Die Kapitel 1 bis 6 im ersten Teil dieses Skriptes beruhen auf einer Vorlesung Ökonometrie I, die zuletzt im WS 2001/02 gehalten wurde, die Kapitel 7 bis 16 beruhen auf einer Vorlesung Ökonometrie II, die zuletzt im SS 2006 gehalten wurde. Das achte Kapitel enthält eine komprimierte Zusammenfassung der Ergebnisse aus dem Teil Ökonometrie I.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2016-03-15T12:52:14Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese_Jarley_Nobrega_CORRIGIDA.pdf: 12392055 bytes, checksum: 30d9ff36e7236d22ddc3a16dd942341f (MD5) / Made available in DSpace on 2016-03-15T12:52:14Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese_Jarley_Nobrega_CORRIGIDA.pdf: 12392055 bytes, checksum: 30d9ff36e7236d22ddc3a16dd942341f (MD5) Previous issue date: 2015-08-24 / Em aplicações de aprendizagem de máquina, é comum encontrar situações onde o conjunto de entrada não está totalmente disponível no início da fase de treinamento. Uma solução conhecida para essa classe de problema é a realização do processo de aprendizagem através do fornecimento sequencial das instâncias de treinamento. Entre as abordagens mais recentes para esses métodos, encontram-se as baseadas em redes neurais do tipo Single Layer Feedforward Network (SLFN), com destaque para as extensões da Extreme Learning Machine (ELM) para aprendizagem sequencial. A versão sequencial da ELM, chamada de Online Sequential Extreme Learning Machine (OS-ELM), utiliza uma solução recursiva de mínimos quadrados para atualizar os pesos de saída da rede através de uma matriz de covariância. Entretanto, a implementação da OS-ELM e suas extensões sofrem com o problema de multicolinearidade entre os elementos da matriz de covariância. Essa tese introduz um novo método para aprendizagem sequencial com capacidade para tratar os efeitos da multicolinearidade. Chamado de Kalman Learning Machine (KLM), o método proposto utiliza o filtro de Kalman para a atualização sequencial dos pesos de saída de uma SLFN baseada na OS-ELM. Esse trabalho também propõe uma abordagem para a estimativa dos parâmetros do filtro, com o objetivo de diminuir a complexidade computacional do treinamento. Além disso, uma extensão do método chamada de Extended Kalman Learning Machine (EKLM) é apresentada, voltada para problemas onde a natureza do sistema em estudo seja não linear. O método proposto nessa tese foi comparado com alguns dos mais recentes e efetivos métodos para o tratamento de multicolinearidade em problemas de aprendizagem sequencial. Os experimentos executados mostraram que o método proposto apresenta um desempenho melhor que a maioria dos métodos do estado da arte, quando medidos o de erro de previsão e o tempo de treinamento. Um estudo de caso foi realizado, aplicando o método proposto a um problema de previsão de séries temporais para o mercado financeiro. Os resultados confirmaram que o KLM consegue simultaneamente reduzir o erro de previsão e o tempo de treinamento, quando comparado com os demais métodos investigados nessa tese. / In machine learning applications, there are situations where the input dataset is not fully available at the beginning of the training phase. A well known solution for this class of problem is to perform the learning process through the sequential feed of training instances. Among most recent approaches for sequential learning, we can highlight the methods based on Single Layer Feedforward Network (SLFN) and the extensions of the Extreme Learning Machine (ELM) approach for sequential learning. The sequential version of the ELM algorithm, named Online Sequential Extreme Learning Machine (OS-ELM), uses a recursive least squares solution for updating the output weights through a covariance matrix. However, the implementation of OS-ELM and its extensions suffer from the problem of multicollinearity for the hidden layer output matrix. This thesis introduces a new method for sequential learning in which the effects of multicollinearity is handled. The proposed Kalman Learning Machine (KLM) updates sequentially the output weights of an OS-ELM based network by using the Kalman filter iterative procedure. In this work, in order to reduce the computational complexity of the training process, a new approach for estimating the filter parameters is presented. Moreover, an extension of the method, named Extended Kalman Learning Machine (EKLM), is presented for problems where the dynamics of the model are non linear. The proposed method was evaluated by comparing the related state-of-the-art methods for sequential learning based on the original OS-ELM. The results of the experiments show that the proposed method can achieve the lowest forecast error when compared with most of their counterparts. Moreover, the KLM algorithm achieved the lowest average training time when all experiments were considered, as an evidence that the proposed method can reduce the computational complexity for the sequential learning process. A case study was performed by applying the proposed method for a problem of financial time series forecasting. The results reported confirm that the KLM algorithm can decrease the forecast error and the average training time simultaneously, when compared with other sequential learning algorithms.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This study aimed to verify the existence of linear relationships among phenological, morphological and productive characters of maize cultivars (Zea mays L.) of early and veryearly cycle and transgenic class and also to identify which characters have high correlation and direct effects on grain productivity. Six experiments were performed with early and veryearly and transgenic maize cultivars in the growing seasons 2009-2010 and 2010-2011, in the experimental area of the Department of Plant Science, of Federal University of Santa Maria. In the 2009-2010 harvest were evaluated 36 early cultivars, 22 veryearly and 18 transgenic and 2010-2011 harvest, 23 early, 9 veryearly and 27 transgenic. The experimental design was a randomized block design with three replications. The experimental unit consisted of two rows of five meters in length, spaced at 0,80 m. The seeding rate was adjusted to 62,500 plants ha-1. In each experimental unit it were tagged, randomized, three plants, and it were evaluated 15 characters of each one. The average of these three plants was the value of repetition. It were evaluated phenological (total number of leaves per plant (NFO), phyllochron estimated with the number of expanded leaves(FNFE), phyllochron estimated with the total number of leaves (FNTF) in ° C day leaf-1, the number of days of seeding until male flowering (FM) and number of days of seeding until female flowering (FF)), morphological (plant height (PH) and ear insertion height (AE), in cm) and productive (ear weight (PE), in g, number of kernel rows per ear (NFI), ear length (CE), in cm, ear diameter (DE), in mm, cob weight (PS), in g, cob diameter (DS), in mm, hundred kernel weight (MCG), in g, and grain productivity (PRO) in g ear-1) characters. Analysis of variance (ANOVA) was performed and the means of the cultivars were compared by Scott-Knott test at 5% probability. The linear correlation coefficients of Pearson among 15 evaluated characters were estimated for each experiment. For the path analysis, the PRO was considered the main character and the other characters were considered explanatory ones. It was accomplished multicollinearity diagnosis in the correlation matrix among the explanatory characters and the characters causing high degree of multicollinearity were eliminated. The direct and indirect effects on the PRO were estimated using path analysis and the verification of characters that influence PRO and their contribution in predicting the PRO were estimated by stepwise regression analysis. There are linear relationships among the phenological, morphological and productive characters maize plants. The characters PE and DE showed linear correlation coefficients of Pearson very strong (r≥0,97) and moderate to strong (0,55≤r≤0,78), respectively, with the PRO. In general, the character DE has high correlation and positive direct effects (0,6686 ≤ direct effect ≤ 1,1818) on the PRO. Allied to DE, the CE has a high positive contribution in predicting the PRO. Therefore, they can be used for indirect selection in maize breeding programs. / Este estudo teve como objetivos verificar a existência de relações lineares entre caracteres fenológicos, morfológicos e produtivos de cultivares de milho (Zea mays L.) de ciclos precoce e superprecoce e classe transgênica, e identificar quais caracteres possuem elevada correlação e efeitos diretos sobre a produtividade de grãos. Para isso, foram conduzidos seis experimentos com cultivares precoces, superprecoces e transgênicas de milho, nas safras agrícolas 2009-2010 e 2010-2011, na área experimental do Departamento de Fitotecnia da Universidade Federal de Santa Maria. Na safra 2009-2010 foram avaliadas 36 cultivares precoces, 22 superprecoces e 18 transgênicas e na safra 2010-2011, 23 precoces, 9 superprecoces e 27 transgênicas. Nos seis experimentos, o delineamento experimental foi de blocos casualizados, com três repetições. As unidades experimentais foram constituídas de duas filas de cinco metros de comprimento, espaçadas em 0,80m. A densidade de semeadura foi ajustada para 62.500 plantas ha-1. Em cada unidade experimental foram marcadas, aleatoriamente, três plantas, onde foram avaliados 15 caracteres. A média dessas três plantas constituiu o valor da repetição. Foram avaliados os caracteres fenológicos (número total de folhas por planta (NFO), filocrono estimado com número de expandidas (FNFE), filocrono estimado com o número total de folhas (FNTF), em °C dia folha-1, número de dias da semeadura até o florescimento masculino (FM) e número de dias da semeadura até o florescimento feminino (FF)), morfológicos (altura de planta (AP) e altura de inserção de espiga (AE), em cm) e produtivos (peso de espiga (PE), em g, número de fileiras de grãos por espiga (NFI), comprimento de espiga (CE), em cm, diâmetro de espiga (DE), em mm, peso de sabugo (PS), em g, diâmetro de sabugo (DS), em mm, massa de cem grãos (MCG), em g, e produtividade de grãos (PRO), em g espiga-1). Foi realizada análise de variância individual e as médias das cultivares foram comparadas por meio do teste de Scott-Knott, a 5% de probabilidade. Posteriormente, foram estimados, para cada experimento, os coeficientes de correlação linear de Pearson entre os 15 caracteres avaliados. Para a análise de trilha, a PRO foi considerada o caractere principal e os demais explicativos. Foi realizado o diagnóstico de multicolinearidade na matriz de correlação entre os caracteres explicativos e eliminados os caracteres causadores de alto grau de multicolinearidade. Os efeitos diretos e indiretos sobre a PRO foram estimados por meio de análise de trilha e a verificação dos caracteres que influenciam a PRO e a contribuição deles na predição da PRO foram estimados por meio de análise de regressão stepwise. Existem relações lineares entre os caracteres fenológicos, morfológicos e produtivos de plantas milho. Os caracteres PE e DE possuem coeficientes de correlação linear de Pearson fortíssimos (r≥0,97) e moderados a fortes (0,55≤r≤0,78), respectivamente, com a PRO. De maneira geral, o caractere DE possui elevada correlação e efeitos diretos (0,6686 ≤ efeito direto ≤ 1,1818) positivos sobre a PRO. Aliado ao DE, o CE possui elevada contribuição positiva na predição da PRO. Portanto, podem ser utilizados para seleção indireta em programas de melhoramento genético de milho.

The United States is the world's largest oil consumer demanding about twenty five percent of the total world oil production. Whenever there are difficulties to supply the increasing quantities of oil demanded by the market, the price of oil escalates leading to what is known as oil price spikes or oil price shocks. The last oil price shock which was the longest sustained oil price run up in history, began its course in year 2004, and ended in 2008. This last oil price shock initiated recognizable changes in transportation dynamics: transit operators realized that commuters switched to transit as a way to save gasoline costs, consumers began to search the market for more efficient vehicles leading car manufactures to close 'gas guzzlers' plants, and the government enacted a new law entitled the Energy Independence Act of 2007, which called for the progressive improvement of the fuel efficiency indicator of the light vehicle fleet up to 35 miles per gallon in year 2020. The past trend of gasoline consumption will probably change; so in the context of the problem a gasoline consumption model was developed in this thesis to ascertain how some of the changes will impact future gasoline demand. Gasoline demand was expressed in oil equivalent million barrels per day, in a two steps Ordinary Least Square (OLS) explanatory variable model. In the first step, vehicle miles traveled expressed in trillion vehicle miles was regressed on the independent variables: vehicles expressed in million vehicles, and price of oil expressed in dollars per barrel. In the second step, the fuel consumption in million barrels per day was regressed on vehicle miles traveled, and on the fuel efficiency indicator expressed in miles per gallon. The explanatory model was run in EVIEWS that allows checking for normality, heteroskedasticty, and serial correlation. Serial correlation was addressed by inclusion of autoregressive or moving average error correction terms. Multicollinearity was solved by first differencing. The 36 year sample series set (1970-2006) was divided into a 30 years sub-period for calibration and a 6 year "hold-out" sub-period for validation. The Root Mean Square Error or RMSE criterion was adopted to select the "best model" among other possible choices, although other criteria were also recorded. Three scenarios for the size of the light vehicle fleet in a forecasting period up to 2020 were created. These scenarios were equivalent to growth rates of 2.1, 1.28, and about 1 per cent per year. The last or more optimistic vehicle growth scenario, from the gasoline consumption perspective, appeared consistent with the theory of vehicle saturation. One scenario for the average miles per gallon indicator was created for each one of the size of fleet indicators by distributing the fleet every year assuming a 7 percent replacement rate. Three scenarios for the price of oil were also created: the first one used the average price of oil in the sample since 1970, the second was obtained by extending the price trend by exponential smoothing, and the third one used a longtime forecast supplied by the Energy Information Administration. The three scenarios created for the price of oil covered a range between a low of about 42 dollars per barrel to highs in the low 100's. The 1970-2006 gasoline consumption trend was extended to year 2020 by ARIMA Box-Jenkins time series analysis, leading to a gasoline consumption value of about 10 millions barrels per day in year 2020. This trend line was taken as the reference or baseline of gasoline consumption. The savings that resulted by application of the explanatory variable OLS model were measured against such a baseline of gasoline consumption. Even on the most pessimistic scenario the savings obtained by the progressive improvement of the fuel efficiency indicator seem enough to offset the increase in consumption that otherwise would have occurred by extension of the trend, leaving consumption at the 2006 levels or about 9 million barrels per day. The most optimistic scenario led to savings up to about 2 million barrels per day below the 2006 level or about 3 millions barrels per day below the baseline in 2020. The "expected" or average consumption in 2020 is about 8 million barrels per day, 2 million barrels below the baseline or 1 million below the 2006 consumption level. More savings are possible if technologies such as plug-in hybrids that have been already implemented in other countries take over soon, are efficiently promoted, or are given incentives or subsidies such as tax credits. The savings in gasoline consumption may in the future contribute to stabilize the price of oil as worldwide demand is tamed by oil saving policy changes implemented in the United States.

This thesis is a case study in collaboration with SJ AB, a government owned railway companyin Sweden. The employees aboard the trains are an essential part of operating thetrains efficiently. Therefore, it is vital to forecast absences well in order to avoid havingto cancel train trips or having employees work over time. The current process SJ usesdivides the total amount of absences into 11 categories representing reasons for not beingpresent. This is done three months in advance, but the model is not based on mathematics.This study is going to examine how well the forecasts compare to reality in addition toinvestigating which variables are possible to estimate using regression analysis. Furthermore,the extent to which the staff on board the trains are affected will be investigatedin terms of having to work less overtime. The financial impact of an enhanced model willbe researched. “Free” days, Vacation and Sickness all have significant regressors and canpotentially be forecast using regression analysis. Future work includes finding more potentialregressor variables that could be significant for more response variables in addition tousing the results of this thesis in an actual estimation model for the total absence. / Denna avhandling ärr en fallstudie i samarbete med SJ AB, ett statligt ägt järnvägsföretagi Sverige. Anställda ombord på tågen utgör en väsentlig del av att driva tågverksamheteneffektivt. Det är därför viktigt att kunna prognostisera frånvaro väl för att undvika attställa in rutter eller tvinga de anställda ombord tåget att arbeta övertid. Den nuvarandeprocessen som SJ använder delar upp den totala mängden frånvaro i 11 kategorier somrepresenterar orsaker till att inte vara närvarande. Detta görs tre månader i förväg, menmodellen är inte baserad på matematik i dagsläget. Denna studie kommer att undersökahur väl prognoserna stämmer överens med verkligheten, samt undersöka vilka variabler somör möjliga att uppskatta med hjälp av regressionsanalys. Dessutom kommer omfattningenav hur personalen ombord på tågen påverkas att undersökas. Den ekonomiska påverkanav en förbättrad modell kommer att analyseras. Lediga dagar, semester och sjukfrånvarohar alla signifikanta beskrivande variabler och kan potentiellt prognostiseras med hjälp avregressionsanalys. Framtida arbete innefattar att hitta fler potentiella beskrivande variablersom kan vara signifikanta för fler beroende variabler, samt att använda resultatenfrån denna avhandling i en faktisk prognosmodell för total frånvaro.

A Modelagem de Equações Estruturais (SEM, do inglês Structural Equation Modeling) é uma metodologia multivariada que permite estudar relações de causa/efeito e correlação entre um conjunto de variáveis (podendo ser elas observadas ou latentes), simultaneamente. A técnica vem se difundindo cada vez mais nos últimos anos, em diferentes áreas do conhecimento. Uma de suas principais aplicações é na conrmação de modelos teóricos propostos pelo pesquisador (Análise Fatorial Conrmatória). Existem diversas medidas sugeridas pela literatura que servem para avaliar o quão bom está o ajuste de um modelo de SEM. Entretanto, é escassa a quantidade de trabalhos na literatura que listem relações entre os valores de diferentes medidas com possíveis problemas na amostra e na especicação do modelo, isto é, informações a respeito de que possíveis problemas desta natureza impactam quais medidas (e quais não), e de que maneira. Tal informação é importante porque permite entender os motivos pelos quais um modelo pode estar sendo considerado mal-ajustado. O objetivo deste trabalho é investigar como diferentes perturbações na amostragem, especicação e estimação de um modelo de SEM podem impactar as medidas de qualidade de ajuste; e, além disso, entender se o tamanho da amostra influencia esta resposta. Simultaneamente, também se avalia como tais perturbações afetam as estimativas, dado que há casos de perturbações em que os parâmetros continuam sendo bem ajustados, mesmo com algumas medidas indicando um mau ajuste; ao mesmo tempo, há ocasiões em que se indica um bom ajuste, enquanto que os parâmetros são estimados de forma distorcida. Tais investigações serão realizadas a partir de simulações de exemplos de amostras de diferentes tamanhos para cada tipo de perturbação. Então, diferentes especicações de modelos de SEM serão aplicados a estas amostras, e seus parâmetros serão estimados por dois métodos diferentes: Mínimos Quadrados Generalizados e Máxima Verossimilhança. Conhecendo tais resultados, um pesquisador que queira aplicar a técnica de SEM poderá se precaver e, dentre as medidas de qualidade de ajuste disponíveis, optar pelas que mais se adequem às características de seu estudo. / The Structural Equation Modeling (SEM) is a multivariate methodology that allows the study of cause-and-efect relationships and correlation of a set of variables (that may be observed or latent ones), simultaneously. The technique has become more diuse in the last years, in different fields of knowledge. One of its main applications is on the confirmation of theoretical models proposed by the researcher (Confirmatory Factorial Analysis). There are several measures suggested by literature to measure the goodness of t of a SEM model. However, there is a scarce number of texts that list relationships between the values of different of those measures with possible problems that may occur on the sample or the specication of the SEM model, like information concerning what problems of this nature impact which measures (and which not), and how does the impact occur. This information is important because it allows the understanding of the reasons why a model could be considered bad fitted. The objective of this work is to investigate how different disturbances of the sample, the model specification and the estimation of a SEM model are able to impact the measures of goodness of fit; additionally, to understand if the sample size has influence over this impact. It will also be investigated if those disturbances affect the estimates of the parameters, given the fact that there are disturbances for which occurrence some of the measures indicate badness of fit but the parameters are not affected; at the same time, that are occasions on which the measures indicate a good fit and there are disturbances on the estimates of the parameters. Those investigations will be made simulating examples of different size samples for which type of disturbance. Then, SEM models with different specifications will be fitted to each sample, and their parameters will be estimated by two dierent methods: Generalized Least Squares and Maximum Likelihood. Given those answers, a researcher that wants to apply the SEM methodology to his work will be able to be more careful and, among the available measures of goodness of fit, to chose those that are more adequate to the characteristics of his study.

A Modelagem de Equações Estruturais (SEM, do inglês Structural Equation Modeling) é uma metodologia multivariada que permite estudar relações de causa/efeito e correlação entre um conjunto de variáveis (podendo ser elas observadas ou latentes), simultaneamente. A técnica vem se difundindo cada vez mais nos últimos anos, em diferentes áreas do conhecimento. Uma de suas principais aplicações é na conrmação de modelos teóricos propostos pelo pesquisador (Análise Fatorial Conrmatória). Existem diversas medidas sugeridas pela literatura que servem para avaliar o quão bom está o ajuste de um modelo de SEM. Entretanto, é escassa a quantidade de trabalhos na literatura que listem relações entre os valores de diferentes medidas com possíveis problemas na amostra e na especicação do modelo, isto é, informações a respeito de que possíveis problemas desta natureza impactam quais medidas (e quais não), e de que maneira. Tal informação é importante porque permite entender os motivos pelos quais um modelo pode estar sendo considerado mal-ajustado. O objetivo deste trabalho é investigar como diferentes perturbações na amostragem, especicação e estimação de um modelo de SEM podem impactar as medidas de qualidade de ajuste; e, além disso, entender se o tamanho da amostra influencia esta resposta. Simultaneamente, também se avalia como tais perturbações afetam as estimativas, dado que há casos de perturbações em que os parâmetros continuam sendo bem ajustados, mesmo com algumas medidas indicando um mau ajuste; ao mesmo tempo, há ocasiões em que se indica um bom ajuste, enquanto que os parâmetros são estimados de forma distorcida. Tais investigações serão realizadas a partir de simulações de exemplos de amostras de diferentes tamanhos para cada tipo de perturbação. Então, diferentes especicações de modelos de SEM serão aplicados a estas amostras, e seus parâmetros serão estimados por dois métodos diferentes: Mínimos Quadrados Generalizados e Máxima Verossimilhança. Conhecendo tais resultados, um pesquisador que queira aplicar a técnica de SEM poderá se precaver e, dentre as medidas de qualidade de ajuste disponíveis, optar pelas que mais se adequem às características de seu estudo. / The Structural Equation Modeling (SEM) is a multivariate methodology that allows the study of cause-and-efect relationships and correlation of a set of variables (that may be observed or latent ones), simultaneously. The technique has become more diuse in the last years, in different fields of knowledge. One of its main applications is on the confirmation of theoretical models proposed by the researcher (Confirmatory Factorial Analysis). There are several measures suggested by literature to measure the goodness of t of a SEM model. However, there is a scarce number of texts that list relationships between the values of different of those measures with possible problems that may occur on the sample or the specication of the SEM model, like information concerning what problems of this nature impact which measures (and which not), and how does the impact occur. This information is important because it allows the understanding of the reasons why a model could be considered bad fitted. The objective of this work is to investigate how different disturbances of the sample, the model specification and the estimation of a SEM model are able to impact the measures of goodness of fit; additionally, to understand if the sample size has influence over this impact. It will also be investigated if those disturbances affect the estimates of the parameters, given the fact that there are disturbances for which occurrence some of the measures indicate badness of fit but the parameters are not affected; at the same time, that are occasions on which the measures indicate a good fit and there are disturbances on the estimates of the parameters. Those investigations will be made simulating examples of different size samples for which type of disturbance. Then, SEM models with different specifications will be fitted to each sample, and their parameters will be estimated by two dierent methods: Generalized Least Squares and Maximum Likelihood. Given those answers, a researcher that wants to apply the SEM methodology to his work will be able to be more careful and, among the available measures of goodness of fit, to chose those that are more adequate to the characteristics of his study.

Multiple regression models play an important role in analyzing and making predictions about data. Prediction accuracy becomes lower when two or more explanatory variables in the model are highly correlated. One solution is to use ridge regression. The purpose of this thesis is to study the performance of available ridge regression estimators for Poisson regression models in the presence of moderately to highly correlated variables. As performance criteria, we use mean square error (MSE), mean absolute percentage error (MAPE), and percentage of times the maximum likelihood (ML) estimator produces a higher MSE than the ridge regression estimator. A Monte Carlo simulation study was conducted to compare performance of the estimators under three experimental conditions: correlation, sample size, and intercept. It is evident from simulation results that all ridge estimators performed better than the ML estimator. We proposed new estimators based on the results, which performed very well compared to the original estimators. Finally, the estimators are illustrated using data on recreational habits.

線性迴歸模型中共線性的問題是導致模型不適當的重大原因之一。共線性 的存在不止會影響到參數的估計，使參數的變異變大，還會妨礙我們評估 自變數對模型重要性的能力，甚至會使我們忽略或去除掉重要的自變數。 而變異膨脹因子是診斷線性迴歸模型共線性問題時常用而有效的方法之一 ，但它只是考慮單一自變數的情況。本文則對於模型同時加入一組自變數 時影響原模型共線性的問題，先推導出廣義的判定係數，再利用它推導出 變異膨脹矩陣。再應用這個變異膨脹矩陣發展出六個準則，使得變異膨脹 矩陣有一個單一的指標來對模型的共線性做診斷。最後並以一個例子以實 際的數據，用六個準則對不同的模型做診斷，並嘗試找出各準則的指標。

In dieser Arbeit wird eine neue Methode für den skalenunabhängigen Vergleich von LD-Strukturen in unterschiedlichen genomischen Regionen vorgeschlagen. Verschiedene Aspekte durch Skalen verursachter Probleme – von der Präzision der Schätzung der Marke-reffekte bis zur Genauigkeit der Vorhersage für neue Individuen - wurden untersucht. Darüber hinaus, basierend auf den Leistungsvergleichen von unterschiedlichen statistischen Methoden, wurden Empfehlungen für die Verwendungen der untersuchten Methoden gege-ben. / In dieser Arbeit wird eine neue Methode für den skalenunabhängigen Vergleich von LD-Strukturen in unterschiedlichen genomischen Regionen vorgeschlagen. Verschiedene Aspekte durch Skalen verursachter Probleme – von der Präzision der Schätzung der Marke-reffekte bis zur Genauigkeit der Vorhersage für neue Individuen - wurden untersucht. Darüber hinaus, basierend auf den Leistungsvergleichen von unterschiedlichen statistischen Methoden, wurden Empfehlungen für die Verwendungen der untersuchten Methoden gegeben