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.

The main objectives of this master thesis are to explore the effectiveness of nonlinear mixed effects model for longitudinal data. Mixed effect models allow to investigate the nature of relationship between the time-varying covariates and the response while also capturing the variations of subjects. I investigate the robustness of the longitudinal models by building up the complexity of the models starting from multiple linear models and ending up with additive nonlinear mixed models. I use a dataset where firms’ leverage are explained by four explanatory variables in addition to a grouping factor that is the firm factor. The models are compared using comparison statistics such as AIC, BIC and by a visual inspection of residuals. Likelihood ratio test has been used in some nested models only. The models are estimated by maximum likelihood and restricted maximum likelihood estimation. The most efficient model is the nonlinear mixed effects model which has lowest AIC and BIC. The multiple linear regression model failed to explain the relation and produced unrealistic statistics

Longitudinal data, which is also known as repeated measures, has grown increasingly within the past years because of its ability to monitor change both within and between subjects. Statisticians in many fields of study have chosen this way of collecting data because it is cost effective and it minimizes the number of subjects required to produce a meaningful outcome. This thesis will explore the world of longitudinal studies to gain a thorough understanding of why this type of collecting data has grown so rapidly. This study will also describe several methods to analyze repeated measures using data collected on the behavior of both adolescent and adult rats. The question of interest is to see if there is a change in the mean response over time and if the covariates (age, bodyweight, gender, and time) influence those changes. After much testing, our data set has a positive nonlinear change in the mean response over time within the age and gender groups. Using a model that included random effects proved to be a better method than models that did not use any random effects. Taking the log of the response variable and using day as the random effect was overall a better fit for our dataset. The transformed model also showed all covariates except for age as being significant.

The individual growth model is a relatively new statistical technique. It is now widely used to examine the trajectories of individuals and groups in repeated measures data. This study examines the association of the receptive vocabulary over time and characteristics of children who were treated for brain tumors. The children undertook different types of treatment from one to any combinations of surgery, radiation and chemotherapy. The individual growth model is used to analyze the longitudinal data and to address the issues behind the data. Results of this study present several factors' influences to the rate of change of PPVT scores. The conclusions of this thesis indicate that the decline in the PPVT scores is associated with gender, age at diagnosis, socioeconomic status, type of treatment and Neurological Predictor Scale.

No description available.

Linear mixed-effects (LME) modeling is a widely used statistical method for analyzing repeated measures or longitudinal data. Such longitudinal studies typically aim to investigate and describe the trajectory of a desired outcome. Longitudinal data have the advantage over cross-sectional data by providing more accuracy for the model. LME models allow researchers to account for random variation among individuals and between individuals. In this project, adolescent health was chosen as a topic of research due to the many changes that occur during this crucial time period as a precursor to overall well-being in adult life. Understanding the factors that influence how adolescents' mental well-being is affected may aid in interventions to reduce the risk of a negative impact. Self-esteem, in particular, has been associated with many components of physical and mental health and is a crucial focus in adolescent health. Research in self-esteem is extensive yet, sometimes inconclusive or contradictory since past research has been cross-sectional in nature. Several factors associated with self-esteem development are considered. Participation in religious services has also been an interest in research for its impact on depression. Depression development and its predictors are evaluated using LME models. Along with this line, this project will address the research problems identified through the following specific topics (i) to investigate the impact of early adolescent anxiety disorders on self-esteem development from adolescence to young adulthood; (ii) to study the role of maternal self-esteem and family socioeconomic status on adolescent self-esteem development through young adulthood; and (iii) to explore the efficacy of religious service attendance in reducing depressive symptoms. These topics present a good introduction to the LME approach and are of significant public health importance. The present study explores varying scenarios of the statistical methods and techniques employed in the analysis of longitudinal data. This thesis provides an overview of LME models and the model selection process with applications. Although this project is motivated by adolescent health study, the basic concepts of the methods introduced have generally broader applications in other fields provided that the relevant technical specifications are met.

abstract: When analyzing longitudinal data it is essential to account both for the correlation inherent from the repeated measures of the responses as well as the correlation realized on account of the feedback created between the responses at a particular time and the predictors at other times. A generalized method of moments (GMM) for estimating the coefficients in longitudinal data is presented. The appropriate and valid estimating equations associated with the time-dependent covariates are identified, thus providing substantial gains in efficiency over generalized estimating equations (GEE) with the independent working correlation. Identifying the estimating equations for computation is of utmost importance. This paper provides a technique for identifying the relevant estimating equations through a general method of moments. I develop an approach that makes use of all the valid estimating equations necessary with each time-dependent and time-independent covariate. Moreover, my approach does not assume that feedback is always present over time, or present at the same degree. I fit the GMM correlated logistic regression model in SAS with PROC IML. I examine two datasets for illustrative purposes. I look at rehospitalization in a Medicare database. I revisit data regarding the relationship between the body mass index and future morbidity among children in the Philippines. These datasets allow us to compare my results with some earlier methods of analyses. / Dissertation/Thesis / Arizona Medicare Data on Rehospitalization / Philippine Data on Children's Morbidity / M.S. Statistics 2012

The development of academic English proficiency and the time it takes to reclassify to fluent English proficient status are key issues in monitoring achievement of English learners. Yet, little is known about academic English language development at the domain-level (listening, speaking, reading, and writing), or how English language development is associated with time-to-reclassification as an English proficient student. Although the substantive findings surrounding English proficiency and reclassification are of great import, the main focus of this dissertation was methodological: the exploration and testing of joint modeling methods for studying both issues. The first joint model studied was a multilevel, multivariate random effects model that estimated the student-specific and school-specific association between different domains of English language proficiency. The second model was a multilevel shared random effects model that estimated English proficiency development and time-to-reclassification simultaneously and treated the student-specific random effects as latent covariates in the time-to-reclassification model. These joint modeling approaches were illustrated using annual English language proficiency test scores and time-to-reclassification data from a large Arizona school district. Results from the multivariate random effects model revealed correlations greater than .5 among the reading, writing and oral English proficiency random intercepts. The analysis of English proficiency development illustrated that some students had attained proficiency in particular domains at different times, and that some students had not attained proficiency in a particular domain even when their total English proficiency score met the state benchmark for proficiency. These more specific domain score analyses highlight important differences in language development that may have implications for instruction and policy. The shared random effects model resulted in predictions of time-to-reclassification that were 97% accurate compared to 80\% accuracy from a conventional discrete-time hazard model. The time-to-reclassification analysis suggested that use of information about English language development is critical for making accurate predictions of the time a student will reclassify in this Arizona school district.

abstract: This paper investigates a relatively new analysis method for longitudinal data in the framework of functional data analysis. This approach treats longitudinal data as so-called sparse functional data. The first section of the paper introduces functional data and the general ideas of functional data analysis. The second section discusses the analysis of longitudinal data in the context of functional data analysis, while considering the unique characteristics of longitudinal data such, in particular sparseness and missing data. The third section introduces functional mixed-effects models that can handle these unique characteristics of sparseness and missingness. The next section discusses a preliminary simulation study conducted to examine the performance of a functional mixed-effects model under various conditions. An extended simulation study was carried out to evaluate the estimation accuracy of a functional mixed-effects model. Specifically, the accuracy of the estimated trajectories was examined under various conditions including different types of missing data and varying levels of sparseness. / Dissertation/Thesis / Masters Thesis Psychology 2016

A mixture model approach for clustering longitudinal data is introduced. The approach, which is based on mixtures of multivariate power exponential distributions, allows for varying tail-weight and peakedness in data. In the longitudinal setting, this corresponds to more or less concentration around the most central time course in a component. The models utilize a modified Cholesky decomposition of the component scale matrices and the associated maximum likelihood estimators are derived via a generalized expectation-maximization algorithm. / Thesis / Master of Science (MSc)