The minimum description length (MDL) principle originated from data compression literature and has been considered for deriving statistical model selection procedures. Most existing methods utilizing the MDL principle focus on models consisting of independent data, particularly in the context of linear regression. The data considered in this thesis are in the form of repeated measurements, and the exploration of MDL principle begins with classical linear mixed-effects models. We distinct two kinds of research focuses: one concerns the population parameters and the other concerns the cluster/subject parameters. When the research interest is on the population level, we propose a class of MDL procedures which incorporate the dependence structure within individual or cluster with data-adaptive penalties and enjoy the advantages of Bayesian information criteria. When the number of covariates is large, the penalty term is adjusted by data-adaptive structure to diminish the under selection issue in BIC and try to mimic the behaviour of AIC. Theoretical justifications are provided from both data compression and statistical perspectives. Extensions to categorical response modelled by generalized estimating equations and functional data modelled by functional principle components are illustrated. When the interest is on the cluster level, we use group LASSO to set up a class of candidate models. Then we derive a MDL criterion for this LASSO technique in a group manner to selection the final model via the tuning parameters. Extensive numerical experiments are conducted to demonstrate the usefulness of the proposed MDL procedures on both population level and cluster level.

A economia brasileira passa por um momento positivo em sua história, devido principalmente a fatores gerados pela estabilidade econômica advinda com o Plano Real. O conjunto de dados apresentados neste trabalho evidencia uma melhora das condições socioeconômicas de grande parte da população, o que levou a um aumento da renda dos indivíduos e um fortalecimento do poder de consumo dos brasileiros. Nesse contexto, esta tese teve como objetivo a busca de evidências que indicassem uma mudança e possível sofisticação do padrão de consumo dos domicílios brasileiros. Além disso, procurou-se verificar em quais níveis socioeconômicos e em quais regiões as mudanças do padrão de consumo foram mais significativas. Os dados utilizados neste trabalho derivam de um painel de consumidores (Homescan) e foram analisadas informações de dez categorias de produtos de consumo doméstico para os anos de 2007, 2008 e 2009, considerando-se as áreas geográficas auditadas pela Nielsen e os níveis socioeconômicos dos domicílios. Nas análises dos dados, utilizaram-se modelos de equações de estimação generalizadas (EEG), além de análises estatísticas descritivas para avaliar a evolução das variáveis não-contempladas nesses modelos. Além disso, utilizaram-se dados de outra pesquisa (Retail Index) para complementar os resultados obtidos com o painel de consumidores. Os resultados das análises realizadas indicam uma mudança do padrão de consumo, primordialmente, nos domicílios de nível socioeconômico médio (classe C) e baixo (classes D e E) no período analisado. Quanto às áreas geográficas pesquisadas, os destaques foram o Nordeste, o grande Rio de Janeiro e a região Sul. Levando-se em consideração que as categorias analisadas são produtos mais elaborados e de maior valor agregado, o aumento do consumo da grande maioria das categorias nesses níveis socioeconômicos evidencia uma sofisticação do consumo desses domicílios. Esse ambiente de sofisticação dos padrões de consumo, principalmente das classes de renda média e baixa, exigirá das empresas que atuam no mercado de bens e serviços novas estratégias para atender as demandas de consumidores mais conscientes e exigentes. Assim, o grande desafio dessas empresas será decifrar o caminho da expansão e diversificação da cesta de compra desses consumidores. / The Brazilian economy is currently going through a positive time in its history, mainly as a result of factors generated by the economic stability conferred by the Plano Real financial plan. The data presented in this work shows an improvement in the socioeconomic conditions of the vast majority of the population, which has led to an increase in income for individuals, and a strengthening of the consumer power of Brazilians. In this context, this thesis looks for evidence that indicates a change and possible sophistication of consumer patterns in Brazilian households. It also seeks to determine the socioeconomic levels, and the regions in which the changes in consumer patterns are most significant. The data used in this work are derived from a panel of consumers (Homescan), and information from ten categories of domestic consumer goods were analyzed for the years 2007, 2008 and 2009, considering the geographic areas audited by Nielsen and the socioeconomic levels of the households. In the data analyses, generalized estimating equation (GEE) models are used, as well as descriptive statistical analyses, to evaluate the evolution of variables not included in these models. Data are also used from another survey (Retail Index), to complement the results obtained with the panel of consumers. The results of the analyses indicate a change in consumer patterns, particularly in households belonging to the middle (class C) and low (classes D and E) socioeconomic classes, for the period analyzed. In terms of geographical areas researched, the areas highlighted were the Northeast, the greater Rio de Janeiro and the South region. Taking into consideration that the categories analyzed consist of more elaborate products, with higher added value, the increased consumption for the majority of categories at these socioeconomic levels shows that consumption in these households has become more sophisticated. This environment of increasing sophistication of consumer patterns, particularly among the middle and low income classes, will require companies in the goods and services market to implement strategies to meet the requirements of these more aware and demanding consumers. Therefore, the greatest challenge for these companies is to seize the expansion and diversification path of the shopping basket for these consumers.

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Utilizando a teoria de função de estimação linear ótima (Crowder, 1987), propomos equações de estimação generalizadas para modelos de regressão beta (Ferrari e Cribari-Neto, 2004) com medidas repetidas. Além disso, apresentamos equações de estimação generalizadas para modelos de regressão simplex baseadas nas propostas de Song e Tan (2000) e Song et al. (2004) e equações de estimação generalizadas para modelos lineares generalizados com medidas repetidas baseadas nas propostas de Artes e Jorgensen (2000) e Liang e Zeger (1986). Todas essas equações de estimação são desenvolvidas sob os enfoques da modelagem da média com homogeneidade da dispersão e da modelagem conjunta da média e da dispersão com intuito de incorporar ao modelo uma possível heterogeneidade da dispersão. Como técnicas de diagnóstico, desenvolvemos uma generalização de algumas medidas de diagnóstico quando abordamos quaisquer equações de estimação definidas tanto para modelagem do parâmetro de posição considerando a homogeneidade do parâmetro de dispersão como para modelagem conjunta dos parâmetros de posição e dispersão. Entre essas medidas, destacamos a proposta da influência local (Cook, 1986) desenvolvida para equações de estimação. Essa medida teve um bom desempenho, em simulações, para destacar corretamente pontos influentes. Por fim, realizamos aplicações a conjuntos de dados reais. / Based on the concept of optimum linear estimating equation (Crowder, 1987), we develop generalized estimating equation (GEE) to analyze longitudinal data considering marginal beta regression models (Ferrari and Cribari-Neto, 2004). The GEEs are also presented to marginal simplex models for longitudinal continuous proportional data proposed by Song and Tan (2000) and Song et al. (2004) and to generalized linear models for longitudinal data based on the proposes of Artes and J$\\phi$rgensen (2000) and Liang and Zeger (1986). All of them are developed focusing the assumption of homogeneous dispersion and with varying dispersion. For the diagnostic techniques, we generalize some diagnostic measures for estimating equations to model the position parameter considering an homogeneous dispersion parameter and for joint modelling of position and dispersion parameters to take in account a possible heterogeneous dispersion. Among these measures, we point out the local influence (Cook, 1986) developed to estimating equations. This measure can correctly show influential observations in simulation study. Finally, the theory is applied to real data sets.

Utilizando a teoria de função de estimação linear ótima (Crowder, 1987), propomos equações de estimação generalizadas para modelos de regressão beta (Ferrari e Cribari-Neto, 2004) com medidas repetidas. Além disso, apresentamos equações de estimação generalizadas para modelos de regressão simplex baseadas nas propostas de Song e Tan (2000) e Song et al. (2004) e equações de estimação generalizadas para modelos lineares generalizados com medidas repetidas baseadas nas propostas de Artes e Jorgensen (2000) e Liang e Zeger (1986). Todas essas equações de estimação são desenvolvidas sob os enfoques da modelagem da média com homogeneidade da dispersão e da modelagem conjunta da média e da dispersão com intuito de incorporar ao modelo uma possível heterogeneidade da dispersão. Como técnicas de diagnóstico, desenvolvemos uma generalização de algumas medidas de diagnóstico quando abordamos quaisquer equações de estimação definidas tanto para modelagem do parâmetro de posição considerando a homogeneidade do parâmetro de dispersão como para modelagem conjunta dos parâmetros de posição e dispersão. Entre essas medidas, destacamos a proposta da influência local (Cook, 1986) desenvolvida para equações de estimação. Essa medida teve um bom desempenho, em simulações, para destacar corretamente pontos influentes. Por fim, realizamos aplicações a conjuntos de dados reais. / Based on the concept of optimum linear estimating equation (Crowder, 1987), we develop generalized estimating equation (GEE) to analyze longitudinal data considering marginal beta regression models (Ferrari and Cribari-Neto, 2004). The GEEs are also presented to marginal simplex models for longitudinal continuous proportional data proposed by Song and Tan (2000) and Song et al. (2004) and to generalized linear models for longitudinal data based on the proposes of Artes and J$\\phi$rgensen (2000) and Liang and Zeger (1986). All of them are developed focusing the assumption of homogeneous dispersion and with varying dispersion. For the diagnostic techniques, we generalize some diagnostic measures for estimating equations to model the position parameter considering an homogeneous dispersion parameter and for joint modelling of position and dispersion parameters to take in account a possible heterogeneous dispersion. Among these measures, we point out the local influence (Cook, 1986) developed to estimating equations. This measure can correctly show influential observations in simulation study. Finally, the theory is applied to real data sets.

This research develops a framework to estimate the effective sample size of Global Positioning System (GPS) based panel surveys in urban travel behavior studies for a variety of planning purposes. Recent advances in GPS monitoring technologies have made it possible to implement panel surveys with lengths of weeks, months or even years. The many advantageous features of GPS-based panel surveys make such surveys attractive for travel behavior studies, but the higher cost of such surveys compared to conventional one-day or two-day paper diary surveys requires scrutiny at the sample size planning stage to ensure cost-effectiveness. The sample size analysis in this dissertation focuses on three major aspects in travel behavior studies: 1) to obtain reliable means for key travel behavior variables, 2) to conduct regression analysis on key travel behavior variables against explanatory variables such as demographic characteristics and seasonal factors, and 3) to examine impacts of a policy measure on travel behavior through before-and-after studies. The sample size analyses in this dissertation are based on the GPS data collected in the multi-year Commute Atlanta study. The sample size analysis with regard to obtaining reliable means for key travel behavior variables utilizes Monte Carlo re-sampling techniques to assess the trend of means against various sample size and survey length combinations. The basis for the framework and methods of sample size estimation related to regression analysis and before-and-after studies are derived from various sample size procedures based on the generalized estimating equation (GEE) method. These sample size procedures have been proposed for longitudinal studies in biomedical research. This dissertation adapts these procedures to the design of panel surveys for urban travel behavior studies with the information made available from the Commute Atlanta study. The findings from this research indicate that the required sample sizes should be much larger than the sample sizes in existing GPS-based panel surveys. This research recommends a desired range of sample sizes based on the objectives and survey lengths of urban travel behavior studies.

近幾年來，國人自殺死亡率不斷提高，且自殺死亡從1997年起已連續多年列於國人十大死亡原因之一，所以自殺防治工作刻不容緩。本研究採用自殺防治中心在桃園縣六家居家服務單位(龍祥、中國、仁愛、紅十字、家輔及寬福)所做之問卷調查資料，目的在於找出何種特性者，BSRS5 (The Five-Item Brief Symptom Rating Scale)分數及自殺意念分數可能較高。本研究屬於時序性追蹤資料，自民國96年5月份起，由居服人員針對受測對象進行訪談，大約每隔兩週收集一次，總共進行四次。 針對問卷進行基本敘述性統計、單項排名分析以及交叉分析後發現，在人口特質方面，男女性比例相當，年齡層主要皆在65~84歲，教育程度以不識字及國小為主；在BSRS5五題排名方面，以第一題「睡眠困難(難以入睡或早醒)」的平均分數最高，第四題「覺得比不上別人」平均分數最低；由交叉分析的結果發現身體狀況為一個重要的變數，身體狀況差的人BSRS5總分6分以上或自殺意念2分以上明顯較多。 對資料配適廣義估計方程式及Alternating Logistic Regressions的結果，發現在反應變數為BSRS5總分時，女性、身體狀況差及曾經看過精神科者BSRS5分數達到6分以上的可能性較高。若反應變數為自殺意念時，無論是利用廣義估計方程式或Alternating Logistic Regressions，從模型配適的結果發現只有BSRS5的效應顯著。不管利用BSRS5總分或是各題分開來看，BSRS5對自殺意念是一個相當有效的檢測工具，BSRS5分數愈高則自殺意念2分以上的機會也愈高。此外利用多層結構分析方法配適廣義估計方程式，針對BSRS5與受測次數間的關聯性分析，發現與配適傳統unstructured相關性矩陣的估計結果差異不大，但是可以減少許多參數估計，並且在電腦計算時間上是較快速的。 / In Taiwan, suicide has been among the top ten causes of death since 1997, and suicide prevention has thus attracted much attention since. Using the data provided by Taiwan Suicide Prevention Center (TSPC), this study is aimed to find out possible personal characteristics that might have some impacts on the BSRS5 (the Five-Item Brief Symptom Rating Scale) and suicide ideation scores The data come from a longitudinal study in which subjects from six elderly home service centers in Taoyuan County, Taiwan were visited four times between May and July, 2007, about two weeks between each visit. The total number of subjects is 1981. The proportions of male and female are nearly the same, the age range is from 65 to 84, and most of them have only an elementary school degree. Preliminary analyses indicate that among the five items in BSRS5, insomnia (the first item) is ranked the highest, and inferiority (the fourth item) is the lowest. In addition, health status is highly correlated to the BSRS5 and suicide ideation scores, the worse the health status, the higher the BSRS5 and suicide ideation scores. Fitting the data with Generalized Estimating Equation (GEE) and Alternating Logistic Regressions models with respect to the BSRS5 score, we further find that female, those who have bad health status, and those who have ever consulted a psychiatrist have higher probability that the BSRS5 score is greater than 6. As far as the suicide ideation score is concerned, the BSRS5 score is the only covariate that is statistically significant, an indication that BSRS5 is a useful tool for screening subjects at risk of committing suicide. While the conclusions stay the same whether the data are analyzed through GEE with commonly used unstructured correlation structure or newly developed multiblock and multilayer correlation structure, the latter approach reduces the computer time significantly.

A literatura dispõe de métodos de diagnóstico para avaliar o ajuste de modelos lineares generalizados (MLGs) para medidas repetidas baseado em equações de estimação generalizada (EEG). No entanto, tais métodos não contemplam a distribuição binomial nem bancos de dados com observações faltantes. O presente trabalho generalizou os métodos já desenvolvidos para essas duas situações. Na construção de gráficos de probabilidade meio-normal com envelope simulado para a distribuição binomial, foi proposto um método para geração de variáveis aleatórias com distribuição marginal binomial correlacionadas, baseado na convolução de variáveis com distribuição de Poisson independentes. Os métodos de diagnóstico desenvolvidos foram aplicados em dados reais e simulados. / Literature provides diagnostic methods to assess the fit of generalized linear models (GLM) for repeated measures based on generalized estimating equations (GEE). Still, such methods do not include the binomial distribution or databases with missing observations. This work generalizes the methods already developed for these two situations. A method for generating random variables with correlated marginal binomial distributions based on convolution of independent Poisson random variables has been proposed for the construction of half-normal probability plots. The diagnostic methods developed were applied to real and simulated data.

A literatura dispõe de métodos de diagnóstico para avaliar o ajuste de modelos lineares generalizados (MLGs) para medidas repetidas baseado em equações de estimação generalizada (EEG). No entanto, tais métodos não contemplam a distribuição binomial nem bancos de dados com observações faltantes. O presente trabalho generalizou os métodos já desenvolvidos para essas duas situações. Na construção de gráficos de probabilidade meio-normal com envelope simulado para a distribuição binomial, foi proposto um método para geração de variáveis aleatórias com distribuição marginal binomial correlacionadas, baseado na convolução de variáveis com distribuição de Poisson independentes. Os métodos de diagnóstico desenvolvidos foram aplicados em dados reais e simulados. / Literature provides diagnostic methods to assess the fit of generalized linear models (GLM) for repeated measures based on generalized estimating equations (GEE). Still, such methods do not include the binomial distribution or databases with missing observations. This work generalizes the methods already developed for these two situations. A method for generating random variables with correlated marginal binomial distributions based on convolution of independent Poisson random variables has been proposed for the construction of half-normal probability plots. The diagnostic methods developed were applied to real and simulated data.

當資料屬於類別型的長期追蹤資料（Longitudinal categorical data）時，除了可以透過廣義估計方程式（General estimate equation, GEE）來求解模型參數估計值外，潛在移轉分析（Latent transition analysis, LTA）法也是一種可行的資料分析方法。若資料的期數不多，也可以選擇將資料適度分群後使用羅吉斯迴歸分析（Logistic regression）法。當探討的反應變數為二元（Binary）型態，且觀察對象於每一期提供多個測量變數值的情況之下，廣義估計方程式與羅吉斯迴歸分析法的使用，文獻上常見先將所有的測量變數值加總後，以「中位數」作為分類的切割點。不同於以上兩種方法，潛在移轉分析法則是直接使用原始資料來取得觀察對象的潛在狀態相關訊息，因此與前二者的作法不同，可能導致後續的各項分析結果有所差異存在。 為了能夠了解造成中位數分類法與移轉分析法差異的可能因素，我們架構在潛在移轉分析法的模型下，以不同的參數設定來進行電腦模擬，比較各參數條件下的兩分類方法差異。結果發現各潛在狀態下的測量變數反應機率形式、第一期潛在狀態的組成比例等皆會對兩分類方法是否具有相同分類有所影響。另外，透過分析「青少年媒體使用與健康生活調查」的實際資料得知，潛在移轉分析會將大部分的觀察對象歸屬於「網路成癮」，而中位數分類法則是將大部分的觀察對象歸屬於「無網路成癮」。此外，可以注意到「沮喪」、「線上情色每星期平均使用天數」、及「父母相處狀況」這幾個控制變數與各分組結果的關聯性，於上述三種資料分析方法中有所不同。 / Several methods can be used to analyze longitudinal categorical data, as among them Latent Transition Analysis (LTA), and Generalized Linear Models estimated by Generalized Estimating Equations (GEE) probably the most popular. In addition, if the number of periods is two, then with certain grouping of data, the Logistic Regression can also be applied to perform the analyses. When there are more than one manifest response variable for each study subject, LTA is able to classify the subjects in terms of the original manifest response variables and proceeds with necessary analyses. On the other hand, GEE method and Logistic Regression lack the flexibility, and require certain transformation to transform the manifest response variables into a categorical response variable first. One common way to form a binary response is to sum all manifest variables, and then taking median as a cut-point. In this study, we explore the differences of the classification resulted from LTA directly and using median as a cut-point through simulations. An empirical study is also provided to illustrate the classification differences, and the differences on the subsequent analyses using LTA, GEE method, and Logistic Regression approach.