esperança condicional da função log-verossilhança dos dados completos. Os procedimentos desenvolvidos são ilustrados com a análise longitudinal da carga viral do HIV, apresentada em dois estudos recentes sobre a AIDS / Abstract: Mixed models are commonly used to represent longitudinal or repeated measures data. An additional complication arises when the response is censored, for example, due to limits of quantification of the assay used. Normal distributions for random effects and residual errors are usually assumed, but such assumptions make inferences vulnerable to the presence of outliers. Motivated by a concern of sensitivity to potential outliers or data with tails longer-than-normal, we aim to develop in this dissertation inference for linear and nonlinear mixed effects models with censored response (NLMEC/LMEC) based on the multivariate Student-t distribution, being a flexible alternative to the use of the corresponding normal distribution. We propose an ECM algorithm for computing the maximum likelihood estimates for NLMEC/LMEC. This algorithm uses closed-form expressions at the E-step, which relies on formulas for the mean and variance of a truncated multivariate-t distribution. The proposed algorithm is implemented in the R package tlmec. We also propose here an exact ECM algorithm for linear and nonlinear mixed effects models with censored response based on the multivariate normal distribution, which enable us to developed local influence analysis for mixed effects models on the basis of the conditional expectation of the complete-data log-likelihood function. The developed procedures are illustrated with two case studies, involving the analysis of longitudinal HIV viral load in two recent AIDS studies / Mestrado / Estatistica / Mestre em Estatística

Prior research has shown that both lead users and opinion leaders may propel the diffusion of innovation. This raises the question of whether lead users and opinion leaders are positioned similarly in social networks, which we address using a sample of 23 school classes consisting of 537 children. Research among children is very scarce in this particular domain. Our statistical analyses based on hierarchical linear modeling reveal two general results: first, lead users among children appear to possess a variety of links between clusters; second, opinion leaders are locally positioned within clusters of children and have many direct links. (authors' abstract)

Abstract not available

Thesis (Ph. D.)--University of Texas Health Science Center at Houston, School of Public Health, 2008. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 0769. Advisers: Claudia Pedroza; Asha S. Kapadia. Includes bibliographical references.

Tez (Yüksek Lisans) - Süleyman Demirel Üniversitesi, Fen Bilimleri Enstitüsü, İnşaat Mühendisliği Anabilim Dalı, 2008. / Bibliyografya var.

Orientador: Henrique Nunes de Oliveira / Banca: Raysildo Barbosa Lobo / Banca: Danísio Prado Munari / Resumo: O presente trabalho objetivou comparar, utilizando dados de um experimento de Microarray com um delineamento simples, os resultados de diferentes testes estatísticos a fim de verificar suas características na detecção de diferenças no nível de expressão dos genes. Os dados foram provenientes da South Dakota State University-EUA, do Department of Biology and Microbiology, Department of Animal Science, onde toda a parte experimental foi realizada. O material biológico envolveu quatro aves infectadas e quatro não infectadas com o vírus de bronquite infecciosa (IBV). O RNA utilizado foi extraído da camada epitelial da traquéia de animais controle e infectados com o vírus da IBV e, após a transcrição reversa foi marcado com os corantes fluorescentes (Cy3 e Cy5) e hibridizados com o microarray 13k cDNA de aves (FHCRC, Seattle, WA). A análise de dados dos resultados do experimento de microarray englobou dois estágios, sendo o primeiro denominado de Normalização, em que os dados foram pré-processados utilizando o procedimento Loess. A seguir foram realizadas as análises estatísticas propriamente ditas com testes de significância. Utilizou-se um modelo simples de ANOVA e aplicaram-se diferentes metodologias de análise. A análise das imagens revelou que dos 16192 spots em cada slide, apenas 10.926 puderam ser lidos sem defeitos no primeiro slide, 11.633 no segundo slide, 12577 no terceiro e 13.154 no quarto slide. A grande maioria dos spots em branco e controles negativos apresentou defeitos que determinaram sua eliminação. Um total de 13.597 spots foi lido no conjunto dos quatro slides, mas apenas 9.853 spots estavam representados em todos os slides. Concluiu-se que os experimentos de microarray, por tratarem de um conjunto muito grande de observações a serem analisados requerem análises estatísticas específicas. O método de Cui et al. (2005) reduziu... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The aim of this research was to compare, using real data of an experiment of Microarray with a simple design, the results of different statistical tests in order to verify their characteristics in the detection of differences in the level of expression of the genes. The data were coming of South Dakota State University-EUA, of the Department of Biology and Microbiology, Department Animal of Science, where the whole experimental part was accomplished. The biological material involved four infected animals and four no infected with the virus of infectious bronchitis (IBV). Used RNA was extracted of the layer epitelial of the windpipe of animals control and infected with the virus of IBV and, after the reverse transcription it was marked with the fluorescent colors (Cy3 and Cy5) and hybridization with the microarray 13k cDNA of birds (FHCRC, Seattle, WA). The analysis of data of the results of the microarray experiment included two apprenticeships, being the first denominated of Normalization, in that the data were pre-processed using the procedure Loess. To follow the statistical analyses they were accomplished properly said through real data with significant tests. A simple model of ANOVA was used and different analysis methodologies were applied. The analysis of the images revealed that of the 16192 spots in each slide, only 10.926 could be read without defects in the first slide, 11.633 in the second slide, 12577 in the third slide and 13.154 in the fourth slide. The great majority of the spots in white and negative controls presented defects that determined it elimination. A total of 13.597 spots was read in the group of the four slides, but only 9.853 spots were represented in all of the slides. It was ended that the microarray experiments, for they treat of a very big group of observations to be analyzed request specific statistical analyses. The method of Cui et al. (2005) it reduced... (Complete abstract click electronic access below) / Mestre