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Statistics, as a critical component in transportation research, has been widely used to analyze driver safety, travel time, traffic flow and numerous other problems. Many of these popular topics can be interpreted as to establish the statistical models for the latent structure of data. Over the past several years, the interest in latent class models has continuously increased due to their great potential in solving practical problems. In this dissertation, I developed several latent class models to quantitatively analyze the hidden structure of transportation data and addressed related application issues. The first model is focused on the uncertainty of travel time, which is critical for assessing the reliability of transportation systems. Travel time is random in nature, and contains substantial variability, especially under congested traffic conditions. A Bayesian mixture model, with the ability to incorporate the influence from covariates such as traffic volume, has been proposed. This model advances the previous multi-state travel time reliability model in which the relationship between response and predictors was lacking. The Bayesian mixture travel time model, however, lack the power to accurately predict the future travel time. The analysis indicates that the independence assumption, which is difficult to justify in real data, could be a potential issue. Therefore, I proposed a Hidden Markov model to accommodate dependency structure, and the modeling results were significantly improved. The second and third parts of the dissertation focus on the driver safety identification. Given the demographic information and crash history, the number of crashes, as a type of count data, is commonly modeled by Poisson regression. However, the over-dispersion issue within the data implies that a single Poisson distribution is insufficient to depict the substantial variability. Poisson mixture model is proposed and applied to identify risky and safe drivers. The lower bound of the estimated misclassification rate is evaluated using the concept of overlap probability. Several theoretical results have been discussed regarding the overlap probability. I also introduced quantile regression based on discrete data to specifically model the high-risk drivers. In summary, the major objective of my research is to develop latent class methods and explore the hidden structure within the transportation data, and the approaches I employed can also be implemented for similar research questions in other areas. / Ph. D.

Ce travail se situe dans le cadre de la régression non paramétrique univariée. Supposant la fonction de régression à variation bornée et partant du résultat selon lequel une telle fonction se décompose en la somme d’une fonction croissante et d’une fonction décroissante, nous proposons de construire et d’étudier un nouvel estimateur combinant les techniques d’estimation des modèles additifs et celles d’estimation sous contraintes de monotonie. Plus précisément, notreméthode consiste à itérer la régression isotonique selon l’algorithme backfitting. On dispose ainsià chaque itération d’un estimateur de la fonction de régression résultant de la somme d’une partiecroissante et d’une partie décroissante.Le premier chapitre propose un tour d’horizon des références relatives aux outils cités à l’instant. Le chapitre suivant est dédié à l’étude théorique de la régression isotonique itérée. Dans un premier temps, on montre que, la taille d’échantillon étant fixée, augmenter le nombre d’itérations conduit à l’interpolation des données. On réussit à identifier les limites des termes individuels de la somme en montrant l’égalité de notre algorithme avec celui consistant à itérer la régressionisotonique selon un algorithme de type réduction itérée du biais. Nous établissons enfin la consistance de l’estimateur.Le troisième chapitre est consacré à l’étude pratique de l’estimateur. Comme augmenter le nombre d’itérations conduit au sur-ajustement, il n’est pas souhaitable d’itérer la méthode jusqu’à la convergence. Nous examinons des règles d’arrêt basées sur des adaptations de critères usuellement employés dans le cadre des méthodes linéaires de lissage (AIC, BIC,...) ainsi que des critères supposant une connaissance a priori sur le nombre de modes de la fonction de régression. Il en ressort un comportement intéressant de la méthode lorsque la fonction de régression possède des points de rupture. Nous appliquons ensuite l’algorithme à des données réelles de type puces CGH où la détection de ruptures est d’un intérêt crucial. Enfin, une application à l’estimation des fonctions unimodales et à la détection de mode(s) est proposée / This thesis is part of non parametric univariate regression. Assume that the regression function is of bounded variation then the Jordan’s decomposition ensures that it can be written as the sum of an increasing function and a decreasing function. We propose and analyse a novel estimator which combines the isotonic regression related to the estimation of monotonefunctions and the backfitting algorithm devoted to the estimation of additive models. The first chapter provides an overview of the references related to isotonic regression and additive models. The next chapter is devoted to the theoretical study of iterative isotonic regression. As a first step we show that increasing the number of iterations tends to reproduce the data. Moreover, we manage to identify the individual limits by making a connexion with the general property of isotonicity of projection onto convex cones and deriving another equivalent algorithm based on iterative bias reduction. Finally, we establish the consistency of the estimator.The third chapter is devoted to the practical study of the estimator. As increasing the number of iterations leads to overfitting, it is not desirable to iterate the procedure until convergence. We examine stopping criteria based on adaptations of criteria usually used in the context of linear smoothing methods (AIC, BIC, ...) as well as criteria assuming the knowledge of thenumber of modes of the regression function. As it is observed an interesting behavior of the method when the regression function has breakpoints, we apply the algorithm to CGH-array data where breakopoints detections are of crucial interest. Finally, an application to the estimation of unimodal functions is proposed

As Web services grow in maturity and use, so do the methods which are being used to test and maintain them. Regression Testing is a major component of most major testing systems but has only begun to be applied to Web services. The majority of the tools and techniques applying regression test to Web services are focused on test-case generation, thus ignoring the potential savings of regression test selection. Regression test selection optimizes the regression testing process by selecting a subset of all tests, while still maintaining some level of confidence about the system performing no worse than the unmodified system. A safe regression test selection technique implies that after selection, the level of confidence is as high as it would be if no tests were removed. Since safe regression test selection techniques generally involve code-based (white-box) testing, they cannot be directly applied to Web services due to their loosely-coupled, standards-based, and distributed nature. A framework which automates both the regression test selection and regression testing processes for Web services in a decentralized, end-to-end manner is proposed. As part of this approach, special consideration is given to the concurrency issues which may occur in an autonomous and decentralized system. The resulting synchronization method will be presented along with a set of algorithms which manage the regression testing and regression test selection processes throughout the system. A set of empirical results demonstrate the feasibility and benefit of the approach.

<p>In regression with near collinear explanatory variables, the least squares predictor has large variance. Ordinary least squares regression (OLSR) often leads to unrealistic regression coefficients. Several regularized regression methods have been proposed as alternatives. Well-known are principal components regression (PCR), ridge regression (RR) and continuum regression (CR). The latter two involve a continuous metaparameter, offering additional flexibility.</p><p>For a univariate response variable, CR incorporates OLSR, PLSR, and PCR as special cases, for special values of the metaparameter. CR is also closely related to RR. However, CR can in fact yield regressors that vary discontinuously with the metaparameter. Thus, the relation between CR and RR is not always one-to-one. We develop a new class of regression methods, LSRR, essentially the same as CR, but without discontinuities, and prove that any optimization principle will yield a regressor proportional to a RR, provided only that the principle implies maximizing some function of the regressor's sample correlation coefficient and its sample variance. For a multivariate response vector we demonstrate that a number of well-established regression methods are related, in that they are special cases of basically one general procedure. We try a more general method based on this procedure, with two meta-parameters. In a simulation study we compare this method to ridge regression, multivariate PLSR and repeated univariate PLSR. For most types of data studied, all methods do approximately equally well. There are cases where RR and LSRR yield larger errors than the other methods, and we conclude that one-factor methods are not adequate for situations where more than one latent variable are needed to describe the data. Among those based on latent variables, none of the methods tried is superior to the others in any obvious way.</p>

In regression with near collinear explanatory variables, the least squares predictor has large variance. Ordinary least squares regression (OLSR) often leads to unrealistic regression coefficients. Several regularized regression methods have been proposed as alternatives. Well-known are principal components regression (PCR), ridge regression (RR) and continuum regression (CR). The latter two involve a continuous metaparameter, offering additional flexibility. For a univariate response variable, CR incorporates OLSR, PLSR, and PCR as special cases, for special values of the metaparameter. CR is also closely related to RR. However, CR can in fact yield regressors that vary discontinuously with the metaparameter. Thus, the relation between CR and RR is not always one-to-one. We develop a new class of regression methods, LSRR, essentially the same as CR, but without discontinuities, and prove that any optimization principle will yield a regressor proportional to a RR, provided only that the principle implies maximizing some function of the regressor's sample correlation coefficient and its sample variance. For a multivariate response vector we demonstrate that a number of well-established regression methods are related, in that they are special cases of basically one general procedure. We try a more general method based on this procedure, with two meta-parameters. In a simulation study we compare this method to ridge regression, multivariate PLSR and repeated univariate PLSR. For most types of data studied, all methods do approximately equally well. There are cases where RR and LSRR yield larger errors than the other methods, and we conclude that one-factor methods are not adequate for situations where more than one latent variable are needed to describe the data. Among those based on latent variables, none of the methods tried is superior to the others in any obvious way.

Behavioral data are frequently plagued with highly intercorrelated variables. Collinearity is an indication of insufficient information in the model or in the data. It, therefore, contributes to the unreliability of the estimated coefficients. One result of collinearity is that regression weights derived in one sample may lead to poor prediction in another model. One technique which was developed to deal with highly intercorrelated independent variables is ridge regression. It was first proposed by Hoerl and Kennard in 1970 as a method which would allow the data analyst to both stabilize his estimates and improve upon his squared error loss. The problem of this study was the application of ridge regression in the analysis of data resulting from educational research.

Samples of stores were drawn from two chains, Pizza Hut and Zale Corporation. Two different samples were taken from Pizza Hut. Site specific material and sales data were furnished by the companies and demographic material relative to each site was gathered. Analysis of variance tests for linearity were run on the three regression equations developed from the data and each of the three regressions equations were found to have a statistically significant linear relationship. Statistically significant differences were found among similar variables used in the prediction of sales by using Fisher's Z' Transformations on the correlation coefficients. Eight of the eighteen variables used in the Pizza Hut study were found to be statistically different between the two regions used in the study. Additionally, analysis of variance tests were used to show that traffic pattern variables were not better predictors than demographic variables.

This thesis focuses on a well-known topic in sports betting, predicting the number of goals in soccer games.The data set used comes from the top English soccer league: Premier League, and consists of games played in the seasons 2015/16 to 2017/18.This thesis approaches the prediction with the auxiliary support of the odds from the betting exchange Betfair. The purpose is to find a model that can create an accurate goal distribution. %The other purpose is to investigate whether Negative binomial distribution regressionThe methods used are Bayesian Negative Binomial regression and Bayesian Poisson regression. The results conclude that the Poisson regression is the better model because of the presence of underdispersion.We argue that the methods can be used to compare different sportsbooks accuracies, and may help creating better models.

Inom programvaruutveckling är testning en viktig aktivitet där regressionstest är centralt. Regressionstestning innebär att exekvera om testfall för att säkerställa att de förändringarna som har gjorts i programmet inte har infört nya fel i systemet. Detta görs också med syfte till att kontrollera att systemets befintliga funktioner inte har påverkats negativt av dessa förändringar. Att genomföra regressionstester manuellt är resurskrävande i form av tid och pengar. Därför rekommenderas det att utföra denna aktivitet på ett automatiserat sätt. Ett problem som finns idag med exekvering av automatiserad regressionstest är att testare blir specialiserade på specifika testmiljöer på grund av det används många olika testmiljöer. Därför skulle de inte kunna stödja förbättringen av andra testares arbetsflöde. Således fokuserar denna studie på att beskriva de aktuella arbetssätt inom området exekvering av automatiserade regressionstester samt hur dessa kan utvecklas. Det har varit nödvändigt att genomföra personliga intervjuer samt litteraturstudie för att kunna besvara studiens forskningsfrågor. I detta arbete har det kommits fram till skapandet av en allmän ram för testare att arbeta mer effektivt med genomförandet av automatiserade regressionstestning oavsett testmiljön. Ramverket innehåller 7 faser: (1) Val av testfall, (2) Utföring/Exekvering av tester, (3) Kontroll/Analysera av resultat, (4) Skrivandet av rapport för testresultat, (5) Arkivering av testresultat rapporter, (6) Värdering och tilldelning av uppkommande problem samt (7) Hantering av testcykeln. / Software testing is an important activity within the software development area, where regression testing is essential. Regression testing implies re-running test cases in order to ensure that changes made to the software do not introduce new errors and to guarantee that the system’s functionalities have not been affected by those changes. To execute regression testing in manual mode involves valuable resources, specifically time and money. Therefore it is recommended to carry out this activity in an automated manner. A problem that faces the execution of automated regression testing is that testers are becoming specialized in specific test environments due to the existing diversity of tools used. Therefore testers would not be able improve test processes related to different environments. Thus, this paper focuses on identifying the current working manner within the domain of execution of automated regression testing and to improve it. Then, it has been necessary to conduct personal interviews (7) and a literature study in order to answer the study’s questions. This work provides a general framework for testers to work more effectively with execution of automated regression testing regardless of the test environment. The framework includes 7 stages: (1) Select test cases, (2) Execute/Run tests, (3) Monitoring/Analyzing results, (4) Write a report of the test results, (5) Archive the reports of the test results, (6) Estimate and assign the raised problems, and (7) Manage the test cycle.