With data describing 110,520 eighth grade students from 592 junior high (middle) schools in China, a three-level hierarchical linear model was developed in this study to create a multivariate multilevel environment to examine (a) the effects of student-level and school-level variables on science achievement in four subject areas (science inquiry skills, biology, earth science, and physics) and (b) the consistency or stability of academic achievement across the four subject areas among students and among schools. Results indicated that (a) student characteristics, including gender, parental SES, time spent in learning, and the type of family separation, were related to high academic achievement in each of the four science subject areas, (b) no school characteristics were found to be significant factors to affect students’ academic performance in any of the four science subject areas, (c) both students and schools with high academic achievement in one subject area also showed high academic achievement in other subject areas, and (d) the consistency or stability of science performance over the four subject areas did not depend on student characteristics and school characteristics.

Cattails (Typha spp.) are invasive and tend to decrease the biodiversity and area of open water of marshes, particularly where the natural hydrological cycles have been altered, as in Delta Marsh, Manitoba. Understanding the distribution of T. latifolia L., T. angustifolia L., their hybrid, T. x glauca Godr., and the environmental variables associated with their habitats, may give valuable insight for managing cattails. The distribution of these cattail species and hybrid were surveyed in 2011 in prairie pothole and roadside ditch marshes across southwestern Manitoba and southeastern Saskatchewan. Plants were identified by analysis of microscopic leaf-lamina margin characteristics. T. x glauca was most widespread, followed by T. latifolia, whereas T. angustifolia was rare and only found as far west as central Manitoba. Current understanding of the correlations between cattail invasions and their environment is conflicting and largely based on lacustrine wetland studies. A generalized linear model was developed. The model explained approximately 40% of the variation in T. x glauca distribution in the prairie potholes and ditches. The model included the environmental variables of sediment Olsen-P, sediment nitrate-N, water pH, litter depth, surrounding land use, and the interaction between Olsen-P and nitrate-N. Olsen-P was the most important of these variables, because its removal from the model significantly reduced the residual deviance of the model (P=0.05). In a survey of 13 transects throughout Delta Marsh in 2009, hybrid cattail, T. x glauca, was dominant, T. angustifolia was rare, and T. latifolia was absent. ANOVA linear regression (P=0.05) revealed that above-ground biomass was correlated with mean cattail ramet height, cattail ramet density, and standing litter biomass. Cattail ramet density was negatively correlated with sampling date and positively correlated with standing litter biomass. Mean cattail height was correlated with fallen litter biomass. One-way ANOVA (P=0.05) revealed that fallen litter biomass was lowest in quadrats closer to the open water, and mean cattail height was greatest at the quadrats closest to the open water. While mean cattail height differed depending on whether the cattail stand was a hybrid monoculture or a mixed stand of T. x glauca and T. angustifolia, no other cattail population variables were correlated with stand type. As revealed by one-way ANOVA (P=0.05), water conductivity, sediment texture, total-N, nitrate-N, Olsen-P, and organic-C were not important variables in the distributions of T. x glauca or T. angustifolia at Delta Marsh. Therefore, managing the nutrient levels at Delta Marsh would not likely be important for limiting the distribution of the cattails at this marsh. However, reducing the P concentration in pothole and ditch marshes may limit cattails in those environments.

This dissertation develops influence diagnostics for crossover models. Mixed linear models and generalised mixed linear models are utilised to investigate continuous and count data from crossover studies, respectively. For both types of models, changes in the maximum likelihood estimates of parameters, particularly in the estimated treatment effect, due to minor perturbations of the observed data, are assessed. The novelty of this dissertation lies in the analytical derivation of influence diagnostics using decompositions of the perturbed mixed models. Consequently, the suggested influence diagnostics, referred to as the delta-beta and variance-ratio influences, provide new findings about how the constructed residuals affect the estimation in terms of different parameters of interest. The delta-beta and variance-ratio influence in three different crossover models are studied in Chapters 5-6, respectively. Chapter 5 analyses the influence of subjects in a two-period continuous crossover model. Possible problems with observation-level perturbations in crossover models are discussed. Chapter 6 extends the approach to higher-order crossover models. Furthermore, not only the individual delta-beta and variance-ratio influences of a subject are derived, but also the joint influences of two subjects from different sequences. Chapters 5-6 show that the delta-beta and variance-ratio influences of a particular parameter are decided by the special linear combination of the constructed residuals. In Chapter 7, explicit delta-beta influence on the estimated treatment effect in the two-period count crossover model is derived. The influence is related to the Pearson residuals of the subject. Graphical tools are developed to visualise information of influence concerning crossover models for both continuous and count data. Illustrative examples are provided in each chapter.

In traffic safety analysis, a large number of distributions have been proposed to analyze motor vehicle crashes. Among those distributions, the traditional Poisson and Negative Binomial (NB) distributions have been the most commonly used. Although the Poisson and NB models possess desirable statistical properties, their application on modeling motor vehicle crashes are associated with limitations. In practice, traffic crash data are often over-dispersed. On rare occasions, they have shown to be under-dispersed. The over-dispersed and under-dispersed data can lead to the inconsistent standard errors of parameter estimates using the traditional Poisson distribution. Although the NB has been found to be able to model over-dispersed data, it cannot handle under-dispersed data. Among those distributions proposed to handle over-dispersed and under-dispersed datasets, the Conway-Maxwell-Poisson (COM-Poisson) and double Poisson (DP) distributions are particularly noteworthy. The DP distribution and its generalized linear model (GLM) framework has seldom been investigated and applied since its first introduction 25 years ago. The objectives of this study are to: 1) examine the applicability of the DP distribution and its regression model for analyzing crash data characterized by over- and under-dispersion, and 2) compare the performances of the DP distribution and DP GLM with those of the COM-Poisson distribution and COM-Poisson GLM in terms of goodness-of-fit (GOF) and theoretical soundness. All the DP GLMs in this study were developed based on the approximate probability mass function (PMF) of the DP distribution. Based on the simulated data, it was found that the COM-Poisson distribution performed better than the DP distribution for all nine mean-dispersion scenarios and that the DP distribution worked better for high mean scenarios independent of the type of dispersion. Using two over-dispersed empirical datasets, the results demonstrated that the DP GLM fitted the over-dispersed data almost the same as the NB model and COM-Poisson GLM. With the use of the under-dispersed empirical crash data, it was found that the overall performance of the DP GLM was much better than that of the COM-Poisson GLM in handling the under-dispersed crash data. Furthermore, it was found that the mathematics to manipulate the DP GLM was much easier than for the COM-Poisson GLM and that the DP GLM always gave smaller standard errors for the estimated coefficients.

The advantage of the geometric approach to linear model and its applications is known to many authors. In spite of that, it still remains to be rather unpopular in teaching statistics around the world and is almost missing in the Czech Republic. In this work, we use geometry of multidimensional vector spaces to derive some well-known properties of the linear model and to explain some of the most familiar statistical methods to show usefulness of this approach, also known as "free-coordinate". Besides, historical background including selected results of R. A. Fisher is briefly discussed; it follows that the geometry approach to linear model is justifiable from the historical point of view, too. Powered by TCPDF (www.tcpdf.org)

abstract: This study concerns optimal designs for experiments where responses consist of both binary and continuous variables. Many experiments in engineering, medical studies, and other fields have such mixed responses. Although in recent decades several statistical methods have been developed for jointly modeling both types of response variables, an effective way to design such experiments remains unclear. To address this void, some useful results are developed to guide the selection of optimal experimental designs in such studies. The results are mainly built upon a powerful tool called the complete class approach and a nonlinear optimization algorithm. The complete class approach was originally developed for a univariate response, but it is extended to the case of bivariate responses of mixed variable types. Consequently, the number of candidate designs are significantly reduced. An optimization algorithm is then applied to efficiently search the small class of candidate designs for the D- and A-optimal designs. Furthermore, the optimality of the obtained designs is verified by the general equivalence theorem. In the first part of the study, the focus is on a simple, first-order model. The study is expanded to a model with a quadratic polynomial predictor. The obtained designs can help to render a precise statistical inference in practice or serve as a benchmark for evaluating the quality of other designs. / Dissertation/Thesis / Doctoral Dissertation Statistics 2017

abstract: The primary purpose of this study is to examine the effect of knowledge for teaching mathematics and teaching practice on student mathematics achievement growth. Thirty two teachers and 299 fourth grade students in three elementary schools from one school district in urban area participated in the study. Most of them are Hispanic in origin and about forty percent is English Language Learners (ELLs). The two level Hierarchical Linear Model (HLM) was used to investigate repeated measures of teaching practice measured by Classroom Assessment Scoring System (CLASS) instrument. Also, linear regression and a multiple regression to examine the relationship between teacher knowledge measured by Learning for Mathematics Teaching (LMT) and Developing Mathematical Ideas (DMI) items and teaching practice were employed. In addition, a three level HLM was employed to analyze repeated measures of student mathematics achievement measured by Arizona Assessment Consortium (AzAC) instruments. Results showed that overall teaching practice did not change weekly although teachers' emotional support for their students improved by week. Furthermore, a statistically significant relationship between teacher knowledge and teaching practice was not found. In terms of student learning, ELLs have significantly lower initial status in mathematics achievement than non-ELLs, as were growth rates for these two groups. Lastly, teaching practice significantly predicted students' monthly mathematics achievement growth but teacher knowledge did not. The findings suggest that school systems and education policy makers need to provide teachers with the chance to reflect on their teaching and change it within themselves in order to better support student mathematics learning. / Dissertation/Thesis / Ph.D. Curriculum and Instruction 2012

abstract: Nowadays product reliability becomes the top concern of the manufacturers and customers always prefer the products with good performances under long period. In order to estimate the lifetime of the product, accelerated life testing (ALT) is introduced because most of the products can last years even decades. Much research has been done in the ALT area and optimal design for ALT is a major topic. This dissertation consists of three main studies. First, a methodology of finding optimal design for ALT with right censoring and interval censoring have been developed and it employs the proportional hazard (PH) model and generalized linear model (GLM) to simplify the computational process. A sensitivity study is also given to show the effects brought by parameters to the designs. Second, an extended version of I-optimal design for ALT is discussed and then a dual-objective design criterion is defined and showed with several examples. Also in order to evaluate different candidate designs, several graphical tools are developed. Finally, when there are more than one models available, different model checking designs are discussed. / Dissertation/Thesis / Ph.D. Industrial Engineering 2013

Modelling of complex corroding industrial systems is ritical to effective inspection and maintenance for ssurance of system integrity. Wall thickness and corrosion rate are modelled for multiple dependent corroding omponents, given observations of minimum wall thickness per component. At each inspection, partial observations of the system are considered. A Bayes Linear approach is adopted simplifying parameter estimation and avoiding often unrealistic distributional assumptions. Key system variances are modelled, making exchangeability assumptions to facilitate analysis for sparse inspection time-series. A utility based criterion is used to assess quality of inspection design and aid decision making. The model is applied to inspection data from pipework networks on a full-scale offshore platform.

A long record of daily data is used to study the lake levels of Lake Neusiedl, a large steppe lake at the eastern border of Austria. Daily lake level changes are modeled as functions of precipitation, temperature, and wind conditions. The occurrence and the amount of daily precipitation are modeled with logistic regressions and generalized linear models.