Regression modeling: Latent structure, theories and algorithms
Xie, Minge
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https://hdl.handle.net/2142/20609
Description
Title
Regression modeling: Latent structure, theories and algorithms
Author(s)
Xie, Minge
Issue Date
1996
Doctoral Committee Chair(s)
Simpson, Douglas G.
Department of Study
Statistics
Discipline
Statistics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Biology, Biostatistics
Statistics
Environmental Sciences
Language
eng
Abstract
The topics of this thesis stem from two EPA/NISS (Environmental Protection Agency/National Institute of Statistical Sciences) projects, which require the use of available data to make risk assessment, estimate uncertainty and suggest future studies. Based on the heterogeneous and batch correlated nature of the data, the thesis invents some new regression modeling methods, provides theoretical background for these newly developed and some other existed ad hoc modeling techniques, and develops associated algorithms. The modeling techniques include scaled link in the class of generalized linear model, newly developed aspects of conditional and marginal modeling techniques, and latent modeling of nonzero control (baseline) regression model. We have Monte-Carlo-Newton-Raphson Algorithm, Gibbs Sampler, EM algorithm and algorithm to evaluate weighted sum $\chi\sp2$ quantile. The associated theories are provided. In scaled link model, some sensitivity studies are made.
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