Kernel mixture models are proposed to cluster univariate, independent multivariate and dependent bivariate longitudinal data. The Gaussian distribution in finite mixture models is replaced by the Gaussian and gamma kernel functions, and the expectation-maximization algorithm is used to estimate bandwidths and compute log-likelihood scores. For dependent bivariate longitudinal data, the bivariate Gaussian copula is used to reveal the correlation between two attributes. After that, we use AIC, BIC and ICL to select the best model. In addition, we also introduce a kernel distance-based clustering method to compare with the kernel mixture models. A simulation is performed to illustrate the performance of this mixture model, and results show that the gamma kernel mixture model performs better than the kernel distance-based clustering method based on misclassification rates. Finally, these two models are applied to COVID-19 data, and sixty countries are classified into ten clusters based on growth rates and death rates. / Thesis / Master of Science (MSc)

Preterm birth is the leading cause of neonatal mortality and long-term morbidity. Neonatologists can adjust nutrition to preterm neonates to control their weight gain so that the possibility of long-term morbidity can be minimized. This optimization of growth trajectories of preterm infants can be achieved by studying a cohort of selected healthy preterm infants with weights observed during day 1 to day 21. However, missing values in such a data poses a big challenge in this case. In fact, missing data is a common problem faced by most applied researchers. Most statistical softwares deal with missing data by simply deleting subjects with missing items. Analyses carried out on such incomplete data result in biased estimates of the parameters of interest and consequently lead to misleading or invalid inference. Even though many statistical methods may provide robust analysis, it will be better to handle missing data by imputing them with plausible values and then carry out a suitable analysis on the full data. In this thesis, several imputation methods are first introduced and discussed. Once the data get completed by the use of any of these methods, the growth trajectories for this cohort of preterm infants can be presented in the form of percentile growth curves. These growth trajectories can now serve as references for the population of preterm babies. To find out the explicit growth rate, we are interested in establishing predictive models for weights at days 7, 14 and 21. I have used both univariate and multivariate linear models on the completed data. The resulting predictive models can then be used to calculate the target weight at days 7, 14 and 21 for any other infant given the information at birth. Then, neonatologists can adjust the amount of nutrition given in order to preterm infants to control their growth so that they will not grow too fast or too slow, thus avoiding later-life complications. / Thesis / Master of Science (MSc)

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Ultrahigh-dimensional variable selection is of great importance in the statistical research. And independence screening is a powerful tool to select important variable when there are massive variables. Some commonly used independence screening procedures are based on single replicate data and are not applicable to longitudinal data. This motivates us to propose a new Sure Independence Screening (SIS) procedure to bring the dimension from ultra-high down to a relatively large scale which is similar to or smaller than the sample size. In chapter 2, we provide two types of SIS, and their iterative extensions (iterative SIS) to enhance the finite sample performance. An upper bound on the number of variables to be included is derived and assumptions are given under which sure screening is applicable. The proposed procedures are assessed by simulations and an application of them to a study on systemic lupus erythematosus illustrates the practical use of these procedures. After the variables screening process, we then explore the relationship among the variables. Graphical models are commonly used to explore the association network for a set of variables, which could be genes or other objects under study. However, graphical modes currently used are only designed for single replicate data, rather than longitudinal data. In chapter 3, we propose a penalized likelihood approach to identify the edges in a conditional independence graph for longitudinal data. We used pairwise coordinate descent combined with second order cone programming to optimize the penalized likelihood and estimate the parameters. Furthermore, we extended the nodewise regression method the for longitudinal data case. Simulation and real data analysis exhibit the competitive performance of the penalized likelihood method. / Doctor of Philosophy / Longitudinal data have received a considerable amount of attention in the fields of health science studies. The information from this type of data could be helpful with disease detection and control. Besides, a graph of factors related to the disease can also be built up to represent their relationships between each other. In this dissertation, we develop a framework to find out important factor(s) from thousands of factors in longitudinal data that is/are related to the disease. In addition, we develop a graphical method that can show the relationship among the important factors identified from the previous screening. In practice, combining these two methods together can identify important factors for a disease as well as the relationship among the factors, and thus provide us a deeper understanding about the disease.

In recent decades, United States public school education has moved toward standards-based curricula. However, performance on standardized tests may not be representative of subject literacy or workforce preparedness. This misalignment may be particularly true in the sciences, where low science literacy and gender-related workforce shortfalls are evident. This study was an exploration of how well standardized test scores and other academic metrics reflected progression to a science major, by gender. This exploratory study used longitudinal data from the Virginia Department of Education, prepared by the Virginia Longitudinal Data System, for students who graduated from Virginia public schools from 2004-2016 (N=1,089,389). Students' standardized assessment scores, science course grades, demographics, and post-secondary major were analyzed using correlation analysis, logistic regression, principal component analysis, and hypothesis testing. Overall, 9% of high school completers enrolled in a post-secondary science major, with approximately half of those students attending 4-year schools. Seventy percent of science majors were female; females were most prevalent in health-related majors and least prevalent in physical sciences. Logistic regression identified the following factors significantly related to enrolling in a post-secondary science major: gender, high school science grades, and the high school's percent of students who majored in science. A student's status as economically disadvantaged or an underrepresented minority was significantly related to enrolling in a 2-year science major. In comparisons among academic metrics, standardized test scores and science grades were uncorrelated, and science grades differed significantly among demographic subgroups. Overall, demographic and school-level factors were more closely related to majoring in science than were academic factors. For both genders and for biological, physical, and health sciences, the percent of students majoring in science doubled from 2005-2015. Standardized test scores and course grades measured different aspects of learning, and higher science grades were related to majoring in science. However, the designation of "science major" is so broad as to be uninformative in a research context; more specificity would be needed to develop academic profiles. From these findings, one can conclude that demographic and cultural factors – rather than academic factors – were more closely related to whether students pursued a science pathway. / Doctor of Philosophy / In recent decades, United States public school education has moved toward standards-based curricula. However, performance on standardized tests may not represent subject knowledge or job preparedness, particularly in the science fields. This study was an exploration of how well standardized test scores and other academic measured were related to majoring in science, for male and female students. This exploratory study used data from the Virginia Department of Education, prepared by the Virginia Longitudinal Data System, for students who graduated from Virginia public schools from 2004-2016. Students' standardized test scores, science course grades, demographics, and college major were analyzed. Overall, 9% of high school completers enrolled in a science major after high school, with approximately half of those students attending 4-year schools. Seventy percent of science majors were female; females were most prevalent in health-related majors and least prevalent in physical sciences. The following factors were significantly related to enrolling in a science major: gender, high school science grades, and the high school's percent of students who majored in science. A student's status as economically disadvantaged or an underrepresented minority was significantly related to enrolling in a 2-year science major. In comparisons among academic measures, standardized test scores and science grades were not related to each other, and science grades differed among demographic groups. Overall, demographic and school-level factors were more closely related to majoring in science than were academic factors. For both genders and for biological, physical, and health sciences, the percent of students majoring in science doubled from 2005-2015. Standardized test scores and course grades measured different aspects of learning, and higher science grades were related to majoring in science. However, the designation of "science major" is so broad as to be uninformative in a research context; more specificity would be needed to develop academic profiles. From these findings, one can conclude that demographic and cultural factors – rather than academic factors – were more closely related to whether students pursued a science pathway.

In modern China, air pollution has become an essential environmental problem. Over the last 2 years, the air pollution problem, as measured by PM 2.5 (particulate matter) is getting worse. My report aims to carry out a longitudinal data analysis of the air quality index (AQI) in 3 main economic zones in China. Longitudinal data, or repeated measures data, can be viewed as multilevel data with repeated measurements nested within individuals. I arrive at some conclusions about why the 3 areas have different AQI, mainly attributed to factors like population, GDP, temperature, humidity, and other factors like whether the area is inland or by the sea. The residual variance is partitioned into a between-zone component (the variance of the zone-level residuals) and a within-zone component (the variance of the city-level residuals). The zone residuals represent unobserved zone characteristics that affect AQI. In this report, the model building is mainly according to the sequence described by West et al (2007) with respect to the bottom-up procedures and the reference by Singer, J. D., & Willett, J. B (2003) which includes the non-linear situations. This report also compares the quartic curve model with piecewise growth model with respect to this data. The final model I reached is a piece wise model with time-level and zone-level predictors and also with temperature by time interactions. / text

Substance use behaviours have been viewed as the end products of a combination of influences. Numerous theories for working with substance use behaviour utilizing a multi-systemic approach have been proposed. In this project, an effort was made to control for limitations and problems that have often beset previous studies utilizing such an approach. The overall objective of the current project was to test, using a multi-systemic approach, the ability of the family socialization framework to explain the development of substance use patterns in youth and young adults. The central hypothesis of this project was that family socialization factors (contextual factors) affect and predict the development of an offspring’s personality (individual factors) and substance use behaviour. The behavioural genetic approach (i.e., the adoption design) was utilized to examine the genetic and environmental impacts on associations between factors. This project used secondary data analyses of general population data to examine the links between aspects of the family environment, personality, and substance use patterns. The Vancouver Family Survey data set used here contained information on fathers, mothers, and offspring from 405 families (328 biological and 77 adoptive) at two points in time. The development of personality and substance use behaviours over time, and associations with family socialization factors, were examined through three studies. Study 1 focused on the associations between offspring’s perspectives of fathers’ and mothers’ parental socialization and offspring’s polysubstance use. Study 2 investigated the development of addiction-prone personality characteristics and the predictive effects of family socialization and demographic variables on these characteristics. Study 3 explored the subscales of the Addiction-Prone Personality scale: impulsivity/recklessness, sensation seeking, negative view of self, and social deviance proneness. The descriptive characteristics of each subscale and changes in subscale scores over time were investigated. Also examined were transgenerational associations on these subscales, and potential relationships between personality subscales and choice of substance. The results of this project suggest that family socialization may be linked with both substance use behaviour and personality development over time. Nurturing family socialization is negatively associated with the development of addiction-prone personality characteristics. It is also negatively associated with the development of substance use behaviours. These results are consistent with previous studies utilizing a family socialization framework. The findings supporting the family socialization framework are very encouraging for the field of child, youth, and family-related practice. Some of the limitations of the current project, implications of the findings, and future research directions are discussed. / Graduate

The foundation for osteoporosis risk is established during the time periods of childhood, adolescence, and young adulthood, periods of development when bone mass is being accrued rapidly. The relative quantity of bone mass accrued is influenced by both lifestyle and genetic factors. The purpose of this dissertation project was to discover single nucleotide polymorphisms (SNPs) associated with: (1) The rate of hip bone accrual (measured as bone mineral content or BMC) during the adolescent growth spurt, and (2) Total hip bone mass measured as BMC around the age of 19 when the amount of bone accrued is approximately at its peak. Additionally, SNP × longitudinal lifestyle factor (calcium intake per day, vitamin D intake per day, and minutes of moderate to vigorous physical activity (MVPA) per day) multiplicative interaction effects were assessed. Each cohort member’s vector of longitudinal physical activity measurements was summarized as belonging to one of a set of specific trajectory groups using finite mixture modeling. The same was then done for calcium intake and vitamin D intake. The source of the data utilized was the Iowa Bone Development Study (IBDS), which includes genetic and longitudinal bone measurement information. To discover SNPs, a genome-wide association study (GWAS) design was utilized. Females and males were analyzed separately and together. The association between SNPs and the rate of hip bone accrual during the adolescent growth spurt was assessed using linear mixed models controlling for body size, and the association between SNPs and peak hip bone mass was assessed using an ordinary linear regression model, also controlling for body size. Approximately 500,000 SNPs were tested in each GWA analysis; significance was assessed at a familywise error rate of 0.05, the individual test cutoff of which was determined by using SimpleM, a modified Šídák correction. No statistically significant SNPs were detected at the 0.05 familywise error rate threshold established by SimpleM (p < 1.76×10-7); however genes near suggestive SNPs (24 total) were assessed for biological relevance. Of most biological relevance were two suggestive SNPs (rs2051756 and rs2866908, p-values of 1.25×10-6 and 4.28×10-6, respectively) that were detected in an intron of the DKK2 gene through the GWA analysis exploring peak bone mass in females. The DKK2 gene is part of the Wnt signaling pathway and is associated with embryonic development; additionally, it is expressed more highly in osteoarthritic osteoblasts than in normal osteoblasts. No statistically significant results were found from the SNP × lifestyle factor multiplicative interaction effect tests. The potential importance of the DKK2 gene to peak hip bone mass accrual in females should be studied further in order to understand the pathophysiology of this suggested novel association identified during a discovery GWA analysis.

The purpose of this library research thesis is to review the "longitudinal study" in terms of problems and present use. A preliminary search of the literature on longitudinal method revealed problems centering around two areas: (1) definition of "longitudinal study" and (2) practical problems of method itself. The purpose of this thesis then is to explore through a search of books and journals the following questions: 1. How can “longitudinal study” be defined? 2. What problems are inherent in the study of the same individuals over time and how can these problems be solved? A third question which emerges from these two is: 3. How is “longitudinal study” being used today? This thesis differentiates traditional longitudinal study from other methods of study: the cross-sectional study, the time-lag study, the experimental study, the retrospective study, and the study from records. Each of these methods of study is reviewed according to its unique problems and best uses and compared with the longitudinal study. Finally, the traditional longitudinal study is defined as the study: (1) of individual change under natural conditions not controlled by the experimenter, (2) which proceeds over time from the present to the future by measuring the same individuals repeatedly, and (3) which retains individuality of data in analyses. Some problem areas of longitudinal study are delineated which are either unique to this method or especially difficult. The following problems related to planning the study are reviewed: definition of study objectives, selection of method of study, statistical methods, cost, post hoc analysis and replication of the study, time factor in longitudinal study, and the problem of allowing variables to operate freely. Cultural shift and attrition are especially emphasized. The dilemma is examined which is posed by sample selection with its related problems of randomization and generalizability of the study, together with the problems of repeated measurements and selection of control groups. These problems are illustrated with studies from the literature. Not only are these problems delineated cut considerable evidence is shown that we have already started to accumulate data that will permit their solution. This paper presents a number of studies which have considered these problems separately or as a side issue of a study on some other topic. Some recommendations for further research in problem areas are suggested. At the same time that this thesis notes differentiation of the longitudinal study from other studies, it also notes integration of results of longitudinal studies with results of other studies. The tenet adopted here is: scientific knowledge is cumulative and not dependent on one crucial experiment. Trends in recent longitudinal studies are found to be toward more strict observance of scientific protocols and toward limitation of time and objectives of the study. When objectives of the study are well defined and time is limited to only enough for specified change to take place, many of the problems of longitudinal study are reduced to manageable proportions. Although modern studies are of improved quality, longitudinal method is not being sufficiently used today to supply the demand for this type of data. Longitudinal study is necessary to answer some of the questions in developmental psychology. We have no alternative but to continue to develop this important research tool.

In the dissertation, a monotone spline-based nonparametric estimation method is proposed for analyzing longitudinal data with mixture distributions. The innovative and efficient algorithm combining the concept of projected Newton-Raphson algorithm with linear mixed model estimation method is developed to obtain the nonparametric estimation of monotone B-spline functions. This algorithm provides an efficient and flexible approach for modeling longitudinal data monotonically. An iterative 'one-step-forward' algorithm based on the K-means clustering is then proposed to classify mixture distributions of longitudinal data. This algorithm is computationally efficient, especially for data with a large number of underlying distributions. To quantify the disparity of underlying distributions of longitudinal data, we also propose an index measure on the basis of the aggregated areas under the curve (AAUC), which makes no distributional assumptions and fits the theme of nonparametric analysis. An extensive simulation study is conducted to assess the empirical performance of our method under different AAUC values, covariance structures, and sample sizes. Finally, we apply the new approach in the PREDICT-HD study, a multi-site observational study of Huntington Disease (HD), to explore and assess clinical markers in motor and cognitive domains for the purpose of distinguishing participants at risk of HD from healthy subjects.