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Statistical methods for serially correlated zero-inflated proportions Public Deposited

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/j3860946w

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  • Proportion data falling in the continuum (0, 1) are very common in practice. It can also happen that an inflated number of zeros (or ones) occur with proportion data. There are extensive studies of zero-inflated data in the literature. Almost all of them, however, focus on zero-inflated count data. Furthermore, because of sampling or experimental procedures, correlation commonly exists in data collected through time and/or space. The contribution of this research is to develop methods for analyzing zero-inflated proportion data with serial correlation. We first propose multiple hypothesis tests for accessing homogeneity of two zero-inflated Beta populations under the assumption of independence of the observations. Fisher’s method is adopted to combine independent likelihood ratio tests and asymptotic independent score tests to assess the equivalence of the populations. We also develop non-parametric and semi-parametric permutation-based tests for simultaneously comparing two or three features of unknown populations. In Chapter 3, we develop a Hidden Markov Model with zero-inflated Beta emission densities. We show that the standard EM algorithm for Hidden Markov Model parameter estimation can be applied in this case with emission distributions that are mixtures of discrete and continuous parts. In Chapter 4, we develop a generalized linear mixed model with an autoregressive random effect. This model involves the non-standard distribution (zero-inflated Beta) as well as components to account for the dependence among observations. We use Bayesian methodology for generalized linear mixed model parameter estimation and statistical inferences. We examine our methods by simulation and by analyzing a real marine science dataset where interest lies in distinguishing two serially correlated samples. We provide code for simultaneous hypothesis testing and for the Hidden Markov Model under open-source software R, as well as for generalized linear mixed model in WinBUGS.
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