本論文從教育社會學角度探討造成數學成就性別差異現象的成因，以班級的性別環境為研究脈絡，研究影響國中女生數學成就的可能原因。假設數學成就的性別差異是受到後天學習歷程影響，班級環境中隱含的性別刻板印象為其中一個重要社會文化影響因素。透過比較國一到國三階段女生班和一般男女合班女生數學成就的異同，嘗試找出造成數學成就性別差異現象的成因，是否與班級性別環境、師生的性別刻板印象等因素有關。利用階層線性模式（Hierarchical Linear Models，HLM）統計方法，分析資料取自由中央研究院、教育部和國科會共同規劃的全國性長期的調查計畫：「台灣教育長期追蹤資料庫」（Taiwan Education Panel Survey，簡稱TEPS）。研究結果發現女生班、數學老師性別及班級學業氣氛等因素對於國中女生數學成就有顯著影響力，但進一步考慮學校公私別變項之後，女生班的影響力即消失。 / The main purpose of this study is to assess the magnitude of individual and contextual influences to explain gender differences in math achievements. Adopting the hierarchical linear model analysis to determine whether or not statistically significant differences between the mathematical achievements of 7th grade students who attend all-girls classes compared with those who attend coeducational classes at the same time, and their academic performance after two years. The result shows that there are three factors that have significant influences on girls’ math achievement in junior high schools, which are the single-sex classes, female math teachers and the academic climate of each class. However, if private schools are taken into consideration, the significant influence of the gender composition of classes will disappear.

多年來，交通運輸與土地使用之交互影響關係受學界所廣泛討論，本研究主要探討高速鐵路與土地使用之交互影響關係。關於高鐵對土地使用影響之研究，分為兩大類別，分別為建立模式預測未來地區發展狀況，以及實證分析高鐵通車後對地區的影響效果。過去研究指出，高鐵營運後，可能對土地使用產生之影響包括：無顯著之土地使用改變、地區間互動改變、聚集效果（Cluster effect）、離散效果(Disparties)以及「隧道效果(Tunnel effect)」或「廊道效果(Corridor effect) 」。 　　本研究為以階層線性模型分析高鐵通車後對台灣土地使用影響之實證研究。根據實證，高鐵站之有無以及高鐵站所在區位對鄉鎮市區土地使用有顯著影響，且相較其他控制變數，為影響鄉鎮市區土地使用之重要變數。有高鐵站之鄉鎮市區與無高鐵站之鄉鎮市區相比，土地使用可能成長較多，而位於高鐵一定服務範圍內之鄉鎮市區之土地使用，亦受高鐵所影響。另外，不同區位之高鐵站對土地使用之效果有所不同，而該區位效果隨產業特性可能有所差異。人口、及業人口以及三級產業及業人口可能因市中心區位之高鐵站聚集，但二級產業及業人口未有因市中心區位高鐵站而聚集的現象；郊區區位之高鐵站鄉鎮市區或縣市，則有人口、及業人口或三級產業及業人口流失的現象。由上述結果可驗證，高鐵服務範圍內有聚集效果之發生，而不同區位之高鐵站，聚集之效果並不同。 / For many years, the interactive relationship between transportation and land use has been widely discussed by scholars. This study is trying to assess the short-term impact of high-speed rail (HSR) on land use. There are two types of studies on the impact of high-speed rail on land use. One is establishing models to predict future land use development; the other is evaluating the effect of HSR empirically. Past studies have shown that possible impacts on land use after the operation of HSR include: no significant land use change, inter-regional interaction change, cluster effect, disparities, and "tunnel effect" or "corridor effect." 　　In this empirical study, the results of hierarchical linear model show that the existence of the HSR station and the location of the HSR station have a significant effect on the land use in the city. Controlling for other control variables, the existence and location of the HSR station are important factors influencing the land use in the city. Land use development in cities with the HSR station may be more evident than those without the HSR station. Cities within the HSR service area are also effected by HSR. In addition, there may be different land use effects due to different locations of the HSR stations, and these location effects may be different due to different industrial characteristics of the area. Population, employment, and employment of tertiary industrial sectors in a city may cluster due to the HSR station in central area location, but employment of secondary industrial sectors doesn’t. Otherwise, population, employment, and employment of tertiary industrial sectors in a city or county may lose due to the HSR station in rural area location. In conclusion, there is a cluster effect within the HSR service area, and this effect varies according to the location of the HSR station.

Les logiciels utilisés sont Splus et R. / Résumé La technique connue comme l'imputation multiple semble être la technique la plus appropriée pour résoudre le problème de non-réponse. La littérature mentionne des méthodes qui modélisent la nature et la structure des valeurs manquantes. Une des méthodes les plus populaires est l'algorithme « Pan » de (Schafer & Yucel, 2002). Les imputations rapportées par cette méthode sont basées sur un modèle linéaire multivarié à effets mixtes pour la variable réponse. La méthode « BHLC » de (Murua et al, 2005) est une extension de « Pan » dont le modèle est bayésien hiérarchique avec groupes. Le but principal de ce travail est d'étudier le problème de sélection du modèle pour l'imputation multiple en termes d'efficacité et d'exactitude des prédictions des valeurs manquantes. Nous proposons une mesure de performance liée à la prédiction des valeurs manquantes. La mesure est une erreur quadratique moyenne reflétant la variance associée aux imputations multiples et le biais de prédiction. Nous montrons que cette mesure est plus objective que la mesure de variance de Rubin. Notre mesure est calculée en augmentant par une faible proportion le nombre de valeurs manquantes dans les données. La performance du modèle d'imputation est alors évaluée par l'erreur de prédiction associée aux valeurs manquantes. Pour étudier le problème objectivement, nous avons effectué plusieurs simulations. Les données ont été produites selon des modèles explicites différents avec des hypothèses particulières sur la structure des erreurs et la distribution a priori des valeurs manquantes. Notre étude examine si la vraie structure d'erreur des données a un effet sur la performance du choix des différentes hypothèses formulées pour le modèle d'imputation. Nous avons conclu que la réponse est oui. De plus, le choix de la distribution des valeurs manquantes semble être le facteur le plus important pour l'exactitude des prédictions. En général, les choix les plus efficaces pour de bonnes imputations sont une distribution de student avec inégalité des variances dans les groupes pour la structure des erreurs et une loi a priori choisie pour les valeurs manquantes est la loi normale avec moyenne et variance empirique des données observées, ou celle régularisé avec grande variabilité. Finalement, nous avons appliqué nos idées à un cas réel traitant un problème de santé. Mots clés : valeurs manquantes, imputations multiples, modèle linéaire bayésien hiérarchique, modèle à effets mixtes. / Abstract The technique known as multiple imputation seems to be the most suitable technique for solving the problem of non-response. The literature mentions methods that models the nature and structure of missing values. One of the most popular methods is the PAN algorithm of Schafer and Yucel (2002). The imputations yielded by this method are based on a multivariate linear mixed-effects model for the response variable. A Bayesian hierarchical clustered and more flexible extension of PAN is given by the BHLC model of Murua et al. (2005). The main goal of this work is to study the problem of model selection for multiple imputation in terms of efficiency and accuracy of missing-value predictions. We propose a measure of performance linked to the prediction of missing values. The measure is a mean squared error, and hence in addition to the variance associated to the multiple imputations, it includes a measure of bias in the prediction. We show that this measure is more objective than the most common variance measure of Rubin. Our measure is computed by incrementing by a small proportion the number of missing values in the data and supposing that those values are also missing. The performance of the imputation model is then assessed through the prediction error associated to these pseudo missing values. In order to study the problem objectively, we have devised several simulations. Data were generated according to different explicit models that assumed particular error structures. Several missing-value prior distributions as well as error-term distributions are then hypothesized. Our study investigates if the true error structure of the data has an effect on the performance of the different hypothesized choices for the imputation model. We concluded that the answer is yes. Moreover, the choice of missing-value prior distribution seems to be the most important factor for accuracy of predictions. In general, the most effective choices for good imputations are a t-Student distribution with different cluster variances for the error-term, and a missing-value Normal prior with data-driven mean and variance, or a missing-value regularizing Normal prior with large variance (a ridge-regression-like prior). Finally, we have applied our ideas to a real problem dealing with health outcome observations associated to a large number of countries around the world. Keywords: Missing values, multiple imputation, Bayesian hierarchical linear model, mixed effects model.

Os modelos mistos são apropriados na análise de dados longitudinais, agrupados e hierárquicos, permitindo descrever e comparar os perfis médios de respostas, levando em conta a variabilidade e a correlação entre as unidades experimentais de um mesmo grupo e entre os valores observados na mesma unidade experimental ao longo do tempo, assim como a heterogeneidade das variâncias. Esses modelos possibilitam a análise de dados desbalanceados, incompletos ou irregulares com relação ao tempo. Neste trabalho, buscou-se mostrar a flexibilidade dos modelos lineares mistos e a sua importância na análise de dados toxicológicos longitudinais. Os modelos lineares mistos foram utilizados para analisar os efeitos de dose no ganho de peso de ratos adultos machos e fêmeas, em teste de toxicidade por doses repetidas e também os efeitos de fase de gestação e dose nos perfis de pesos de filhotes de ratas tratadas. Foram comparados os modelos lineares mistos de regressão polinomial de grau 3, spline e de regressão por partes, ambos com um único ponto de mudança na idade média de abertura dos olhos dos filhotes, buscando o mais apropriado para descrever o crescimento dos mesmos ao longo do período de amamentação. São apresentados os códigos escritos no SAS/STAT para a análise exploratória dos dados, ajuste, comparação e validação dos modelos. Espera-se que o detalhamento da teoria e das aplicações apresentado contribua para a compreensão, interesse e uso desta metodologia por estatísticos e pesquisadores da área. / Mixed models are appropriate in the analysis of longitudinal, grouped and hierarchical data, allowing describe and compare the average response profiles, taking into account the variability and correlation among the experimental units of the same group and among the values observed over the time in the same experimental unit, as well as the heterogeneity of variances. These models allow the analysis of unbalanced, incomplete or irregular data with respect to time. This work aimed to show the flexibility of linear mixed models and its importance in the analysis of longitudinal toxicological data. Linear mixed models were used to evaluate the effects of doses in the body weight gain of adult male and female Wistar rats, in repeated doses toxicity test and also the effects of pregnancy period and dose in the pups growth of treated dams. It were compared the linear mixed models of third degree polynomial regression, spline and piecewise regression, both with a single point of change in the average time of pups eyes opening, searching for the most appropriate one to describe their growth along the lactation period. The SAS/STAT codes used for exploratory data analysis, comparison and validation of fitted models are presented. It is expected that the detailing of the theory and of the applications presented contribute with the understanding, interest and use of this methodology by statisticians and researchers in the area.

Résumé La technique connue comme l'imputation multiple semble être la technique la plus appropriée pour résoudre le problème de non-réponse. La littérature mentionne des méthodes qui modélisent la nature et la structure des valeurs manquantes. Une des méthodes les plus populaires est l'algorithme « Pan » de (Schafer & Yucel, 2002). Les imputations rapportées par cette méthode sont basées sur un modèle linéaire multivarié à effets mixtes pour la variable réponse. La méthode « BHLC » de (Murua et al, 2005) est une extension de « Pan » dont le modèle est bayésien hiérarchique avec groupes. Le but principal de ce travail est d'étudier le problème de sélection du modèle pour l'imputation multiple en termes d'efficacité et d'exactitude des prédictions des valeurs manquantes. Nous proposons une mesure de performance liée à la prédiction des valeurs manquantes. La mesure est une erreur quadratique moyenne reflétant la variance associée aux imputations multiples et le biais de prédiction. Nous montrons que cette mesure est plus objective que la mesure de variance de Rubin. Notre mesure est calculée en augmentant par une faible proportion le nombre de valeurs manquantes dans les données. La performance du modèle d'imputation est alors évaluée par l'erreur de prédiction associée aux valeurs manquantes. Pour étudier le problème objectivement, nous avons effectué plusieurs simulations. Les données ont été produites selon des modèles explicites différents avec des hypothèses particulières sur la structure des erreurs et la distribution a priori des valeurs manquantes. Notre étude examine si la vraie structure d'erreur des données a un effet sur la performance du choix des différentes hypothèses formulées pour le modèle d'imputation. Nous avons conclu que la réponse est oui. De plus, le choix de la distribution des valeurs manquantes semble être le facteur le plus important pour l'exactitude des prédictions. En général, les choix les plus efficaces pour de bonnes imputations sont une distribution de student avec inégalité des variances dans les groupes pour la structure des erreurs et une loi a priori choisie pour les valeurs manquantes est la loi normale avec moyenne et variance empirique des données observées, ou celle régularisé avec grande variabilité. Finalement, nous avons appliqué nos idées à un cas réel traitant un problème de santé. Mots clés : valeurs manquantes, imputations multiples, modèle linéaire bayésien hiérarchique, modèle à effets mixtes. / Abstract The technique known as multiple imputation seems to be the most suitable technique for solving the problem of non-response. The literature mentions methods that models the nature and structure of missing values. One of the most popular methods is the PAN algorithm of Schafer and Yucel (2002). The imputations yielded by this method are based on a multivariate linear mixed-effects model for the response variable. A Bayesian hierarchical clustered and more flexible extension of PAN is given by the BHLC model of Murua et al. (2005). The main goal of this work is to study the problem of model selection for multiple imputation in terms of efficiency and accuracy of missing-value predictions. We propose a measure of performance linked to the prediction of missing values. The measure is a mean squared error, and hence in addition to the variance associated to the multiple imputations, it includes a measure of bias in the prediction. We show that this measure is more objective than the most common variance measure of Rubin. Our measure is computed by incrementing by a small proportion the number of missing values in the data and supposing that those values are also missing. The performance of the imputation model is then assessed through the prediction error associated to these pseudo missing values. In order to study the problem objectively, we have devised several simulations. Data were generated according to different explicit models that assumed particular error structures. Several missing-value prior distributions as well as error-term distributions are then hypothesized. Our study investigates if the true error structure of the data has an effect on the performance of the different hypothesized choices for the imputation model. We concluded that the answer is yes. Moreover, the choice of missing-value prior distribution seems to be the most important factor for accuracy of predictions. In general, the most effective choices for good imputations are a t-Student distribution with different cluster variances for the error-term, and a missing-value Normal prior with data-driven mean and variance, or a missing-value regularizing Normal prior with large variance (a ridge-regression-like prior). Finally, we have applied our ideas to a real problem dealing with health outcome observations associated to a large number of countries around the world. Keywords: Missing values, multiple imputation, Bayesian hierarchical linear model, mixed effects model. / Les logiciels utilisés sont Splus et R.

Os modelos mistos são apropriados na análise de dados longitudinais, agrupados e hierárquicos, permitindo descrever e comparar os perfis médios de respostas, levando em conta a variabilidade e a correlação entre as unidades experimentais de um mesmo grupo e entre os valores observados na mesma unidade experimental ao longo do tempo, assim como a heterogeneidade das variâncias. Esses modelos possibilitam a análise de dados desbalanceados, incompletos ou irregulares com relação ao tempo. Neste trabalho, buscou-se mostrar a flexibilidade dos modelos lineares mistos e a sua importância na análise de dados toxicológicos longitudinais. Os modelos lineares mistos foram utilizados para analisar os efeitos de dose no ganho de peso de ratos adultos machos e fêmeas, em teste de toxicidade por doses repetidas e também os efeitos de fase de gestação e dose nos perfis de pesos de filhotes de ratas tratadas. Foram comparados os modelos lineares mistos de regressão polinomial de grau 3, spline e de regressão por partes, ambos com um único ponto de mudança na idade média de abertura dos olhos dos filhotes, buscando o mais apropriado para descrever o crescimento dos mesmos ao longo do período de amamentação. São apresentados os códigos escritos no SAS/STAT para a análise exploratória dos dados, ajuste, comparação e validação dos modelos. Espera-se que o detalhamento da teoria e das aplicações apresentado contribua para a compreensão, interesse e uso desta metodologia por estatísticos e pesquisadores da área. / Mixed models are appropriate in the analysis of longitudinal, grouped and hierarchical data, allowing describe and compare the average response profiles, taking into account the variability and correlation among the experimental units of the same group and among the values observed over the time in the same experimental unit, as well as the heterogeneity of variances. These models allow the analysis of unbalanced, incomplete or irregular data with respect to time. This work aimed to show the flexibility of linear mixed models and its importance in the analysis of longitudinal toxicological data. Linear mixed models were used to evaluate the effects of doses in the body weight gain of adult male and female Wistar rats, in repeated doses toxicity test and also the effects of pregnancy period and dose in the pups growth of treated dams. It were compared the linear mixed models of third degree polynomial regression, spline and piecewise regression, both with a single point of change in the average time of pups eyes opening, searching for the most appropriate one to describe their growth along the lactation period. The SAS/STAT codes used for exploratory data analysis, comparison and validation of fitted models are presented. It is expected that the detailing of the theory and of the applications presented contribute with the understanding, interest and use of this methodology by statisticians and researchers in the area.

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[pt] O comportamento do consumo de energia elétrica do setor industrial tem sido amplamente investigado ao longo dos últimos anos, devido a sua importância econômica, social e ambiental. Mais especificamente, o consumo de eletricidade dos subsetores da indústria brasileira exerce grande importância para o sistema energético brasileiro. Neste contexto, as projeções de longo prazo do seu consumo de energia elétrica para um país ou uma região são informações de grande relevância na tomada de decisão de órgãos e entidades que atuam no setor energético. A abordagem bottom-up determinística tem sido utilizada para obter a previsão de longo prazo em diversas áreas de pesquisa. Neste trabalho, propõe-se uma metodologia que combina a abordagem bottom-up com os modelos lineares hierárquicos para a previsão de longo prazo considerando os cenários de eficiência energética. Além disso, foi utilizada a inferência bayesiana para a estimação dos parâmetros do modelo, permitindo a incorporação de incerteza nessas previsões. Os resultados utilizando os dados de consumo de eletricidade de subsetores da indústria brasileira mostraram que a metodologia proposta consegue capturar a tajetória do consumo de eletricidade, em particular, dos subsetores de papel e celulose, e de metais não-ferrosos e outros de metalurgia. Por exemplo, os intervalos de credibilidade de 95 por cento construídos a partir do modelo estocástico contemplam os valores reais observados nos anos de 2015 e 2016. / [en] The electricity consumption behaviour in the Brazilian industry has been extensively investigated over the past years due to its economic, social and environmental importance. Specifically, the electricity consumption of the subsectors of Brazilian industry have great importance for the Brazilian energy system. In this context, the long-term projections of energy consumption of a country or region are highly relevant information to decision-making of organs and entities operating in the energy sector. The deterministic bottom-up approach has been used for the long-term forecast in several areas of research. In this paper, we propose a methodology that combines the bottom-up approach with hierarchical linear models for long-term forecasting considering energy efficiency scenarios. In addition, Bayesian inference was used to estimate the parameters of the model, allowing the uncertainty incorporation in these forecasts. The results using the electricity consumption data from subsectors of the Brazilian industry showed that the proposed methodology is able to capture the trajectory of their electricity consumption, in particular of the pulp and paper, and of non-ferrous metals and other metallurgical subsectors. For example, the 95 percent credibility intervals constructed from the stochastic model contemplate the actual values observed in the years 2015 and 2016.