Keywords: MCEM algorithm; Gibbs sampler; Multivariate probit model; Multi-group; BIC. / The main purpose of this paper is to develop maximum likelihood and Bayesian approach for the multivariate probit model in several populations. A Monte Carlo EM algorithm is proposed for obtaining the maximum likelihood estimates and the Gibbs sampler is used to produce the joint Bayesian estimates. To test hypotheses involving constraints among the structural parameters of MP model across groups, we use the method of Bayesian Information Criterion(BIC). The simulation study will be given to certify the accuracy of our algorithm. / Yu, Yin. / "March 2007." / Adviser: Sik Yum Lee. / Source: Dissertation Abstracts International, Volume: 68-09, Section: B, page: 6054. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 135-137). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

Au Kin-Chung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 49-54). / Abstracts in English and Chinese. / ACKNOWLEDGEMENTS --- p.2 / TABLE OF CONTENTS --- p.3 / ABSTRACT --- p.4 / INTRODUCTION --- p.6 / Media Choice Theories --- p.7 / Performance Feedback and Media Choice --- p.11 / Research Approach --- p.18 / METHOD --- p.20 / Participants --- p.20 / Design --- p.21 / Manipulations --- p.22 / Dependent Measures --- p.24 / Survey Measures --- p.25 / Procedure --- p.27 / Data Analysis --- p.27 / RESULTS --- p.29 / HLM Analysis --- p.32 / DISCUSSION --- p.39 / Media Preference And Bias --- p.43 / Using HLM in Survey Yielding Two-Level Data Set --- p.45 / LIMITATIONS AND FUTURE DIRECTIONS --- p.46 / CONCLUSION --- p.47 / REFERENCES --- p.49 / FOOTNOTES AND APPENDIX --- p.55 / TABLES AND FIGURES --- p.60

Recursive estimation is an essential procedure in econometrics which appears in many applications when the underlying dataset or model is modi ed. Data arrive consecutively and thus already estimated models will have to be updated with new available information. Moreover, in many cases, data will have to be deleted from a model in order to remove their effect, either because they are old (obsolete) or because they have been detected to be outliers or extreme values and further investigation is required. The aim of this thesis is to develop numerically stable and computationally efficient methods for the recursive estimation of large-scale linear econometric models. Estimation of multivariate linear models is a computationally costly procedure even for moderate-sized models. In particular, when the model needs to be estimated recursively, its estimation will be even more computationally demanding. Moreover, conventional methods yield often, misleading results. The aim is to derive new methods which effectively utilise previous computations, in order to reduce the high computational cost, and which provide accurate results as well. Novel numerical methods for the recursive estimation of the general linear, the seemingly unrelated regressions, the simultaneous equations, the univariate and multivariate timevarying parameters models are developed. The proposed methods are based on numerically stable strategies which provide accurate and precise results. Moreover, the new methods estimate the unknown parameters of the modi ed model even when the variance covariance matrix is singular.

Lee Shun-yi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 57-61). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Tests of Hypotheses --- p.4 / Chapter 1.2.1 --- Likelihood Ratio Statistic --- p.4 / Chapter 1.2.2 --- The Rao´ة s Score Statistic --- p.5 / Chapter 1.2.3 --- Wald's Statistic --- p.6 / Chapter 1.3 --- Notation --- p.6 / Chapter 2 --- Fixed Effects Model --- p.8 / Chapter 2.1 --- Introduction --- p.8 / Chapter 2.2 --- Pearson Chi-square Statistic --- p.9 / Chapter 2.3 --- Logistic Regression Model --- p.11 / Chapter 2.3.1 --- Testing Linear Hypotheses about the Regression Coefficients --- p.12 / Chapter 2.4 --- Combining Proportions --- p.16 / Chapter 2.4.1 --- Classical Estimators --- p.17 / Chapter 2.4.2 --- Jackknife Estimator --- p.18 / Chapter 2.4.3 --- Cross-validatory estimators --- p.19 / Chapter 3 --- Random Effects Model --- p.21 / Chapter 3.1 --- Introduction --- p.21 / Chapter 3.2 --- DerSimonian and Laird Method --- p.22 / Chapter 3.3 --- Generalized linear model with random effect --- p.24 / Chapter 3.3.1 --- Quasi-Likelihood --- p.25 / Chapter 3.3.2 --- Testing Linear Hypotheses about the Regression Coefficients --- p.26 / Chapter 3.3.3 --- MINQUE --- p.27 / Chapter 3.3.4 --- Score Test --- p.31 / Chapter 4 --- Overdispersion and Intraclass Correlation --- p.36 / Chapter 4.1 --- Introduction --- p.36 / Chapter 4.2 --- C(α) Test --- p.39 / Chapter 4.2.1 --- Correlated Binomial model and Beta-Binomial model --- p.40 / Chapter 4.2.2 --- C(α) Statistic Based On Quasi-likclihood --- p.46 / Chapter 4.3 --- Donner Statistic --- p.48 / Chapter 4.4 --- Rao and Scott Statistic --- p.51 / Chapter 5 --- Example and Discussion --- p.53 / Bibliography --- p.57

Diversas situações práticas exigem a análise de series temporais de contagem, que podem apresentar tendência, sazonalidade e efeitos de variáveis explicativas. A motivação do nosso trabalho é a análise de internações diárias por doenças respiratórias para pessoas com mais que 65 anos residentes no município de São Paulo. O efeito de variáveis climáticas e concentrações de poluentes foram incluídos nos modelos e foram usadas as funções seno e cosseno com periodicidade de um ano para explicar o padrão sazonal e obter os efeitos das variáveis climáticas e poluentes controlando essa sazonalidade. Outro aspecto a ser considerado é a inclusão da população nas análises de modo que a interpretação dos efeitos seja para as taxas diárias de internações. Diferentes modelos paramétricos foram propostos para as internações. O mais simples é o modelo de regressão linear para o logaritmo das taxas. Foram ajustados os modelos lineares generalizados (MLG) para as internações com função de ligação logaritmo e com a população como offset, por este modelo permitir o uso das distribuições Poisson e Binomial Negativa, usadas para dados de contagem. Devido à heteroscedasticidade extra, foram propostos modelos GAMLSS incluindo variáveis para explicar o desvio padrão. Foram ajustados modelos ARMA e GARMA, por incluírem uma estrutura de correlação serial. O objetivo desse trabalho é comparar as estimativas, os erros padrões, a cobertura dos intervalos de confiança e o erro quadrático médio para o valor predito segundo os vários modelos e a escolha do modelo mais apropriado, que depende da completa análise de resíduos, geralmente omitida na literatura. O modelo GARMA com distribuição Binomial Negativa apresentou melhor ajuste, pois os erros parecem seguir a distribuição proposta e tem baixa autocorrelação, além de ter tido uma boa cobertura pelo intervalo de confiança e um baixo erro quadrático médio. Também foi analisado o efeito da autocorrelação dos dados nas estimativas nos vários modelos baseado em dados simulados. / Many practical situations require the analysis of time series of counts, which may present trend, seasonality and effects of covariates. The motivation of this work is the analysis of daily hospital admissions for respiratory diseases in people over 65 living in the city of São Paulo. The effect of climatic variables and concentrations of pollutants were included in the models and the sine and cosine functions with annual period were included to explain the seasonal pattern and obtain the effects of pollutants and climatic variables partially controlled by this seasonality. Another aspect to be considered is the inclusion of the population in the analys es in order to interpret the effects based on daily hospitalization rates . Different parametric models have been proposed for hospitalizations. The simplest is the linear regression model for the logarithm of the hospitalization rate. The generalized linear models (GLM) were adjusted for daily admissions with logarithmic link function and the population as offset to consider the Poisson and Negative Binomial distributions for counting data. Due to the extra heteroscedasticity, GAMLSS models were proposed including variables to explain the standard error. Moreover, the ARMA and GARMA models were fitted to include the serial correlation structure. The aim of this work is to compare estimates, standard errors, coverage of confidence intervals and mean squared error of predicted value for the various models and choose the most appropriate model, which depends on a complete analysis of residuals, usually omitted in the literature. The GARMA model with Negative Binomial distribution was the best fit since the errors seem to follow the proposed distribution and they have small values of autocorrelation. Besides, this model had low mean squared error and a good coverage of confidence interval. The effect of autocorrelation of data in the estimates was also analyzed in the setting of several models based on simulated data.

O municÃpio de Fortaleza, capital do estado do CearÃ, apresenta-se como municÃpio prioritÃrio para o combate à hansenÃase no Brasil. Este estudo objetivou caracterizar os padrÃes epidemiolÃgicos e clÃnico-operacionais da hansenÃase, bem como a tendÃncia temporal e distribuiÃÃo espacial em cortes temporais dos seus principais indicadores, no municÃpio de Fortaleza, de 2001 a 2012. O municÃpio de Fortaleza à subdivido em 114 bairros (IBGE, 2000) e seis Secretarias Executivas Regionais (SER). A anÃlise se deu atravÃs da caracterizaÃÃo de indicadores epidemiolÃgicos e operacionais da hansenÃase, alÃm de sua tendÃncia, atravÃs do mÃtodo de pontos de inflexÃo, e estimativa de prevalÃncia oculta. Foram utilizadas trÃs tÃcnicas de anÃlises espaciais (Abordagem Descritiva, Bayesiana Local e EstatÃstica Scan Espacial) dos indicadores: detecÃÃo geral, detecÃÃo em menores de 15 anos e detecÃÃo em casos com grau 2 de incapacidades fÃsicas (incapacidades visÃveis), visando encontrar agregados de bairros de alto risco para a presenÃa, transmissÃo e diagnÃstico tardio da endemia. No perÃodo de estudo, foram registrados 9.658 casos novos da doenÃa, sendo 677 (7,0%) em menores de 15 anos. Foi estimada a ocorrÃncia de 197,7 casos ocultos de hansenÃase por 100 mil habitantes no municÃpio nos Ãltimos cinco anos (mÃdia de 39,5 casos por 100 mil ao ano). O coeficiente de detecÃÃo apresentou reduÃÃo no perÃodo, variando de 40,07 (2001) a 23,39 (2012) casos por 100 mil habitantes (Average Annual Percent Change - AAPC: -4,0; IC95%: -5,6 a -2,3). Apesar de diminuiÃÃes nos valores dos indicadores do outros dois coeficientes estudados, os mesmos permaneceram estÃveis. O coeficiente de detecÃÃo em menores de 15 anos de idade reduziu de 8,56/100 mil hab. em 2001 a 5,49/100 mil hab. em 2012, (AAPC: -1,4; IC95%: -5,4 a 2,8), e o coeficiente de grau 2, com 2,28/100 mil hab. em 2001 a 1,95/100 mil hab. em 2012, (AAPC: -0,8; IC95%: -4,5 a 3,1). Foram identificados na anÃlise espaÃo-temporal agregados espaciais com risco elevado para transmissÃo da doenÃa, principalmente, em bairros localizados nas SER 3 e 5 que estÃo a oeste da cidade, com o principal agregado envolvendo 22 bairros. AlÃm disso, verificou-se a existÃncia de transmissÃo ativa pelos altos valores para o coeficiente de detecÃÃo em menores de 15 anos, principalmente nas SER 3 e 5. A anÃlise espaÃo-temporal identificou, para este indicador, como principal cluster, trÃs bairros, todos localizados na SER 5. Foi constatado, tambÃm, diagnÃstico tardio nessas mesmas SERâs (3 e 5), assim como a existÃncia de indÃcios em SERâs que nÃo haviam apresentado risco significativo para detecÃÃo, como alguns bairros das SERâs 4 e 6, que estÃo mais a leste do municÃpio. Identificou-se que as SERâs que mais se destacaram como risco para ocorrÃncia da hansenÃase sÃo constituÃdas de grandes desigualdades sociais, alÃm de altos nÃveis de pobreza e aglomerados populacionais. Essas caracterÃsticas reafirmam a Ãntima relaÃÃo que a hansenÃase tem com a pobreza, assim como sua desigual distribuiÃÃo no municÃpio de Fortaleza.

This thesis concerns the identification of quantitative trait loci (QTL) for important traits in cattle line crosses. One of these traits is birth weight of calves, which affects both animal production and welfare through correlated effects on parturition and subsequent growth. Birth weight was one of the traits measured in the Davies' Gene Mapping Project. These data form the motivation for the methods presented in this thesis. Multiple QTL models have been previously proposed and are likely to be superior to single QTL models. The multiple QTL models can be loosely divided into two categories : 1 ) model building methods that aim to generate good models that contain only a subset of all the potential QTL ; and 2 ) methods that consider all the observed marker explanatory variables. The first set of methods can be misleading if an incorrect model is chosen. The second set of methods does not have this limitation. However, a full fixed effect analysis is generally not possible as the number of marker explanatory variables is typically large with respect to the number of observations. This can be overcome by using constrained estimation methods or by making the marker effects random. One method of constrained estimation is the least absolute selection and shrinkage operator (LASSO). This method has the appealing ability to produce predictions of effects that are identically zero. The LASSO can also be specified as a random model where the effects follow a double exponential distribution. In this thesis, the LASSO is investigated from a random effects model perspective. Two methods to approximate the marginal likelihood are presented. The first uses the standard form for the double exponential distribution and requires adjustment of the score equations for unbiased estimation. The second is based on an alternative probability model for the double exponential distribution. It was developed late in the candidature and gives similar dispersion parameter estimates to the first approximation, but does so in a more direct manner. The alternative LASSO model suggests some novel types of predictors. Methods for a number of different types of predictors are specified and are compared for statistical efficiency. Initially, inference for the LASSO effects is performed using simulation. Essentially, this treats the random effects as fixed effects and tests the null hypothesis that the effect is zero. In simulation studies, it is shown to be a useful method to identify important effects. However, the effects are random, so such a test is not strictly appropriate. After the specification of the alternative LASSO model, a method for making probability statements about the random effects being above or below zero is developed. This method is based on the predictive distribution of the random effects (posterior in Bayesian terminology). The random LASSO model is not sufficiently flexible to model most QTL mapping data. Typically, these data arise from large experiments and require models containing terms for experimental design. For example, the Davies' Gene Mapping experiment requires fixed effects for different sires, a covariate for birthdate within season and random normal effects for management group. To accommodate these sources of variation a mixed model is employed. The marker effects are included into this model as random LASSO effects. Estimation of the dispersion parameters is based on an approximate restricted likelihood (an extension of the first method of estimation for the simple random effects model). Prediction of the random effects is performed using a generalisation of Henderson's mixed model equations. The performance of the LASSO linear mixed model for QTL identification is assessed via simulation. It performs well against other commonly used methods but it may lack power for lowly heritable traits in small experiments. However, the rate of false positives in such situations is much lower. Also, the LASSO method is more precise in locating the correct marker rather than a marker in its vicinity. Analysis of the Davies' Gene Mapping Data using the methods described in this thesis identified five non-zero marker-within-sire effects ( there were 570 such effects). This analysis clearly shows that most of the genome does not affect the trait of interest. The simulation results and the analysis of the Davies' Gene Mapping Project Data show that the LASSO linear mixed model is a competitive method for QTL identification. It provides a flexible method to model the genetic and experimental effects simultaneously. / Thesis (Ph.D.)--School of Agriculture, Food and Wine, 2006.

"February 1992" Bibliography: leaf 323-344. Develops a general strategy for factorial linear model analysis for experimental and observational studies, an iterative, four-stage, model comparison procedure. The approach is applicable to studies characterized as being structure-balanced, multitiered and based on Tjur structures unless the structure involves variation factors when it must be a regular Tjur structure. It covers a wide range of experiments including multiple-error, change-over, two-phase, superimposed and unbalanced experiments.

Detecting both the majors genes that control the phenotypic mean and those controlling phenotypic variance has been raised in quantitative trait loci analysis. In order to mapping both kinds of genes, we applied the idea of the classic Haley-Knott regression to double generalized linear models. We performed both kinds of quantitative trait loci detection for a Red Jungle Fowl x White Leghorn F2 intercross using double generalized linear models. It is shown that double generalized linear model is a proper and efficient approach for localizing variance-controlling genes. We compared two models with or without fixed sex effect and prefer including the sex effect in order to reduce the residual variances. We found that different genes might take effect on the body weight at different time as the chicken grows.

Thesis (M.A.S.), Memorial University of Newfoundland, 2000. / Bibliography: leaves 71-73.