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Browsing by Subject "Functional data analysis"
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Item Novel statistical models for ecological momentary assessment studies of sexually transmitted infections(2016-07-18) He, Fei; Harezlak, Jaroslaw; Liu, Ziyue; Monahan, Patrick; Hensel, Devon J.The research ideas included in this dissertation are motivated by a large sexually trans mitted infections (STIs) study (IU Phone study), which is also an ecological momentary assessment (EMA) study implemented by Indiana University from 2008 to 2013. EMA, as a group of methods used to collect subjects’ up-to-date behaviors and status, can increase the accuracy of this information by allowing a participant to self-administer a survey or diary entry, in their own environment, as close to the occurrence of the behavior as possible. IU Phone study’s high reporting level shows one of the benefits gain from introducing EMA in STIs study. As a prospective study lasting for 84 days, participants in IU Phone study undergo STI testing and complete EMA forms with project-furnished cellular telephones according to the predetermined schedules. At pre-selected eight-hour intervals, participants respond to a series of questions to identify sexual and non-sexual interactions with specific partners including partner name, relationship satisfaction and sexual satisfaction with this partner, time of each coital event and condom use for each event. etc. STIs lab results of all the participants are collected weekly as well. We are interested in several variables related to the risk of infection and sexual or non-sexual behaviors, especially the relationship among the longitudinal processes of those variables. New statistical models and applications are established to deal with the data with complex dependence and sampling data structures. The methodologies covers various of statistical aspect like generalized mixed models, mul tivariate models and autoregressive and cross-lagged model in longitudinal data analysis, misclassification adjustment in imperfect diagnostic tests, and variable-domain functional regression in functional data analysis. The contribution of our work is we bridge the meth ods from different areas with EMA data in the IU Phone study and also build up a novel understanding of the association among all the variables of interest from different perspec tives based on the characteristic of the data. Besides all the statistical analyses included in this dissertation, variety of data visualization techniques also provide informative support in presenting the complex EMA data structure.Item Principal component analysis of hybrid functional and vector data(Wiley, 2021) Jang, Jeong Hoon; Biostatistics and Health Data Science, School of MedicineWe propose a practical principal component analysis (PCA) framework that provides a nonparametric means of simultaneously reducing the dimensions of and modeling functional and vector (multivariate) data. We first introduce a Hilbert space that combines functional and vector objects as a single hybrid object. The framework, termed a PCA of hybrid functional and vector data (HFV-PCA), is then based on the eigen-decomposition of a covariance operator that captures simultaneous variations of functional and vector data in the new space. This approach leads to interpretable principal components that have the same structure as each observation and a single set of scores that serves well as a low-dimensional proxy for hybrid functional and vector data. To support practical application of HFV-PCA, the explicit relationship between the hybrid PC decomposition and the functional and vector PC decompositions is established, leading to a simple and robust estimation scheme where components of HFV-PCA are calculated using the components estimated from the existing functional and classical PCA methods. This estimation strategy allows flexible incorporation of sparse and irregular functional data as well as multivariate functional data. We derive the consistency results and asymptotic convergence rates for the proposed estimators. We demonstrate the efficacy of the method through simulations and analysis of renal imaging data.