Developing sound or reliable statistical models for analyzing vehicle crashes is very important in highway safety studies. A difficulty arises when crash data exhibit overdispersion. Over-dispersion caused by unobserved heterogeneity is a serious problem and has been addressed in a variety ways within the negative binomial (NB) modeling framework. However, the true factors that affect heterogeneity are often unknown to researchers, and failure to accommodate such heterogeneity in the model can undermine the validity of the empirical results. Given the limitations of the NB regression model for addressing over-dispersion of crash data due to heterogeneity, this research examined an alternative model formulation that could be used for capturing heterogeneity through the use of finite mixture regression models. A Finite mixture of Poisson or NB regression models is especially useful when the count data were generated from a heterogeneous population. To evaluate these models, Poisson and NB mixture models were estimated using both simulated and empirical crash datasets, and the results were compared to those from a single NB regression model. For model parameter estimation, a Bayesian approach was adopted, since it provides much richer inference than the maximum likelihood approach. Using simulated datasets, it was shown that the single NB model is biased if the underlying cause of heterogeneity is due to the existence of multiple counting processes. The implications could be poor prediction performance and poor interpretation. Using two empirical datasets, the results demonstrated that a two-component finite mixture of NB regression models (FMNB-2) was quite enough to characterize the uncertainty about the crash occurrence, and it provided more opportunities for interpretation of the dataset which are not available from the standard NB model. Based on the models from the empirical dataset (i.e., FMNB-2 and NB models), their relative performances were also examined in terms of hotspot identification and accident modification factors. Finally, using a simulation study, bias properties of the posterior summary statistics for dispersion parameters in FMNB-2 model were characterized, and the guidelines on the choice of priors and the summary statistics to use were presented for different sample sizes and sample-mean values.

Over the past twenty years, the geographical bases of state legislative parties have shifted substantially. In statehouses across the country, legislators from densely-populated districts with large racial minority populations have become a larger presence inside Democratic caucuses while legislators from exurban and sparsely-populated districts have become a larger presence inside Republican caucuses. These changes have had important consequences for roll-call voting and policy outcomes inside legislatures, as new coalitional configurations formed by the intersection of party and geography have replaced older ones. In this dissertation, I examine the causes and consequences of these changes in a new way, one that more closely approximates a legislator's relationship to her "geographical constituency" (to use Richard Fenno's famous term). Unlike traditional studies of the social origins of legislative conflict, which have focused on how the constituency bases of legislative parties can be distinguished by reference to a small set of district-level demographic variables examined independently of each other, my approach views district demographic variables as the empirical manifestations of a wide variety of distinct, if latent, geographical contexts. My efforts to model the geographical constituency are centered upon a technique called Latent Profile Analysis (LPA), which estimates a latent categorical variable (in this case, legislative district categories indicative of distinct socioeconomic contexts) that captures covariation among a set of observed continuous variables (in this case, district-level demographic and geographical variables). The LPA analysis, which incorporates over 3,500 districts from seventeen chambers in the 1990s and 2000s, yields a nine-fold district categorization scheme that serves as the basis for subsequent inquiries of the dissertation. These inquiries examine how demographic and electoral change have interacted to influence trends in partisan representation of the district categories, how party and district category come together to explain patterns of roll-call ideology among state legislators, and how social cleavages over public policy within state electorates are translated into particular voting alignments involving the district categories. The dissertation speaks to a large literature in political science on the constituency-legislator relationship, as well to current debates about geographical sorting, legislative polarization, and the role of policy content in shaping voting coalitions. / text

In this thesis, we analyse the relationship between the hedging activities and return on equity, and the relationship between profit on hedging and other factors. Fully conditional specification is used to impute the missing values. Instrumental variable estimation and finite mixture of regression models are then used to predict the return on equity and hedging gain. We find the instrumental variable estimation is better than the OLS estimation to deal with the hedging data since it eliminates the endogeneity. By finite mixture of regression models, we show that different firms have different hedging strategies, which cause different profits in hedging. We also find the companies with large total assets prefer to hedge.

<p>This dissertation consists of three parts of empirical analyses investigating temporal patterns and consequences of (childhood) overweight and obesity, mainly in the United States and the People's Republic of China. Based on the China Health and Nutrition Survey, the first part conducts hierarchical age-period-cohort analyses of childhood overweight in China and finds a strong cohort effect driving the overweight epidemic. Results from the growth-curve models show that childhood overweight and underweight are related such that certain socio-economic groups with higher levels of childhood overweight also exhibit lower levels of childhood underweight. The second part situates the discussion on childhood obesity in a broader context. It compares temporal patterns of childhood overweight in China with these of adulthood overweight and finds that the salient cohort component is absent in rising adulthood overweight, which is dominated by strong period effects. A positive association between human development index and overweight/obesity prevalence across countries is also documented. Using multiple waves of survey data from the National Longitudinal Study of Adolescent Health, the third part analyzes the (latent) trajectory of childhood overweight/obesity in the United States. It finds that individuals with obesity growth trajectories are less likely to avoid mental depression, tend to have higher levels of neuroticism and lower levels of agreeableness/conscientiousness, and show less delinquent behaviors.</p> / Dissertation

In the present paper we discuss Bayesian estimation of a very general model class where the distribution of the observations is assumed to depend on a latent mixture or switching variable taking values in a discrete state space. This model class covers e.g. finite mixture modelling, Markov switching autoregressive modelling and dynamic linear models with switching. Joint Bayesian estimation of all latent variables, model parameters and parameters determining the probability law of the switching variable is carried out by a new Markov Chain Monte Carlo method called permutation sampling. Estimation of switching and mixture models is known to be faced with identifiability problems as switching and mixture are identifiable only up to permutations of the indices of the states. For a Bayesian analysis the posterior has to be constrained in such a way that identifiablity constraints are fulfilled. The permutation sampler is designed to sample efficiently from the constrained posterior, by first sampling from the unconstrained posterior - which often can be done in a convenient multimove manner - and then by applying a suitable permutation, if the identifiability constraint is violated. We present simple conditions on the prior which ensure that this method is a valid Markov Chain Monte Carlo method (that is invariance, irreducibility and aperiodicity hold). Three case studies are presented, including finite mixture modelling of fetal lamb data, Markov switching Autoregressive modelling of the U.S. quarterly real GDP data, and modelling the U .S./U.K. real exchange rate by a dynamic linear model with Markov switching heteroscedasticity. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

The planet is experiencing a dramatic loss of species. The majority of species are unknown to science, and it is usually infeasible to conduct a census of a region to acquire a complete inventory of all life forms. Therefore, it is important to estimate and conduct statistical inference on the total number of species in a region based on samples obtained from field observations. Such estimates may suggest the number of species new to science and at potential risk of extinction. In this thesis, we develop novel methodology to conduct statistical inference, based on abundance-based data collected from multiple sampling locations, on the number of species within a taxonomic group residing in a region. The primary contribution of this work is the formulation of novel statistical methodology for analysis in this setting, where abundances of species are recorded at multiple sampling units across a region. This particular area has received relatively little attention in the literature. In the first chapter, the problem of estimating the number of species is formulated in a broad context, one that occurs in several seemingly unrelated fields of study. Estimators are commonly developed from statistical sampling models. Depending on the organisms or objects under study, different sampling techniques are used, and consequently, a variety of statistical models have been developed for this problem. A review of existing estimation methods, categorized by the associated sampling model, is presented in the second chapter. The third chapter develops a new negative binomial mixture model. The negative binomial model is employed to account for the common tendency of individuals of a particular species to occur in clusters. An exponential mixing distribution permits inference on the number of species that exist in the region, but were in fact absent from the sampling units. Adopting a classical approach for statistical inference, we develop the maximum likelihood estimator, and a corresponding profile-log-likelihood interval estimate of species richness. In addition, a Gaussian-based confidence interval based on large-sample theory is presented. The fourth chapter further extends the hierarchical model developed in Chapter 3 into a Bayesian framework. The motivation for the Bayesian paradigm is explained, and a hierarchical model based on random effects and discrete latent variables is presented. Computing the posterior distribution in this case is not straight-forward. A data augmentation technique that indirectly places priors on species richness is employed to compute the model using a Metropolis-Hastings algorithm. The fifth chapter examines the performance of our new methodology. Simulation studies are used to examine the mean-squared error of our proposed estimators. Comparisons to several commonly-used non-parametric estimators are made. Several conclusions emerge, and settings where our approaches can yield superior performance are clarified. In the sixth chapter, we present a case study. The methodology is applied to a real data set of oribatid mites (a taxonomic order of micro-arthropods) collected from multiple sites in a tropical rainforest in Panama. We adjust our statistical sampling models to account for the varying masses of material sampled from the sites. The resulting estimates of species richness for the oribatid mites are useful, and contribute to a wider investigation, currently underway, examining the species richness of all arthropods in the rainforest. Our approaches are the only existing methods that can make full use of the abundance-based data from multiple sampling units located in a single region. The seventh and final chapter concludes the thesis with a discussion of key considerations related to implementation and modeling assumptions, and describes potential avenues for further investigation. / Graduate

Finite mixtures of von Mises-Fisher distributions allow to apply model-based clustering methods to data which is of standardized length, i.e., all data points lie on the unit sphere. The R package movMF contains functionality to draw samples from finite mixtures of von Mises-Fisher distributions and to fit these models using the expectation-maximization algorithm for maximum likelihood estimation. Special features are the possibility to use sparse matrix representations for the input data, different variants of the expectationmaximization algorithm, different methods for determining the concentration parameters in the M-step and to impose constraints on the concentration parameters over the components. In this paper we describe the main fitting function of the package and illustrate its application. In addition we compare the clustering performance of finite mixtures of von Mises-Fisher distributions to spherical k-means. We also discuss the resolution of several numerical issues which occur for estimating the concentration parameters and for determining the normalizing constant of the von Mises-Fisher distribution. (authors' abstract)

This thesis is intent on using mixtures of probability distributions in generalized linear model. The theoretical part is divided into two parts. In the first chapter a generalized linear model (GLM) is defined as an alternative to the classical linear regression model. The second chapter describes the mixture of probability distributions and estimate of their parameters. At the end of the second chapter, the previous theories are connected into the finite mixture generalized linear model. The last third part is practical and shows concrete examples of these models.

Finite mixture models have had a profound impact on the history of statistics, contributing to modelling heterogeneous populations, generalizing distributional assumptions, and lately, presenting a convenient framework for classification and clustering. A novel approach, via Gaussian mixture distribution, is introduced for modelling receiver operating characteristic curves. The absence of a closed-form for a functional form leads to employing the Monte Carlo method. This approach performs excellently compared to the existing methods when applied to real data. In practice, the data are often non-normal, atypical, or skewed. It is apparent that non-Gaussian distributions be introduced in order to better fit these data. Two non-Gaussian mixtures, i.e., t distribution and skew t distribution, are proposed and applied to real data. A novel mixture is presented to cluster spatial and temporal data. The proposed model defines each mixture component as a mixture of autoregressive polynomial with logistic links. The new model performs significantly better compared to the most well known model-based clustering techniques when applied to real data. / Thesis / Doctor of Philosophy (PhD)

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