Dissertations / Theses on the topic 'Count data modelling'

This thesis consists of four papers concerning modelling of count data and tourism demand. For three of the papers the focus is on the integer-valued autoregressive moving average model class (INARMA), and especially on the ENAR(l) model. The fourth paper studies the interaction between households' choice of number of leisure trips and number of overnight stays within a bivariate count data modelling framework. Paper [I] extends the basic INAR(1) model to enable more flexible and realistic empirical economic applications. The model is generalized by relaxing some of the model's basic independence assumptions. Results are given in terms of first and second conditional and unconditional order moments. Extensions to general INAR(p), time-varying, multivariate and threshold models are also considered. Estimation by conditional least squares and generalized method of moments techniques is feasible. Monte Carlo simulations for two of the extended models indicate reasonable estimation and testing properties. An illustration based on the number of Swedish mechanical paper and pulp mills is considered. Paper[II] considers the robustness of a conventional Dickey-Fuller (DF) test for the testing of a unit root in the INAR(1) model. Finite sample distributions for a model with Poisson distributed disturbance terms are obtained by Monte Carlo simulation. These distributions are wider than those of AR(1) models with normal distributed error terms. As the drift and sample size, respectively, increase the distributions appear to tend to T-2) and standard normal distributions. The main results are summarized by an approximating equation that also enables calculation of critical values for any sample and drift size. Paper[III] utilizes the INAR(l) model to model the day-to-day movements in the number of guest nights in hotels. By cross-sectional and temporal aggregation an INARMA(1,1) model for monthly data is obtained. The approach enables easy interpretation and econometric modelling of the parameters, in terms of daily mean check-in and check-out probability. Empirically approaches accounting for seasonality by dummies and using differenced series, as well as forecasting, are studied for a series of Norwegian guest nights in Swedish hotels. In a forecast evaluation the improvements by introducing economic variables is minute. Paper[IV] empirically studies household's joint choice of the number of leisure trips and the total night to stay on these trips. The paper introduces a bivariate count hurdle model to account for the relative high frequencies of zeros. A truncated bivariate mixed Poisson lognormal distribution, allowing for both positive as well as negative correlation between the count variables, is utilized. Inflation techniques are used to account for clustering of leisure time to weekends. Simulated maximum likelihood is used as estimation method. A small policy study indicates that households substitute trips for nights as the travel costs increase.

Härtill 4 uppsatser.

digitalisering@umu

Bayesian approaches to prediction and the assessment of predictive uncertainty in generalized linear models are often based on averaging predictions over different models, and this requires methods for accounting for model uncertainty. In this thesis we describe computational methods for Bayesian inference and model selection for generalized linear models, which improve on existing techniques. These methods are applied to the building of flexible models for gamma ray count data (data measuring the natural radioactivity of rocks) at the Castlereagh Waste Management Centre, which served as a hazardous waste disposal facility for the Sydney region between March 1978 and August 1998. Bayesian model selection methods for generalized linear models enable us to approach problems of smoothing, change point detection and spatial prediction for these data within a common methodological and computational framework, by considering appropriate basis expansions of a mean function. The data at Castlereagh were collected in the following way. A number of boreholes were drilled at the site, and for each borehole a gamma ray detector recorded gamma ray emissions at different depths as the detector was raised gradually from the bottom of the borehole to ground level. The profile of intensity of gamma counts can be informative about the geology at each location, and estimation of intensity profiles raises problems of smoothing and change point detection for count data. The gamma count profiles can also be modelled spatially, to inform the geological profile across the site. Understanding the geological structure of the site is important for modelling the transport of chemical contaminants beneath the waste disposal area. The structure of the thesis is as follows. Chapter 1 describes the Castlereagh hazardous waste site and the geophysical data, which motivated the methodology developed in this research. We summarise the principles of Gamma Ray (GR) logging, a method routinely employed by geophysicists and environmental engineers in the detailed evaluation of hazardous site geology, and detail the use of the Castlereagh data in this research. In Chapter 2 we review some fundamental ideas of Bayesian inference and computation and discuss them in the context of generalised linear models. Chapter 3 details the theoretical basis of our work. Here we give a new Markov chain Monte Carlo sampling scheme for Bayesian variable selection in generalized linear models, which is analogous to the well-known Swendsen-Wang algorithm for the Ising model. Special cases of this sampling scheme are used throughout the rest of the thesis. In Chapter 4 we discuss the use of methods for Bayesian model selection in generalized linear models in two specific applications, which we implement on the Castlereagh data. First, we consider smoothing problems where we flexibly estimate the dependence of a response variable on one or more predictors, and we apply these ideas to locally adaptive smoothing of gamma ray count data. Second, we discuss how the problem of multiple change point detection can be cast as one of model selection in a generalized linear model, and consider application to change point detection for gamma ray count data. In Chapter 5 we consider spatial models based on partitioning a spatial region of interest into cells via a Voronoi tessellation, where the number of cells and the positions of their centres is unknown, and show how these models can be formulated in the framework of established methods for Bayesian model selection in generalized linear models. We implement the spatial partition modelling approach to the spatial analysis of gamma ray data, showing how the posterior distribution of the number of cells, cell centres and cell means provides us with an estimate of the mean response function describing spatial variability across the site. Chapter 6 presents some conclusions and suggests directions for future research. A paper based on the work of Chapter 3 has been accepted for publication in the Journal of Computational and Graphical Statistics, and a paper based on the work in Chapter 4 has been accepted for publication in Mathematical Geology. A paper based on the spatial modelling of Chapter 5 is in preparation and will be submitted for publication shortly. The work in this thesis was collaborative, to a smaller or larger extent in its various components. I authored Chapters 1 and 2 entirely, including definition of the problem in the context of the CWMC site, data gathering and preparation for analysis, review of the literature on computational methods for Bayesian inference and model selection for generalized linear models. I also authored Chapters 4 and 5 and benefited from some of Dr Nott's assistance in developing the algorithms. In Chapter 3, Dr Nott led the development of sampling scheme B (corresponding to having non-zero interaction parameters in our Swendsen-Wang type algorithm). I developed the algorithm for sampling scheme A (corresponding to setting all algorithm interaction parameters to zero in our Swendsen-Wang type algorithm), and performed the comparison of the performance of the two sampling schemes. The final discussion in Chapter 6 and the direction for further research in the case study context is also my work.

Capture-recapture methods are used to estimate the unknown size of a target population whose size cannot be reasonably enumerated. This thesis proposes the estimators and the models specifically designed to estimate the size of a population for one-inflated capture-recapture count data allowing for heterogeneity. These estimators can assist with overestimation problems occurring from one-inflation that can be seen in several areas of researches. The estimators are developed under three approaches. The first approach is based on a modification by truncating singletons and applying the conventional Turing and maximum likelihood estimation approach to the one-truncated geometric data for estimating the parameter p₀. These p₀ are applied to the Horvitz-Thompson approach for the modified Turing estimator (T_OT) and the modified maximum likelihood estimator (MLE_OT). The second approach is the model-based approach. It focuses on developing a statistical model that describes the mechanism to generate the extra of count ones. The new estimator MLE_ZTOI is developed from a maximum likelihood approach by using the nested EM algorithm based upon the zero-truncated one-inflated geometric distribution. The last approach focuses on modifying a classical Chao’s estimator to involve the frequency of counts of twos and threes instead of the frequency of counts of ones and twos. The modified Chao estimator (MC) is asymptotic unbiased estimator for a power series distribution with and without one-inflation and provides a lower bound estimator under a mixture of power series distributions with and without one-inflation. The three bias-correction versions of the modified Chao estimator have been developed to reduce the bias when the sample size is small. A variance approximation of MC and MC3 are also constructed by using a conditioning technique. All of the proposed estimators are assessed through simulation studies. The real data sets are provided for understanding the methodologies.

Capture-recapture modelling is a powerful tool for estimating an elusive target population size. This thesis proposes four new population size estimators allowing for population heterogeneity. The first estimator is developed under the zero-truncated of generalised Poisson distribution (ZTGP), called the MLEGP. The two parameters of the ZTGP are estimated by using a maximum likelihood with the Expectation-Maximisation algorithm (EM algorithm). The second estimator is the population size estimator under the zero-truncated Conway-Maxwell-Poisson distribution (ZTCMP). The benefits of using the Conway-Maxwell-Poisson distribution (CMP) are that it includes the Bernoulli, Poisson and geometric distribution as special cases. It is also flexible for over- and under-dispersions relative to the original Poisson model. Moreover, the parameter estimates can be achieved by a simple linear regression approach. The uncertainty in estimating variances of the unknown population size under new estimator is studied with analytic and resampling approaches. The geometric distribution is one of the nested models under the Conway-Maxwell-Poisson distribution, the Turing and the Zelterman estimators are extended for the geometric distribution and its related model, respectively. Variance estimation and confidence intervals are constructed by the normal approximation method. An uncertainty of variance estimation of population size estimators for single marking capture-recapture data is studied in the final part of the research. Normal approximation and three resample approaches of variance estimation are compared for the Chapman and the Chao estimators. All of the approaches are assessed through simulations, and real data sets are provided as guidance for understanding the methodologies.

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.

Digital camera monitoring has evolved as an active application-oriented scheme to help address questions in areas such as fisheries, ecology, computer vision, artificial intelligence, and criminology. In recreational fisheries research, digital camera monitoring has become a viable option for probability-based survey methods, and is also used for corroborative and validation purposes. In comparison to onsite surveys (e.g. boat ramp surveys), digital cameras provide a cost-effective method of monitoring boating activity and fishing effort, including night-time fishing activities. However, there are challenges in the use of digital camera monitoring that need to be resolved. Notably, missing data problems and the cost of data interpretation are among the most pertinent. This study provides relevant statistical support to address these challenges of digital camera monitoring of boating effort, to improve its utility to enhance recreational fisheries management in Western Australia and elsewhere, with capacity to extend to other areas of application. Digital cameras can provide continuous recordings of boating and other recreational fishing activities; however, interruptions of camera operations can lead to significant gaps within the data. To fill these gaps, some climatic and other temporal classification variables were considered as predictors of boating effort (defined as number of powerboat launches and retrievals). A generalized linear mixed effect model built on fully-conditional specification multiple imputation framework was considered to fill in the gaps in the camera dataset. Specifically, the zero-inflated Poisson model was found to satisfactorily impute plausible values for missing observations for varied durations of outages in the digital camera monitoring data of recreational boating effort. Additional modelling options were explored to guide both short- and long-term forecasting of boating activity and to support management decisions in monitoring recreational fisheries. Autoregressive conditional Poisson (ACP) and integer-valued autoregressive (INAR) models were identified as useful time series models for predicting short-term behaviour of such data. In Western Australia, digital camera monitoring data that coincide with 12-month state-wide boat-based surveys (now conducted on a triennial basis) have been read but the periods between the surveys have not been read. A Bayesian regression framework was applied to describe the temporal distribution of recreational boating effort using climatic and temporally classified variables to help construct data for such missing periods. This can potentially provide a useful cost-saving alternative of obtaining continuous time series data on boating effort. Finally, data from digital camera monitoring are often manually interpreted and the associated cost can be substantial, especially if multiple sites are involved. Empirical support for low-level monitoring schemes for digital camera has been provided. It was found that manual interpretation of camera footage for 40% of the days within a year can be deemed as an adequate level of sampling effort to obtain unbiased, precise and accurate estimates to meet broad management objectives. A well-balanced low-level monitoring scheme will ultimately reduce the cost of manual interpretation and produce unbiased estimates of recreational fishing indexes from digital camera surveys.

Pharmacodynamic processes and disease progression are increasingly characterized with pharmacometric models. However, modelling options for discrete-type responses remain limited, although these response variables are commonly encountered clinical endpoints. Types of data defined as discrete data are generally ordinal, e.g. symptom severity, count, i.e. event frequency, and time-to-event, i.e. event occurrence. Underlying assumptions accompanying discrete data models need investigation and possibly adaptations in order to expand their use. Moreover, because these models are highly non-linear, estimation with linearization-based maximum likelihood methods may be biased. The aim of this thesis was to explore pharmacometric methods and novel models for discrete data through (i) the investigation of benefits of treating discrete data with different modelling approaches, (ii) evaluations of the performance of several estimation methods for discrete models, and (iii) the development of novel models for the handling of complex discrete data recorded during (pre-)clinical studies. A simulation study indicated that approaches such as a truncated Poisson model and a logit-transformed continuous model were adequate for treating ordinal data ranked on a 0-10 scale. Features that handled serial correlation and underdispersion were developed for the models to subsequently fit real pain scores. The performance of nine estimation methods was studied for dose-response continuous models. Other types of serially correlated count models were studied for the analysis of overdispersed data represented by the number of epilepsy seizures per day. For these types of models, the commonly used Laplace estimation method presented a bias, whereas the adaptive Gaussian quadrature method did not. Count models were also compared to repeated time-to-event models when the exact time of gastroesophageal symptom occurrence was known. Two new model structures handling repeated time-to-categorical events, i.e. events with an ordinal severity aspect, were introduced. Laplace and two expectation-maximisation estimation methods were found to be performing well for frequent repeated time-to-event models. In conclusion, this thesis presents approaches, estimation methods, and diagnostics adapted for treating discrete data. Novel models and diagnostics were developed when lacking and applied to biological observations.

This study is a multidisciplinary approach to Species Distribution Modelling (SDM) where predictive models have been developed regarding the current distribution and potential spread of two invasive species found in Baltic Sea waters. Invasive species in the Baltic have long been an ecological and economic problem and the two species studied are well known for their adaptability in colonization and detrimental effects on local ecology all over the world. First, the Round Goby (Neogobius Melanostomus) has been steadily colonizing the Swedish Baltic coastline since 2008, the impact of which on local ecosystems is not fully understood. Also, the Chinese Mitten Crab (Eriocheir Sinensis), found in Swedish waters since the 1930’s, has been known to be a robust invader of ecosystems but presence in the Baltic is still not well explained. Four high spatial resolution models have been developed, three respective Round Goby and one for Mitten Crab. Two models are specific to the Blekinge/Hanöbukten region of the Swedish Baltic Sea coast, showing predicted current distribution of Round Goby. Two are predictions of Round Goby and Mitten Crab transferred or projected to other regions, with different approaches in setting model parameters and choosing variables, showing current and potential distribution. This study features: exploratory data analysis and filtering using GIS tools, highly discriminant environmental variable selection and rejection, and several different approaches to modelling in Maxent using custom and default settings. Predictive maps have been developed showing current distribution and potential spread as well as explanatory tabular data outlining direct and indirect drivers of species presence. Maxent has proven to be a powerful predictive tool on a regional basis, and proximity to introduction locations play a major role. Maxent, used in combination with spatial data modelling, exploration and filtering techniques has yielded a valid explanatory model as well. Transferring predictions to other regions is quite sensitive, however, and can depend heavily on species, sampling strategy and similarity of habitat type. Round Goby predictions were successfully created regionally and transferred to Stockholm, but Mitten Crab predictions were not successfully transferred to Blekinge.

The objectives of this thesis is to explore different approaches of modelling clustered correlated data in the form of repeated or longitudinal counts data leading to a replicated Poisson process. The specific application is from repeated epileptic seizure time to events data. Two main classes of models will be considered in this thesis. These are the marginal and subject or cluster specific effects models. Under the marginal class of models the generalized estimating equations approach due to Liang and Zeger (1986) is first considered. These models are concerned with population averaged effects as opposed to subject-specific effects which include random subject-specific effects such that multiple or repeated outcomes within a subject or cluster are assumed to be independent conditional on the subject−specific effects. Finally we consider a distinct class of marginal models which include three common variants namely the approach due to Anderson and Gill (1982), Wei et al (1989) and Prentice et al. (1981)
Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2010.

This research develops and applies a methodology to calculate vehicle activity inputs for modelling of emissions from on-road vehicles using traffic count data. The thesis: (1) provides an understanding of emissions modelling in Canada and the U.S. and discusses the traffic activity data inputs required by vehicle emissions modelling software; (2) develops a methodology to collect and prepare vehicle activity data for an urban centre and applies this methodology by estimating vehicle activity for Winnipeg and Saskatoon; and (3) estimates vehicle emissions and then compares the sensitivity of estimating emissions using locally developed vehicle activity to estimating emissions using default vehicle activity. The methodology this research develops and applies to Winnipeg and Saskatoon is applicable to any jurisdiction in need of developing their own vehicle activity inputs for emissions modelling. The emissions estimates calculated using these different inputs emphasizes the importance of obtaining jurisdiction-specific input values for emissions modelling.