In a regression context, the aim is to analyse a response variable of interest conditional to a set of covariates. In many applications the response variable is discrete. Examples include the event of surviving a heart attack, the number of hospitalisation days, the number of times that individuals benefit of a health service, and so on. This thesis advances the methodology and the application of regression models with discrete response. First, we present a difference-in-differences approach to model a binary response in a health policy evaluation framework. In particular, generalized linear mixed methods are employed to model multiple dependent outcomes in order to quantify the effect of an adopted pay-for-performance program while accounting for the heterogeneity of the data at the multiple nested levels. The results show how the policy had a positive effect on the hospitals' quality in terms of those outcomes that can be more influenced by a managerial activity. Next, we focus on regression models for count response variables. In a parametric framework, Poisson regression is the simplest model for count data though it is often found not adequate in real applications, particularly in the presence of excessive zeros and in the case of dispersion, i.e. when the conditional mean is different to the conditional variance. Negative Binomial regression is the standard model for over-dispersed data, but it fails in the presence of under-dispersion. Poisson-Inverse Gaussian regression can be used in the case of over-dispersed data, Generalised-Poisson regression can be employed in the case of under-dispersed data, and Conway-Maxwell Poisson regression can be employed in both cases of over- or under-dispersed data, though the interpretability of these models is ot straightforward and they are often found computationally demanding. While Jittering is the default non-parametric approach for count data, inference has to be made for each individual quantile, separate quantiles may cross and the underlying uniform random sampling can generate instability in the estimation. These features motivate the development of a novel parametric regression model for counts via a Discrete Weibull distribution. This distribution is able to adapt to different types of dispersion relative to Poisson, and it also has the advantage of having a closed form expression for the quantiles. As well as the standard regression model, generalized linear mixed models and generalized additive models are presented via this distribution. Simulated and real data applications with different type of dispersion show a good performance of Discrete Weibull-based regression models compared with existing regression approaches for count data.

A practical problem often encountered with observed count data is the presence of excess zeros. Zero-inflation in count data can easily be handled by zero-inflated models, which is a two-component mixture of a point mass at zero and a discrete distribution for the count data. In the presence of predictors, zero-inflated Poisson (ZIP) regression models are, perhaps, the most commonly used. However, the fully parametric ZIP regression model could sometimes be restrictive, especially with respect to the mixing proportions. Taking inspiration from some of the recent literature on semiparametric mixtures of regressions models for flexible mixture modeling, we propose a semiparametric ZIP regression model. We present an "EM-like" algorithm for estimation and a summary of asymptotic properties of the estimators. The proposed semiparametric models are then applied to a data set involving clandestine methamphetamine laboratories and Alzheimer's disease.

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The current study contributes to the already substantial scholarly literature on telecommuting by estimating a joint model of three dimensions- option, choice and frequency of telecommuting. In doing so, we focus on workers who are not self-employed workers and who have a primary work place that is outside their homes. The unique methodological features of this study include the use of a general and flexible generalized hurdle count model to analyze the precise count of telecommuting days per month, and the formulation and estimation of a model system that embeds the count model within a larger multivariate choice framework. The unique substantive aspects of this study include the consideration of the "option to telecommute" dimension and the consideration of a host of residential neighborhood built environment variables. The 2009 NHTS data is used for the analysis, and allows us to develop a current perspective of the process driving telecommuting decisions. This data set is supplemented with a built environment data base to capture the effects of demographic, work-related, and built environment measures on the telecommuting-related dimensions. In addition to providing important insights for policy analysis, the results in this study indicate that ignoring the "option" dimension of telecommuting can, and generally will, lead to incorrect conclusions regarding the behavioral processes governing telecommuting decisions. The empirical results have implications for transportation planning analysis as well as for the worker recruitment/retention and productivity literature. / text

Safety reviews of existing roads are becoming a popular practice of many agencies nationally and internationally. Knowing road safety information is of great importance to both policymakers in addressing safety concerns and travelers in managing their trips. There have been various efforts in developing methodologies to measure and assess road safety in an effective manner. However, the existing research and practices are still constrained by their subjective and reactive nature. The goal of this research is to develop a framework of Road Risk Indices (RRIs) to assess road risks of existing highway infrastructure for both road users and agencies based on road geometrics, traffic conditions, and historical crash data. The proposed RRIs are intended to give a comprehensive and objective view of road safety, so that safety problems can be identified at an early stage before they rise in the form of accidents. A methodological framework of formulating RRIs that integrates results from crash prediction models and historical crash data is proposed, and Linear Referencing tools in the ArcGIS software are used to develop digital maps to publish estimated RRIs. These maps provide basic Geographic Information System (GIS) functions, including viewing and querying RRIs, and performing spatial analysis tasks. A semi-parameter count model and quantile regression based estimation are proposed to capture the specific characteristics of crash data and provide more robust and accurate predictions on crash counts. Crash data collected on Interstate Highways in Washington State for the year 2002 was extracted from the Highway Safety Information System (HSIS) and used for the case study. The results from the case study show that the proposed framework is capable of capturing statistical correlations between traffic crashes and influencing factors, leading to the effective integration of safety information in composite indices. / text

Στην παρούσα διατριβή πραγματοποιούμε εμπειρικές αναλύσεις στο αντικείμενο της Χρηματοοικονομικής Μόλυνσης στον χρηματοπιστωτικό τομέα και στις αγορές μετοχών και ομολόγων, με την χρήση υποδειγμάτων απαραριθμητών δεδομένων και δεδομένων διάρκειας. / In the current thesis we focus on Financial Contagion modeling in the domain of bank failures, stock and bond markets, with the use of Count and Duration data models.

This dissertation applies economic theories and econometric methods to analyze the interactions between government policies and economic agents in two important and current topics: the protection of the environment and illegal migration.Following the introduction, the second chapter studies the empirical strength of bi-directional linkages between environmental standards and performance, on the one hand, and environmental innovation, on the other. Our empirical results reveal that environmental R&D both spurs the tightening of government environmental standards and is spurred by the anticipation of such tightening, suggesting that U.S. environmental policy (at least in the context of the manufacturing industries that we study) has been responsive to innovation and effective in inducing innovation.The third chapter studies whether a voluntary reduction pollution programs can prompt firms to develop new environmental technologies that yield future emission reduction benefits. Conversely, a VRP may induce a participating firm to divert resources from environmental research to environmental monitoring and compliance activities that yield short-term benefits in reduced emissions. We find evidence that higher rates of program participation are associated with significant reductions in the number of successful environmental patent applications four to six years after the program ended.The fourth chapter examines the migration duration of Mexican immigrants in the U.S. using data from the Mexican Migration Project (MMP). In the past, temporary migrations were frequent, and often the rule rather than the exception in the case of Mexican immigrants. This pattern may be changing due to the tightening of the border between Mexico and the Unites States. Moreover, this paper examines whether migration experience, demographic characteristics, economic conditions or social networks drive the time Mexican immigrants to reside illegally in the United States. The empirical analysis shows that the migration duration increases as the U.S. expected real wage increases. Tighter U.S. migration policies have an ambiguous effect on the migration duration while longer distances decrease the hazard of return to their state of origin.In the final chapter of this dissertation, the general findings are concluded and some future avenues of research are discussed.

Time series involving count data are present in a wide variety of applications. In many applications, the observed counts are usually small and dependent. Failure to take these facts into account can lead to misleading inferences and may detect false relationships. To tackle such issues, a Poisson parameter-driven model is assumed for the time series at hand. This model can account for the time dependence between observations through introducing an autoregressive latent process. In this thesis, we consider Bayesian approaches for estimating the Poisson parameter-driven model. The main challenge is that the likelihood function for the observed counts involves a high dimensional integral after integrating out the latent variables. The main contributions of this thesis are threefold. First, I develop a new single-move (SM) Markov chain Monte Carlo (MCMC) method to sample the latent variables one by one. Second, I adopt the idea of the particle Gibbs sampler (PGS) method \citep{andrieu} into our model setting and compare its performance with the SM method. Third, I consider Bayesian composite likelihood methods and compare three different adjustment methods with the unadjusted method and the SM method. The comparisons provide a practical guide to what method to use. We conduct simulation studies to compare the latter two methods with the SM method. We conclude that the SM method outperforms the PGS method for small sample size, while they perform almost the same for large sample size. However, the SM method is much faster than the PGS method. The adjusted Bayesian composite methods provide closer results to the SM than the unadjusted one. The PGS and the selected adjustment method from simulation studies are compared with the SM method via a real data example. Similar results are obtained: first, the PGS method provides results very close to those of the SM method. Second, the adjusted composite likelihood methods provide closer results to the SM than the unadjusted one.

The pharmaceutical industry now recognises the importance of the newly defined discipline of pharmacometrics. Pharmacometrics uses mathematical models to describe and then predict the performance of new drugs in clinical development. To ensure these models are useful, the clinical studies need to be designed such that the data generated allows the model predictions to be sufficiently accurate and precise. The capability of the available software to reliably estimate the model parameters must also be well understood.  This thesis investigated two important areas in pharmacometrics: optimal design and software estimation performance. The three optimal design papers progressed significant areas of optimal design research, especially relevant to phase II dose response designs. The use of exposure, rather than dose, was investigated within an optimal design framework. In addition to using both optimal design and clinical trial simulation, this work employed a wide range of metrics for assessing design performance, and was illustrative of how optimal designs for exposure response models may yield dose selections quite different to those based on standard dose response models. The investigation of the optimal designs for Poisson dose response models demonstrated a novel mathematical approach to the necessary matrix calculations for non-linear mixed effects models. Finally, the enormous potential of using optimal adaptive designs over fixed optimal designs was demonstrated. The results showed how the adaptive designs were robust to initial parameter misspecification, with the capability to "learn" the true dose response using the accruing subject data. The two estimation performance papers investigated the relative performance of a number of different algorithms and software programs for two complex pharmacometric models. In conclusion these papers, in combination, cover a wide spectrum of study designs for non-linear dose/exposure response models, covering: normal/non-normal data, fixed/mixed effect models, single/multiple design criteria metrics, optimal design/clinical trial simulation, and adaptive/fixed designs.