O objetivo do trabalho é apresentar os métodos mais consagrados de Análise Discriminante quando temos uma mistura de variáveis categóricas e contínuas. / The purpose of this dissertation is to analyze and compare Discriminant Analysis techniques in the presence of mixed categorical and continuous data.

Empreendedorismo tem sido objeto de incentivo no mundo e no Brasil, dada a sua significante contribuição para o desenvolvimento econômico e social de uma nação. Observa-se que a maioria das empresas, existentes ou novas, evolui de forma lenta e gradual; no entanto, reduzida parcela apresenta um padrão diferente, com crescimento elevado em faturamento ou número de colaboradores: são as empresas de alto crescimento (EACs). Tais empresas são as responsáveis por grande parte da geração de empregos (Birch, 1981; Coad, Daunfeldt, Holzl, Johansson, & Nightingale, 2014; Henrekson & Johansson, 2010; OECD, 2010). A presente tese procurou identificar as variáveis que ajudam a explicar o desempenho das EACs no Brasil, classificadas conforme critério da OECD (2007). Foi conduzida uma pesquisa com 470 empresas brasileiras, que coletou mais de 30 variáveis preditoras categóricas ou métricas, utilizadas no modelo Regressão Logística. Foram identificadas algumas variáveis alinhadas com a literatura e outras menos intuitivas e documentadas. Comprovou-se o aumento da probabilidade de EACs quando se relacionavam com aceleradoras, recebiam premiações ou eram spin-offs de outras empresas. Em função das altas taxas de juros bancários e da cultura empreendedora no Brasil, surpreendeu o impacto positivo de empréstimos bancários e a percepção dos empreendedores sobre registrar marcas comerciais, bem como o impacto negativo da percepção sobre propaganda em mídia digital e doações de instituições de fomento, relacionadas às EACs. Análises adicionais com o subgrupo de EACs caracterizadas como gazelas foram feitas. Embora apresente limitações de surveys e outras, a tese confirmou parte dos resultados da literatura sobre empreendedorismo e identificou avenidas para futuras pesquisas. / Entrepreneurship has been object of encouragement in the world and in Brazil, given its significant contribution to the economic and social development of a nation. It is observed that the majority of companies, existing or new, are developing slowly and gradually; however, small share presents a different pattern, with high growth in sales or number of employees: they are the high growth firms (HGFs). These firms are responsible for a large part of job creation (Birch, 1981; Coad, Daunfeldt, Holzl, Johansson, & Nightingale, 2014, Henrekson & Johansson, 2010, OECD, 2010). This thesis aimed to identify the variables that help to explain the performance of HGFs in Brazil, according to OECD (2007) criterion. A survey with 470 Brazilian companies was conducted, collecting more than 30 categorical or metric predictor variables, used in the Logistic Regression model. Some identified variables were aligned to literature, but others less intuitive or documented. It was confirmed the increase in the probability of HGFs when they related to accelerators, received awards, or were spin-offs of other companies. As a consequence of the high banking interest rates and the entrepreneurship culture in Brazil, surprised the positive impact of bank loans and the entrepreneurs\' perception of trademark registration, as well as the negative impact of perception on advertising in digital media and donations from development institutions, related to HGFs. Additional analyzes with the subgroup of HGFs characterized as gazelles were made. Although it presents limitations of surveys and others, the thesis confirmed part of the results of the literature on entrepreneurship and identified avenues for future researches.

O conhecimento do padrão de deslocamento populacional bem como a estimativa de demanda por transportes são de fundamental importância para a tomada de decisões relativas ao planejamento urbano e de transportes. Em geral, a obtenção destas informações é realizada por modelos tradicionais como o modelo quatro etapas. Entretanto, modelos clássicos não levam em conta a dependência espacial das variáveis . A Geoestatística, valendo-se da utilização de variáveis regionalizadas, apresenta-se como uma ferramenta auxiliar capaz de modelar informações espaciais. Este trabalho tem por objetivo estimar dados desagregados de demanda por transportes através de modelagem geoestatística e tradicional. Neste estudo, a modelagem tradicional e a geoestatística puderam ser comparadas por meio de um banco de dados referente à pesquisa Origem/Destino da Região Metropolitana de São Paulo, realizada em 2007. A abordagem tradicional se baseou em um modelo de regressão enquanto que a abordagem geoestatística consistiu na estimação espacial de variáveis com base na modelagem de semivariogramas e Krigagem. Ao final do trabalho, foi possível realizar a comparação dos resultados da abordagem tradicional e geoestatística em coordenadas de valores conhecidos. Os resultados indicaram que a modelagem tradicional apontou uma taxa de acertos de 96 % pelo modelo de Regressão Logística Múltipla adotada para a variável dicotômica de preferência por modo motorizado (variável objeto de estudo). A abordagem tradicional baseou-se na calibração de um modelo por meio de outras oito variáveis. Entretanto, a modelagem geoestatística, utilizando -se apenas das coordenadas geográficas domiciliares, resultou em 67% de taxa de acertos de previsão da variável. Isso demonstrou que, apesar de possuir menor taxa de acertos, a modelagem geoestatística, por utilizar menor número de informações para previsão da variável, teve um resultado satisfatório e demonstra-se promissora na área de planejamento de transportes , sobretudo considerando sua habilidade de estimação em outras coordenadas geográficas além das amostradas. / The comprehension of population displacement patterns and travel demand forecasting is crucial on making decisions related to urban transportation planning. In order to obtain this information, classic models like the sequential Four -step mo del are applied. However, classic models do not consider spatial location in their approach. Geostatistics is displayed as a suitable complementary instrument able to model spatial information. This work intends to forecast disaggregated data on transportation demand through traditional and geostatistical modeling. The present study compares the results from classic approach and Geostatistics through an Origin-Destination Survey dataset, carried out in São Paulo Metropolitan Area in 2007. The classic approach was based on regression models whereas Geostatistics consisted in variable spatial estimation by semivariograms modeling and Kriging. At the end of the study, a comparison between regression and geostatistical analysis was conducted through results of prediction in locations where the values of the variable are known. Results indicated that classic modeling had a 96% hit rate by Multiple Logistic Regression adopted for the dummy variable preference for motorized travel mode (object of study variable). Classic modeling was based on a training model using other eight predictor variables. Meanwhile, Geostatistics, using only residential geographical coordinate, resulted in a 67% hit rate for predicting the variable object of study. This demonstrates that, even though Geostatiscs had lower hit rate compared to Multiple Logistic Regression, it had satisfactory outcome and proves tobe a promising approach in transport planning, given that it considered less informati on to predict the variable, especially considering its ability of estimating in other geographical coordinates in addition to those sampled.

Uma etapa importante após a formulação e ajuste de um modelo de regressão é a análise de diagnóstico. A regressão logística tem se constituído num dos principais métodos de modelagem estatística de dados; mesmo quando a resposta de interesse não é originalmente do tipo binário, alguns pesquisadores tem dicotomizado a resposta de modo que a probabilidade de sucesso pode ser modelado através da regressão logística. Neste trabalho consideramos um estudo de diagnóstico no modelo da regressão logística, utilizando as medidas proposta por Pregibon (1981) e a técnica de influência local Cook (1986). Investigamos a aplicação da técnica de influência local sob diferentes esquemas de perturbação. Como ilustração, apresentamos a aplicação dos resultados desenvolvidos em dois conjuntos de dados reais. / An important stage after the formularization and adjustment of a regression model is the diagnosis analysis. Logistic regression is one of the main methods for modeling data and even when the response of interest is is not originally of the binary type, some researchers have dichotomized the response in a way that the success probability can be modeled through logistic regression. In this work we consider a study of diagnosis methods with logistic regression, using the measures proposed by Pregibon (1981) and the local influence technique of Cook (1986). We investigate the application of the local influence technique of under different types of disturbance. As as illustration, we show the application of the developed results obtained with real data sets.

O conhecimento do padrão de deslocamento populacional bem como a estimativa de demanda por transportes são de fundamental importância para a tomada de decisões relativas ao planejamento urbano e de transportes. Em geral, a obtenção destas informações é realizada por modelos tradicionais como o modelo quatro etapas. Entretanto, modelos clássicos não levam em conta a dependência espacial das variáveis . A Geoestatística, valendo-se da utilização de variáveis regionalizadas, apresenta-se como uma ferramenta auxiliar capaz de modelar informações espaciais. Este trabalho tem por objetivo estimar dados desagregados de demanda por transportes através de modelagem geoestatística e tradicional. Neste estudo, a modelagem tradicional e a geoestatística puderam ser comparadas por meio de um banco de dados referente à pesquisa Origem/Destino da Região Metropolitana de São Paulo, realizada em 2007. A abordagem tradicional se baseou em um modelo de regressão enquanto que a abordagem geoestatística consistiu na estimação espacial de variáveis com base na modelagem de semivariogramas e Krigagem. Ao final do trabalho, foi possível realizar a comparação dos resultados da abordagem tradicional e geoestatística em coordenadas de valores conhecidos. Os resultados indicaram que a modelagem tradicional apontou uma taxa de acertos de 96 % pelo modelo de Regressão Logística Múltipla adotada para a variável dicotômica de preferência por modo motorizado (variável objeto de estudo). A abordagem tradicional baseou-se na calibração de um modelo por meio de outras oito variáveis. Entretanto, a modelagem geoestatística, utilizando -se apenas das coordenadas geográficas domiciliares, resultou em 67% de taxa de acertos de previsão da variável. Isso demonstrou que, apesar de possuir menor taxa de acertos, a modelagem geoestatística, por utilizar menor número de informações para previsão da variável, teve um resultado satisfatório e demonstra-se promissora na área de planejamento de transportes , sobretudo considerando sua habilidade de estimação em outras coordenadas geográficas além das amostradas. / The comprehension of population displacement patterns and travel demand forecasting is crucial on making decisions related to urban transportation planning. In order to obtain this information, classic models like the sequential Four -step mo del are applied. However, classic models do not consider spatial location in their approach. Geostatistics is displayed as a suitable complementary instrument able to model spatial information. This work intends to forecast disaggregated data on transportation demand through traditional and geostatistical modeling. The present study compares the results from classic approach and Geostatistics through an Origin-Destination Survey dataset, carried out in São Paulo Metropolitan Area in 2007. The classic approach was based on regression models whereas Geostatistics consisted in variable spatial estimation by semivariograms modeling and Kriging. At the end of the study, a comparison between regression and geostatistical analysis was conducted through results of prediction in locations where the values of the variable are known. Results indicated that classic modeling had a 96% hit rate by Multiple Logistic Regression adopted for the dummy variable preference for motorized travel mode (object of study variable). Classic modeling was based on a training model using other eight predictor variables. Meanwhile, Geostatistics, using only residential geographical coordinate, resulted in a 67% hit rate for predicting the variable object of study. This demonstrates that, even though Geostatiscs had lower hit rate compared to Multiple Logistic Regression, it had satisfactory outcome and proves tobe a promising approach in transport planning, given that it considered less informati on to predict the variable, especially considering its ability of estimating in other geographical coordinates in addition to those sampled.

Recent Next Generation Sequencing methods provide a count of RNA molecules in the form of short reads, yielding discrete, often highly non-normally distributed gene expression measurements. Due to this feature of RNA sequencing (RNA-seq) data, appropriate statistical inference methods are required. Although Negative Binomial (NB) regression has been generally accepted in the analysis of RNA-seq data, its appropriateness in the application to genetic studies has not been exhaustively evaluated. Additionally, adjusting for covariates that have an unknown relationship with expression of a gene has not been extensively evaluated in RNA-seq studies using the NB framework. Finally, the dependent structures in RNA-Seq data may violate the assumptions of some multiple testing correction methods. In this dissertation, we suggest an alternative regression method, evaluate the effect of covariates, and compare various multiple testing correction methods. We conduct simulation studies and apply these methods to a real data set. First, we suggest Firth’s logistic regression for detecting differentially expressed genes in RNA-seq data. We also recommend the data adaptive method that estimates a recalibrated distribution of test statistics. Firth’ logistic regression exhibits an appropriately controlled Type-I error rate using the data adaptive method and shows comparable power to NB regression in simulation studies. Next, we evaluate the effect of disease-associated covariates where the relationship between the covariate and gene expression is unknown. Although the power of NB and Firth’s logistic regression is decreased as disease-associated covariates are added in a model, Type-I error rates are well controlled in Firth’ logistic regression if the relationship between a covariate and disease is not strong. Finally, we compare multiple testing correction methods that control family-wise error rates and impose false discovery rates. The evaluation reveals that an understanding of study designs, RNA-seq data, and the consequences of applying specific regression and multiple testing correction methods are very important factors to control family-wise error rates or false discovery rates. We believe our statistical investigations will enrich gene expression studies and influence related statistical methods.

O objetivo geral desta dissertação é traçar um panorama da evolução do dativo em -e dentro do contexto do paradigma dos demais casos morfológicos existentes no alemão e detectar prováveis fatores atuando concomitantemente na variação da (não) ocorrência desse marcador de caso. Para tanto, revisitamos o desenvolvimento do sistema de casos do alemão e descrevemos o comportamento e padrões exibidos pelos marcadores de caso de substantivos no singular e no plural. Discutimos a útil noção de declinações forte e fraca, de Grimm (1822), bem como algumas teorias sobre mudança linguística, tais como o enfraquecimento de sílabas átonas (SAPIR, 1921), o surgimento do artigo definido (PHILLIPI, 1997) e da teoria baseada no uso (BARðDAL, 2009). As questões levantadas por essas teorias podem ter contribuído com o paulatino apagamento de marcadores de caso nas línguas germânicas. Não rejeitamos nenhuma delas, haja vista que todas fornecem hipóteses plausíveis, entretanto, a mudança não ocorreu de forma homogênea em diferentes contextos e parece exibir certos padrões que podem ser explicados pela interação de diversos fatores, e não com base apenas nas grandes ideias das teorias descritas acima. Testar a hipótese dessa policausalidade requer o emprego de metodologia específica. Como o fenômeno aqui estudado é a realização vs. não realização do dativo em -e, empregamos o método de regressão logística binária, o mais adequado para descrever e testar hipóteses sobre relações entre uma variável-resposta categórica e variáveis explanatórias também categóricas e/ou contínuas (PENG; LEE; INGERSOLL, 2002). Obtivemos robusta evidência de que fatores tipológicos, fonológicos e prosódicos desempenham importante papel na variação da realização do dativo em -e e observamos que a interação de fatores tem maior poder explanatório sobre os padrões exibidos na variação do que uma análise que considere a influência de diferentes fatores de maneira isolada. A maior vantagem em aplicarmos um teste como o de regressão logística binária consiste na possibilidade de captar a existência de determinados padrões interacionais, e, portanto, podemos analisar a variação e mudança, como no exemplo do dativo em -e, de um ponto de vista multifatorial, e não limitando nosso escopo a fatores isolados, pois, em um sistema complexo como é a língua, eles parecem indissociáveis. / The main goal of this investigation is to outline an overview of the development of the dative -e within the context of the paradigm of other morphological cases existing in German and to identify factors that play a concomitant role in the variation of the (non-)occurence of the case marker. In order to perform this task, we revisited the development of the German case system and described the behaviour and patterns exhibited by the case markers of singular and plural nouns. We discussed the useful notion of strong and weak declensions such as thought of by Grimm (1822), as well as some theories on language change, as the weakening of unstressed syllables (SAPIR, 1921), the rise of the definite article (PHILLIPI, 1997) and the usage-based approach to language (BARðDAL, 2009). The questions raised within the framework of these theories might have contributed to the non-occurrence of the case marker in Germanic languages. We did not reject any of the theories, since they provide plausible hypotheses, however, the change did not occur homogeneously in different contexts and it seems to exhibit certain patterns that may be accounted for by the interaction between diverse factors and therefore not only by the general ideas mentioned above. In order to test this multicausality hypothesis, it is necessary to apply a specific methodology. Given that the phenomenon studied in this investigation is the occurrence vs. non-occurrence of the dative -e, we performed a binary logistic regression analysis, which is well suited for describing and testing hypotheses about relationships between categorical outcome variables and explanatory variables that are also categorical and/or continuous (PENG; LEE; INGERSOLL, 2002). We obtained strong evidence that typological, phonological and prosodic factors play an important role in the variation of the dative -e and we observed that the interaction between such factors can better explain the patterns exhibited in the variation than an approach that only takes into account the influence of individual factors. The advantage in performing a binary logistic regression is based on the fact that it highlights the existence of interactional factors, and therefore we can analyse the variation and change, using the example of the dative -e, from a multifactorial point of view without limiting our scope to individual factors only, since they do not seem to work individually within a complex system such as the human language.

Modelo multinível é uma ferramenta estatística cada vez mais popular para análise de dados com estrutura hierárquica. O objetivo deste trabalho é propor um método para realizar a predição de observações de novos grupos usando modelos de regressão logística multinível com 2 níveis. Além disso, é apresentado e comparado dois métodos de estimação para o modelo multinível: Quase-verossimilhança Penalizada (QVP) e Quadratura de Gauss-Hermite (QGH). A idéia central está baseada no trabalho de (Jiang e Lahiri, 2006) no qual se propõe o uso do chamado melhor estimador empírico para o efeito aleatório. Através deste estimador, utilizou-se a parte fixa do modelo em conjunto com uma estimativa do desvio padrão do efeito aleatório para fazer a predição de observações de novos grupos, encontrando a probabilidade estimada dessa observação apresentar o evento de interesse, dadas suas características. / Multilevel model is an statistical tool which is becoming more and more popular in data analysis with hierachical structure. The purpose of this dissertation is to present a method to make a prediction of new group observation in multilevel logistic regression models with 2 levels. Besides, were presented and compared two estimation methods for multilevel model: Penalized Quase-likelihood and Gauss-Hermite Quadrature. The central idea is based on the paper of Jiang and Lahiri (2006), which is presented the empirical best estimator for the random effect. Through this estimator was used the fixed part of the model with an estimative of the standard deviation of the random effect to find the estimated probability of this observation presenting the target event, in accordance with its characteristic.

Buried pipelines are vulnerable to the threat of corrosion. Hence, they are normally coated with a protective coating to isolate the metal substrate from the surrounding environment with the addition of CP current being applied to the pipeline surface to halt any corrosion activity that might be taking place. With time, this barrier will deteriorate which could potentially lead to corrosion of the pipe. The External Corrosion Direct Assessment (ECDA) methodology was developed with the intention of upholding the structural integrity of pipelines. Above ground indirect inspection techniques such as the DCVG which is an essential part of an ECDA, is commonly used to determine coating defect locations and measure the defect's severity. This is followed by excavation of the identified location for further examination on the extent of pipeline damage. Any coating or corrosion defect found at this stage is repaired and remediated. The location of such excavations is determined by the measurements obtained from the DCVG examination in the form of %IR and subjective inputs from experts which bases their justification on the environment and the physical characteristics of the pipeline. Whilst this seems to be a straight forward process, the factors that comes into play which gave rise to the initial %IR is not fully understood. The lack of understanding with the additional subjective inputs from the assessors has led to unnecessary excavations being conducted which has put tremendous financial strain on pipeline operators. Additionally, the threat of undiscovered defects due to the erroneous nature of the current method has the potential to severely compromise the pipeline's safe continual operation. Accurately predicting the coating defect size (TCDA) and interpretation of the indication signal (%IR) from an ECDA is important for pipeline operators to promote safety while keeping operating cost at a minimum. Furthermore, with better estimates, the uncertainty from the DCVG indication is reduced and the decisions made on the locations of excavation is better informed. However, ensuring the accuracy of these estimates does not come without challenges. These challenges include (1) the need of proper methods for large data analysis from indirect assessment and (2) uncertainty about the probability distribution of quantities. Standard mean regression models e.g. the OLS, were used but fail to take the skewness of the distributions involved into account. The aim of this thesis is thus, to come up with statistical models to better predict TCDA and to interpret the %IR from the indirect assessment of an ECDA more precisely. The pipeline data used for the analyses is based on a recent ECDA project conducted by TWI Ltd. for the Middle Eastern Oil Company (MEOC). To address the challenges highlighted above, Quantile Regression (QR) was used to comprehensively characterise the underlying distribution of the dependent variable. This can be effective for example, when determining the different effect of contributing variables towards different sizes of TCDA (different quantiles). Another useful advantage is that the technique is robust to outliers due to its reliance on absolute errors. With the traditional mean regression, the effect of contributing variables towards other quantiles of the dependent variable is ignored. Furthermore, the OLS involves the squaring of errors which makes it less robust to outliers. Other forms of QR such as the Bayesian Quantile Regression (BQR) which has the advantage of supplementing future inspection projects with prior data and the Logistic Quantile Regression (LQR) which ensures the prediction of the dependent variable is within its specified bounds was applied to the MEOC dataset. The novelty of research lies in the approaches (methods) taken by the author in producing the models highlighted above. The summary of such novelty includes: * The use of non-linear Quantile Regression (QR) with interacting variables for TCDA prediction. * The application of a regularisation procedure (LASSO) for the generalisation of the TCDA prediction model.* The usage of the Bayesian Quantile Regression (BQR) technique to estimate the %IR and TCDA. * The use of Logistic Regression as a guideline towards the probability of excavation * And finally, the use of Logistic Quantile Regression (LQR) in ensuring the predicted values are within bounds for the prediction of the %IR and POPD. Novel findings from this thesis includes: * Some degree of relationship between the DCVG technique (%IR readings) and corrosion dimension. The results of the relationship between TCDA and POPD highlights a negative trend which further supports the idea that %IR has some relation to corrosion. * Based on the findings from Chapter 4, 5 and 6 suggests that corrosion activity rate is more prominent than the growth of TCDA at its median depth. It is therefore suggested that for this set of pipelines (those belonging to MEOC) repair of coating defects should be done before the coating defect has reached its median size. To the best of the Author's knowledge, the process of employing such approaches has never been applied before towards any ECDA data. The findings from this thesis also shed some light into the stochastic nature of the evolution of corrosion pits. This was not known before and is only made possible by the usage of the approaches highlighted above. The resulting models are also of novelty since no previous model has ever been developed based on the said methods. The contribution to knowledge from this research is therefore the greater understanding of relationship between variables stated above (TCDA, %IR and POPD). With this new knowledge, one has the potential to better prioritise location of excavation and better interpret DCVG indications. With the availability of ECDA data, it is also possible to predict the magnitude of corrosion activity by using the models developed in this thesis. Furthermore, the knowledge gained here has the potential to translate into cost saving measures for pipeline operators while ensuring safety is properly addressed.

This thesis assesses the usefulness of confidence indicators for short term forecasting of the economic activity in the Czech Republic. The predictive power of both the business confidence indicator and the customer confidence indicator is examined using two empirical approaches. First we predict the likelihood of economic downturn defined as a discrete event using logit models, later we estimate GDP growth out of sample forecasts in the framework of vector autoregression models. The results obtained from the downturn probability models confirm the ability of confidence indicators (especially the business confidence indicator) to estimate the current economic situation and to anticipate economic downturn one quarter ahead. Results from the out-of-sample GDP growth value forecasting are ambiguous. Nevertheless the customer confidence indicator significantly improved original forecasts based on a model with standard macroeconomic variables and therefore we conclude in favour of its predictive power. This result was indirectly confirmed by OECD as the Czech customer confidence indicator has been included as a new component in the OECD domestic composite leading indicator since April 2012.