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.

Made available in DSpace on 2017-05-12T14:46:53Z (GMT). No. of bitstreams: 1 Wagner.pdf: 5111902 bytes, checksum: b4edf3498cca6f9c7e2a9dbde6e62e18 (MD5) Previous issue date: 2013-12-07 / The purpose of hydrologic frequency analysis is to relate magnitude of events with their occurrence frequency based on probability distribution. The generalized probability distributions can be used on the study concerning extreme hydrological events: extreme events, logistics and Pareto. There are several methodologies to estimate probability distributions parameters, however, L-moments are often used due to computational easiness. Reliability of quantiles with high return period can be increased by LH-moments or high orders L-moments. L-moments have been widely studied; however, there is little information about LH-moments on literature, thus, there is a great research requirement on such area. Therefore, in this study, LH-moments were studied under two approaches commonly used in hydrology: (i) local frequency analysis (LFA) and (ii) regional frequency analysis (RFA). Moreover, a database with 227 rainfall stations was set (daily maximum annual), in Paraná State, from 1976 to 2006. LFA was subdivided into two steps: (i) Monte Carlo simulations and (ii) application of results to database. The main result of Monte Carlo simulations was that LH-moments make 0.99 and 0.995 quantiles less biased. Besides, simulations helped on creating an algorithm to perform LFA by generalized distributions. The algorithm was applied to database and enabled an adjustment of 227 studied series. In RFA, the 227stations have been divided into 11 groups and regional growth curves were obtained; while local quantiles were obtained from the regional growth curves. The difference between local quantiles obtained by RFA was quantified with those obtained via LFA. The differences may be approximately 33 mm for return periods of 100 years. / O objetivo da análise de frequência das variáveis hidrológicas é relacionar a magnitude dos eventos com sua frequência de ocorrência por meio do uso de uma distribuição de probabilidade. No estudo de eventos hidrológicos extremos, podem ser usadas as distribuições de probabilidade generalizadas: de eventos extremos, logística e Pareto. Existem diversas metodologias para a estimativa dos parâmetros das distribuições de probabilidade, no entanto, devido às facilidades computacionais, utilizam-se frequentemente os momentos-L. A confiabilidade dos quantis com alto período de retorno pode ser aumentada utilizando os momentos-LH ou momentos-L de altas ordens. Os momentos-L foram amplamente estudados, todavia, os momentos-LH apresentam literatura reduzida, logo, mais pesquisas são necessárias. Portanto, neste estudo, os momentos-LH foram estudados sob duas abordagens comumente utilizadas na hidrologia: (i) Análise de frequência local (AFL) e (ii) Análise de frequência regional (AFR). Além disso, foi montado um banco de dados com 227 estações pluviométricas (máximas diárias anuais), localizadas no Estado do Paraná, no período de 1976 a 2006. A AFL subdividiu-se em duas etapas: (i) Simulações de Monte Carlo e (ii) Aplicação dos resultados ao banco de dados. O principal resultado das simulações de Monte Carlo foi que os momentos-LH tornam os quantis 0,99 e 0,995 menos enviesados. Além disso, as simulações viabilizaram a criação de um algoritmo para realizar a AFL utilizando as distribuições generalizadas. O algoritmo foi aplicado ao banco de dados e possibilitou ajuste das 227 séries estudadas. Na AFR, as 227 estações foram dividas em 11 grupos e foram obtidas as curvas de crescimento regional. Os quantis locais foram obtidos a partir das curvas de crescimento regional. Foi quantificada a diferença entre os quantis locais obtidos via AFL com aqueles obtidos via AFR. As diferenças podem ser de aproximadamente 33 mm para períodos de retorno de 100 anos.

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.

The aim of this thesis was to investigate the use of effect sizes to report the results of statistical credit rating models in a more practical way. Rating systems in the form of statistical probability models like logistic regression models are used to forecast the behaviour of clients and guide business in rating clients as “high” or “low” risk borrowers. Therefore, model results were reported in terms of statistical significance as well as business language (practical significance), which business experts can understand and interpret. In this thesis, statistical results were expressed as effect sizes like Cohen‟s d that puts the results into standardised and measurable units, which can be reported practically. These effect sizes indicated strength of correlations between variables, contribution of variables to the odds of defaulting, the overall goodness-of-fit of the models and the models‟ discriminating ability between high and low risk customers. / Statistics / M. Sc. (Statistics)

在處理列聯表(Contingency table)資料時，一般我們常用卡方適合度檢定(chi-squared goodess-of-fit test)來判定模式配適的好壞。如果這個檢定是顯著的，則意謂著配適的模式並不恰當，我們則希望進一步探討可能的原因何在。這其中的一個可能原因是資料中存在所謂的離群細格(outlying cell)，這些細格的觀測次數和其他細格的觀測次數呈現某種不一致的現象。 　　在以往的文獻中，離群細格的偵測，通常藉由不同定義的殘差(residual)作為工具，進而衍生出各種不同的偵測方法。只是，這些探討基本上僅局限於二維列聯表的情形，對於高維度的列聯表，並沒有作更進一步的詮釋。Brown (1974)提出一個逐步偵測的方法，可依序找出所有可能的離群細格，直到近似獨立(quasi-independence)的模式假設不再顯著為止。但是我們認為他所引介的這個方法所牽涉的計算程序似乎過於繁複，因此藉由簡化修改計算過程，我們提供了另一種離群細格偵測的方法。依據模擬實驗的結果發現，本文所介紹的方法與Brown的方法作比較只有過之而無不及。此外我們也探討了應用此種方法到三維列聯表的可行性和可能遭遇到的困難。 / Chi-squared goodness-of-fit tests are usually employed to test whether a model fits a contingency table well. When the test is significant, we would then like to identify the sources that cause significance. The existence of outlying cells that contribute heavily to the test statistic may be one of the reasons. 　　Brown (1974) offered a stepwise criteria for detecting outlying cells in two-way con-tingency tables. In attempt to simplify the lengthy calculations that are required in Brown's method, we suggest an alternative procedure in this study. Based on simulation results, we find that the procedure performs reasonably well, it even outperforms Brown's method on several occasions. In addition, some extensions and issues regarding three-way contingency tables are also addressed.

線性結構關係模式是一種考慮以多個直線方程式來分析處理變數間因果關 係的統計方法，其結合了因徑分析及因素分析之優點並將之融合於整體模 式中。線性結構關係模式經過參數估計後，需評估整個模式之好壞，因此 許多學者嘗試提出一些評估模式好壞的適合度指標，如一般常用的卡方檢 定、殘差均方根、適合度指標、調整後適合度指標以及基準指標等。這些 指標中有的指標會受到樣本數大小或樣本分布的影響，有些指標受模式隱 藏變數多寡或因素指標多寡的影響，有些指標需有嚴格的條件（如樣本需 服從常態分布）及前提方可適用，且有些指標的分布是未知的，因此欲對 這些指標進行區間估計、假設檢定、或顯著性差異比較是不可能的。基於 上述各種適合度指標的缺點，本論文利用拔靴法進行重抽樣求得拔靴分布 來解決上述各種問題。然而傳統的拔靴法在線性結構關係模式上是不適用 的，因此，再提出一改良拔靴法程序，求得拔靴分布來做為評估模式好壞 的依據，並利用改良拔靴法來做巢狀模式之顯著性差異比較及利用抽樣誤 差和非抽樣誤差觀念來評估模式適合度。

賽局理論(Game Theory)大多假設理性決策，單一回合賽局通常可由理論證明均衡(Equilibrium)或是最佳決策，然而如果賽局重複進行，不見得只存在單一均衡，光從理論推導可能無法找到所有均衡。以囚犯困境(Prisoner Dilemma)為例，理論均衡為不合作，若重複的賽局中存有互利關係，不合作可能不是最佳選擇。近年來，經濟學家藉由和統計實驗設計類似的賽局實驗(Game Experiment)，探討賽局在理論與實際間的差異，並以學習模型(Learning Model)描述參賽者的決策及行為，但學習模型的優劣大多依賴誤差大小判定，但誤差分析結果可能與資料有關(Data Dependent)。有鑑於學習模型在模型選取上的不足，本文引進統計分析的模型選取及殘差檢定，以實證資料、配合電腦模擬評估學習模型。 本文使用的實證資料，屬於囚犯困境的重複賽局(Repeated Game)，包括四種不同的實驗設定，參加賽局實驗者（或是「玩家」）為政治大學大學部學生；比較學習模型有四種：增強學習模型(Reinforcement Learning model)、延伸的增強學習模型(Extend Reinforcement Learning Model)、信念學習模型(Belief Learning Model)、加權經驗吸引模型(Experience-Weighted Attraction Model)。實證及模擬分析發現，增強學習模型較適合用於描述囚犯困境資料，無論是較小的誤差或是適合度分析，增強學習模型都有較佳的結果；另外，也發現玩家在不同實驗設定中的反應並不一致，將玩家分類後會有較佳的結果。 / In game theory, the optimal strategy (or equilibrium) of one-shot games usually can be solved theoretically. But, the optimal strategies of repeated games are likely not unique and are more difficult to find. For example, the defection is the optimal decision for the one-shot Prisoner Dilemma (PD) game. But for the repeated PD game, if the players can benefit from cooperation between rounds then the defection won’t be the only optimal rule. In recent years, economists design game experiments to explore the behavior in repeated games and use the learning models to evaluate the player’s choices. Most of the evaluation criteria are based on the estimation and prediction errors, but the results are likely to be data dependent. In this study, we adapt the model selection process in regression analysis and apply the idea to evaluate learning models. We use empirical data, together with Monte Carlo simulation, to demonstrate the evaluation process. The empirical data used are repeated PD game, including four different experimental settings, and the players of the game are from National Chengchi University in Taiwan. Also, we consider four learning models: Reinforcement learning (RL) model, Extend Reinforcement learning (ERL) model, Belief Learning (BL) model, and Experience-weighted attraction (EWA) model. We found that the RL model is more appropriate to describe the PD data. In addition, the behaviors of players in a group can be quite different and separating the players into different sets can reduce the estimation errors.

Biological invasions are major threats to any nation’s economy and biodiversity. To detect new biological incursions of some species biosecurity agencies deploy pheromone sentinel traps for targeted species at high risk sites such as airports, seaports and transitional facilities. A good example is the gypsy moth surveillance program in New Zealand. Following the detection of an incursion by an unwanted organism, ground-based searches to locate the source can be very expensive, but are essential to identify the introduction pathway and to increase the chances of success eradicating the unwanted organism. In such circumstances, the possibility of better targeting the search for the source of the incursion using a modelling approach is worthy of investigation A stochastic mechanistic model to hindcast moth flight from a recapture location to the release location was developed based on insect behaviour in response to wind and pheromones. The model was composed of two main processes, 1) downwind dispersal, assumed to result from an appetitive behaviour, indicated by an analysis of a previous mark-release-recapture experiment on painted apple moth (Teia anartoides, Walker) and, 2) anemotaxic dispersal inspired by pheromone anemotaxis theory but up-scaled from a fine-scaled behaviour model to a 2 m scale. A genetic algorithm was used to fit some model parameters. A specialised fitness function was developed to allow the genetic algorithm to identify parameters that resulted in models that reflected both the spread and density patterns in the trapping data. The resulting function allowed the stochastic model results to be compared with the inherently stochastic trapping data. The resulting individual based model simulates the spatio-temporal dispersal pattern of painted apple moth recorded during a previous mark-release-recapture experiment. While the proposed model is shown to have limitations with respect to accuracy and precision it is also demonstrated to greatly improve biosecurity incursion response capability, by more efficient targeting of search effort for the proximal source of an incursion.

Το αντικείμενο της παρούσας διατριβής είναι η διερεύνηση μεθόδων στατιστικής συμπερασματολογίας για την προσαρμογή και έλεγχο της κατανομής γάμα και της αντίστροφης κανονικής (inverse Gaussian) κατανομής σε δεδομένα με θετική λοξότητα. Τα πρότυπα αυτά χρησιμοποιούνται ευρέως στην ανάλυση αξιοπιστίας και ελέγχου μακροβιότητας καθώς και σε άλλες εφαρμογές. Αρχικά γίνεται μια περιγραφή εναλλακτικών μεθόδων στατιστικής συμπερασματολογίας για τις διπαραμετρικές και τις τριπαραμετρικές οικογένειες κατανομών γάμα και αντίστροφης κανονικής. Στη συνέχεια διερευνάται η χρήση μεθόδων στατιστικής συμπερασματολογίας για την εκτίμηση των παραμέτρων της διπαραμετρικής γάμα κατανομής με χρήση της εμπειρικής ροπογεννήτριας συνάρτησης. Μέθοδοι εκτιμητικής, όπως είναι η μέθοδος των μικτών ροπών και των γενικευμένων ελαχίστων τετραγώνων, εφαρμόζονται και συγκρίνονται με την μέθοδο της μέγιστης πιθανοφάνειας μέσω πειραμάτων προσομοίωσης Monte Carlo. Επίσης, διερευνώνται έλεγχοι καλής προσαρμογής για τη διπαραμετρική γάμα κατανομή. Οι έλεγχοι αυτοί περιλαμβάνουν τους κλασικούς ελέγχους και έναν έλεγχο που χρησιμοποιεί την εμπειρική ροπογεννήτρια συνάρτηση. Με χρήση πειραμάτων προσομοίωσης Monte Carlo, γίνεται σύγκριση των ελέγχων ως προς το πραγματικό επίπεδο σημαντικότητας και την ισχύ έναντι άλλων λοξών προς τα δεξιά κατανομών. Στη συνέχεια εφαρμόζονται έλεγχοι καλής προσαρμογής γάμα κατανομών σε πραγματικά δεδομένα, τα οποία έχουν αναλυθεί νωρίτερα από άλλους ερευνητές. Για τον έλεγχο της τριπαραμετρικής γάμα κατανομής εφαρμόζεται μόνο ο έλεγχος με χρήση της εμπειρικής ροπογεννήτριας συνάρτησης, αφού δεν είναι γνωστοί κλασικοί έλεγχοι που χρησιμοποιούν την εμπειρική συνάρτηση κατανομής. Τέλος, γίνεται εκτίμηση ποσοστιαίων σημείων της αντίστροφης κανονικής κατανομής. Αρχικά, εκτιμώνται ποσοστιαία σημεία για την τριπαραμετρική κατανομή και στη συνέχεια εφαρμόζονται δύο μέθοδοι υπολογισμού ποσοστιαίων σημείων για την περίπτωση της διπαραμετρικής κατανομής. Η εκτίμηση των ποσοστιαίων σημείων σε κάθε οικογένεια κατανομών χρησιμοποιεί δύο μεθόδους ενδιάμεσης εκτίμησης των παραμέτρων της κατανομής. Οι μέθοδοι συγκρίνονται ως προς το μέσο τετραγωνικό σφάλμα και τη σχετική μεροληψία με τη βοήθεια πειραμάτων προσομοίωσης. / The subject of the present dissertation is the investigation of procedures of statistical inference for fitting and testing the gamma distribution and inverse Gaussian distribution, with data having positive skewness. These distributions are used widely in reliability analysis and lifetime models as well as in other applications. In the beginning, we describe alternative methods of statistical inference for the two and three-parameter families of gamma and inverse Gaussian distributions. Then, we examine methods of statistical inference in order to estimate the parameters of the two-parameter gamma distribution using the empirical moment generating function. Estimation procedures, like the method of mixed moments and the method of generalized least squares, are applied and compared with the method of maximum likelihood through Monte Carlo simulations. Also, we investigate goodness of fit tests for the two-parameter gamma distribution. These tests include the classical tests and a test based on the empirical moment generating function. Using Monte Carlo simulations, we compare the actual level of the tests and the power of the tests against skewed to the right distributions. We apply goodness of fit tests of gamma distributions to real life data, which have been examined earlier by other researchers. For the three-parameter gamma distribution we apply only one test using the empirical moment generating function since there are no classical tests using the empirical distribution function. Finally, we estimate quantiles of the inverse Gaussian distribution. We start estimating quantiles for the three-parameter distribution and then we apply two procedures which estimate quantiles for the two-parameter distribution. The estimates of the quantiles for each family of distributions use two procedures for estimating intermediary the parameters of the distribution. The procedures are compared with respect to the normalized mean square error and the relative bias using simulations.

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