This thesis deals with the development, implementation and application of statistical modeling techniques which can be employed in the analysis of credit ratings. Credit ratings are one of the most widely used measures of credit risk and are relevant for a wide array of financial market participants, from investors, as part of their investment decision process, to regulators and legislators as a means of measuring and limiting risk. The majority of credit ratings is produced by the "Big Three" credit rating agencies Standard & Poors', Moody's and Fitch. Especially in the light of the 2007-2009 financial crisis, these rating agencies have been strongly criticized for failing to assess risk accurately and for the lack of transparency in their rating methodology. However, they continue to maintain a powerful role as financial market participants and have a huge impact on the cost of funding. These points of criticism call for the development of modeling techniques that can 1) facilitate an understanding of the factors that drive the rating agencies' evaluations, 2) generate insights into the rating patterns that these agencies exhibit. This dissertation consists of three research articles. The first one focuses on variable selection and assessment of variable importance in accounting-based models of credit risk. The credit risk measure employed in the study is derived from credit ratings assigned by ratings agencies Standard & Poors' and Moody's. To deal with the lack of theoretical foundation specific to this type of models, state-of-the-art statistical methods are employed. Different models are compared based on a predictive criterion and model uncertainty is accounted for in a Bayesian setting. Parsimonious models are identified after applying the proposed techniques. The second paper proposes the class of multivariate ordinal regression models for the modeling of credit ratings. The model class is motivated by the fact that correlated ordinal data arises naturally in the context of credit ratings. From a methodological point of view, we extend existing model specifications in several directions by allowing, among others, for a flexible covariate dependent correlation structure between the continuous variables underlying the ordinal credit ratings. The estimation of the proposed models is performed using composite likelihood methods. Insights into the heterogeneity among the "Big Three" are gained when applying this model class to the multiple credit ratings dataset. A comprehensive simulation study on the performance of the estimators is provided. The third research paper deals with the implementation and application of the model class introduced in the second article. In order to make the class of multivariate ordinal regression models more accessible, the R package mvord and the complementary paper included in this dissertation have been developed. The mvord package is available on the "Comprehensive R Archive Network" (CRAN) for free download and enhances the available ready-to-use statistical software for the analysis of correlated ordinal data. In the creation of the package a strong emphasis has been put on developing a user-friendly and flexible design. The user-friendly design allows end users to estimate in an easy way sophisticated models from the implemented model class. The end users the package appeals to are practitioners and researchers who deal with correlated ordinal data in various areas of application, ranging from credit risk to medicine or psychology.

Os modelos de regressão logística ordinais são usados para descrever a relação entre uma variável resposta categórica ordinal e uma ou mais variáveis explanatórias. Uma vez ajustado o modelo de regressão, se faz necessário verificar a qualidade do ajuste do modelo. As estatísticas qui-quadrado de Pearson e da razão de verossimilhanças não são adequadas para acessar a qualidade do ajuste do modelo de regressão logística ordinal quando variáveis contínuas estão presentes no modelo. Para este caso, foram propostos os testes de Lipsitz, a versão ordinal do teste de Hosmer-Lemeshow e os testes qui-quadrado e razão de verossimilhanças de Pulkistenis-Robinson. Nesta dissertação é feita uma revisão das técnicas de diagnóstico disponíveis para os Modelos logito cumulativo, Modelos logito categorias adjacentes e Modelos logito razão contínua, bem como uma aplicação a fim de investigar a relação entre a perda auditiva, o equilíbrio e aspectos emocionais nos idosos. / Ordinal regression models are used to describe the relationship between an ordered categorical response variable and one or more explanatory variables which could be discrete or continuous. Once the regression model has been fitted, it is necessary to check the goodness-of-fit of the model. The Pearson and likelihood-ratio statistics are not adequate for assessing goodness-of-fit in ordinal logistic regression model with continuous explanatory variables. For this case, the Lipsitz test, the ordinal version of the Hosmer-Lemeshow test and Pulkstenis-Robinson chi-square and likelihood ratio tests were proposed. This dissertation aims to review the diagnostic techniques available for the cumulative logit models, categories adjacent logit models and continuous ratio logistic models. In addition, an application was developed in order to investigate the relationship between hearing loss, balance and emotional aspects in the elderly.

Submitted by Secretaria Pós de Produção (tpp@vm.uff.br) on 2017-07-27T18:53:19Z No. of bitstreams: 1 D2014 - Thiago Graça Ramos.pdf: 589803 bytes, checksum: d74ab5e26ec9908670c7d3320d45fe61 (MD5) / Made available in DSpace on 2017-07-27T18:53:19Z (GMT). No. of bitstreams: 1 D2014 - Thiago Graça Ramos.pdf: 589803 bytes, checksum: d74ab5e26ec9908670c7d3320d45fe61 (MD5) / Esse estudo visa construir um modelo para identificar a forma ideal de transporte de carga no Brasil, para pequenas e médias empresas que contratam este tipo de serviço. O trabalho utilizou as técnicas DEA, preferência declarada e logito ordinal para avaliar as pequenas e médias empresas que contratam transporte de carga no Brasil, verificando os aspectos importantes para a tomada de decisão na contratação deste serviço. Inicialmente, aplicou-se a ferramenta DEA para classificar as eficiências em alta, média e baixa, utilizandose o resultado de tal classificação como a variável dependente do modelo logito ordinal. As variáveis independentes deste modelo foram as utilidades oriundas da preferência declarada e do modelo de MaxDiff, que avaliou características não pertencentes ao modelo de preferência declarada. A análise dos dados indicou que a migração do modo rodoviário para o ferroviário seria melhor para as empresas, já que o primeiro acaba sendo utilizado pela falta de opção pelo segundo. Outro importante resultado do estudo foi a indicação de que as empresas com produtos de maior valor agregado são mais eficientes. Por fim, o modelo indicou que o modo de operação a ser buscado pelas empresas de transporte de carga deve incluir segurança e rapidez na entrega, propiciando facilidade de acesso ao consumidor. / This paper aims to identify efficient businesses in daily freight transport and to evaluate the main aspects to picking and hiring a cargo transportation service. To make this evaluation, some techniques will be used, such as Data Envelopment Analysis, ordinal logit and revealed preference. By using the DEA technique, the efficiency will be ranked between high, medium and low, and this ranking will be the dependent variable of the ordinal logit model, and the independent variables of this model are derived from the utilities from the revealed preference model and the maxdiff model that evaluated some features that were not declared on the preference model. Data analysis indicated that the migration from road to rail would be better for companies since the first ends up being used by a lack of options for the second. Another important result was the indication that firms with higher value-added products are more efficient. Finally, the model indicated that the mode of operation being sought by cargo shipping companies should include safety and speed in delivery, providing easy access to the consumer.

Made available in DSpace on 2016-06-02T20:30:50Z (GMT). No. of bitstreams: 1 3599.pdf: 897828 bytes, checksum: 2907ecfaa5c269b68d9428025801268b (MD5) Previous issue date: 2011-03-03 / Universidade Federal de Minas Gerais / The bilingual approach, adopted for educating deaf people in Brazil, regards the Brazilian Sign Language (Libras) as the first language and the written Portuguese Language as the instrumental language. The acquisition of the written language may be more difficult than the acquisition of the sign language due to the differences between their ordinal grammatical structures. The ordinal grammatical structure of the written Portuguese consists in a subject verb preposition complement order, whereas the structure of the Sign Language allows not only this order, but also different combinations of the elements. Such differences usually result, for the deaf people, in a writing repertoire of the Portuguese Language that has a different grammatical order than that one used by the verbal community in which they are inserted. This study investigated variables that control the transfer of ordinal functions through classes of equivalent stimuli. The experimental stimuli used were 32 printed words divided into four stimuli categories (A1A2A3A4; B1B2B3B4; C1C2C3C4 e D1D2D3D4), corresponding to subject, verb, preposition/article and complement, respectively. The categories were taught through matching-to-sample (MTS) tasks, while the sequences were taught through constructed-response matching-to-sample (CRMTS). All participants showed the formation of four stimulus classes, and learned one sequence (A1A2A3A4). After that, they showed the transference of ordinal functions to untaught sequences. In summary, results showed the transference of ordinal functions through equivalence classes. / O ensino para surdos no Brasil prioriza, atualmente, a abordagem bilíngue em que se ensina a Língua Brasileira de Sinais (Libras) como primeira língua e a Língua Portuguesa escrita como língua instrumental. A aquisição da Língua Portuguesa escrita por surdos pode ser dificultada em função das diferenças entre as estruturas ordinais - gramaticais da Língua Portuguesa escrita e da Libras. A estrutura ordinal - gramatical da primeira é composta por sujeito verbo preposição - complemento, enquanto que a da Libras permite o uso não apenas dessa estrutura, mas também de diferentes combinações dos mesmos elementos. Tais diferenças costumam resultar em um repertório de escrita da Língua Portuguesa com ordem gramatical diferente daquela utilizada pela comunidade verbal onde os surdos estão inseridos. Este estudo investigou a transferência das funções ordinais para novas sequências compostas por novos estímulos experimentais após o estabelecimento das classes de estímulos equivalentes, seguido do ensino de uma única sequência. Os participantes foram uma criança e três adolescentes surdos com idades entre oito e 16 anos. Os estímulos experimentais consistiram em 32 palavras impressas, divididas em oito conjuntos de estímulos, sendo que cada conjunto foi composto por quatro estímulos, (A1A2A3A4; B1B2B3B4; C1C2C3C4; D1D2D3D4; X1X2X3X4; Y1Y2Y3Y4; W1W2W3W4 e Z1Z2Z3Z4) correspondentes, respectivamente, a sujeito, verbo, preposição/artigo e complemento. O procedimento de escolha de acordo com o modelo (matching to sample - MTS) foi utilizado para estabelecimento das quatro classes de estímulos, e uma adaptação desse procedimento (constructed response matching to sample - CRMTS) foi utilizada para o ensino de uma sequência. Todos os participantes mostraram a formação das quatro classes de estímulos equivalentes e alcançaram o critério de aprendizagem no ensino da sequência A1A2A3A4. Observou-se a transferência de funções ordinais para novas sequências após o ensino da primeira sequência. Os resultados sugerem que o estabelecimento de classes de estímulos equivalentes pode facilitar a expansão do comportamento de sequenciar por crianças e adolescentes surdos.

This thesis concerns cleavability. A space X is said to be cleavable over a space Y along a set A subset of X if there exists a continuous function f from X to Y such that f(A) cap f(X setminus A) = emptyset. A space X is cleavable over a space Y if it is cleavable over Y along all subsets A of X. In this thesis we prove three results regarding cleavability. First we discover the conditions under which cleavability of an infinite compactum X over a first-countable scattered linearly ordered topological space (LOTS) Y implies embeddability of X into Y. In particular, we provide a class of counter-examples in which cleavability does not imply embeddability, and show that if X is an infinite compactum cleavable over ω₁, the first uncountable ordinal, then X is embeddable into ω₁. We secondly show that if X is an infinite compactum cleavable over any ordinal, then X must be homeomorphic to an ordinal. X must also therefore be a LOTS. This answers two fundamental questions in the area of cleavability. We also leave it as an open question whether cleavability of an infinite compactum X over an uncountable ordinal λ implies X is embeddable into λ. Lastly, we show that if X is an infinite compactum cleavable over a separable LOTS Y such that for some continuous function f from X to Y, the set of points on which f is not injective is scattered, then X is a LOTS. In addition to providing these three results, we introduce a new area of research developed from questions within cleavability. This area of research is called almost-injectivity. Given a compact T₂ space X and a LOTS Y, we say a continuous function f from X to Y is almost-injective if the set of points on which f is not injective has countable cardinality. In this thesis, we state some questions concerning almost-injectivity, and show that if lambda is an ordinal, X is a T₂ compactum, and f is an almost-injective function from X to lambda, then X must be a LOTS.

Ordinal coefficient alpha is a newly derived non-parametric reliability estimate. As with any point estimate, ordinal coefficient alpha is merely an estimate of a population parameter and tends to vary from sample to sample. Researchers report the confidence interval to provide readers with the amount of precision obtained. Several methods with differing computational approaches exist for confidence interval estimation for alpha, including the Fisher, Feldt, Bonner, and Hakstian and Whalen (HW) techniques. Overall, coverage rates for the various methods were unacceptably low with the Fisher method as the highest performer at 62%. Because of the poor performance across all four confidence interval methods, a need exists to develop a method which works well for ordinal coefficient alpha.

In this paper several equivalences of the axiom of choice are examined. In particular, the axiom of choice, Zorn's lemma, Tukey's lemma, the Hausdorff maximal principle, and the well-ordering theorem are shown to be equivalent. Cardinal and ordinal number theory is also studied. The Schroder-Bernstein theorem is proven and used in establishing order results for cardinal numbers. It is also demonstrated that the first uncountable ordinal space is unique up to order isomorphism. We conclude by encountering several applications of the axiom of choice. In particular, we show that every vector space must have a Hamel basis and that any two Hamel bases for the same space must have the same cardinality. We establish that the Tychonoff product theorem implies the axiom of choice and see the use of the axiom of choice in the proof of the Hahn- Banach theorem.

Nineteen selected self-perception characteristics of university students were related to sex and to ordinal position. The 60 selected males and 120 selected females were enrolled during the summer of 1976 at North Texas State University in Denton County, Texas. A self-rating, group-administered instrument was originated for collecting information. Ordinal positions were only child, first-born with later siblings, intermediate, and last-born. The intermediates had the most positive self-perceptions. Of the males, intermediates were highest and only children lowest. Of the females, only children reported more positive self-perceptions. Females had more positive self-perceptions than males. Effects of ordinal positions tended to depend on the child's sex. Further study was recommended utilizing a larger, more varied population.

Recursive binary partitioning is a popular tool for regression analysis. Two fundamental problems of exhaustive search procedures usually applied to fit such models have been known for a long time: Overfitting and a selection bias towards covariates with many possible splits or missing values. While pruning procedures are able to solve the overfitting problem, the variable selection bias still seriously effects the interpretability of tree-structured regression models. For some special cases unbiased procedures have been suggested, however lacking a common theoretical foundation. We propose a unified framework for recursive partitioning which embeds tree-structured regression models into a well defined theory of conditional inference procedures. Stopping criteria based on multiple test procedures are implemented and it is shown that the predictive performance of the resulting trees is as good as the performance of established exhaustive search procedures. It turns out that the partitions and therefore the models induced by both approaches are structurally different, indicating the need for an unbiased variable selection. The methodology presented here is applicable to all kinds of regression problems, including nominal, ordinal, numeric, censored as well as multivariate response variables and arbitrary measurement scales of the covariates. Data from studies on animal abundance, glaucoma classification, node positive breast cancer and mammography experience are re-analyzed. / Series: Research Report Series / Department of Statistics and Mathematics

Data from rating scale assessments have rank-invariant properties only, which means that the data represent an ordering, but lack of standardized magnitude, inter-categorical distances, and linearity. Even though the judgments often are coded by natural numbers they are not really metric. The aim of this thesis is to further develop the nonparametric rank-based Svensson methods for paired ordinal data that are based on the rank-invariant properties only. The thesis consists of five papers. In Paper I the asymptotic properties of the measure of systematic disagreement in paired ordinal data, the Relative Position (RP), and the difference in RP between groups were studied. Based on the findings of asymptotic normality, two tests for analyses of change within group and between groups were proposed. In Paper II the asymptotic properties of rank-based measures, e.g. the Svensson’s measures of systematic disagreement and of additional individual variability were discussed, and a numerical method for approximation was suggested. In Paper III the asymptotic properties of the measures for paired ordinal data, discussed in Paper II, were verified by simulations. Furthermore, the Spearman rank-order correlation coefficient (rs) and the Svensson’s augmented rank-order agreement coefficient (ra) were compared. By demonstrating how they differ and why they differ, it is emphasized that they measure different things. In Paper IV the proposed test in Paper I for comparing two groups of systematic changes in paired ordinal data was compared with other nonparametric tests for group changes, both regarding different approaches of categorising changes. The simulation reveals that the proposed test works better for small and unbalanced samples. Paper V demonstrates that rank invariant approaches can also be used in analysis of ordinal data from multi-item scales, which is an appealing and appropriate alternative to calculating sum scores.