Thesis (Ph. D.)--University of Washington, 2002. / Vita. Includes bibliographical references (p. 129-135).

The analysis of proportions is interesting and noteworthy in that there are no commonly accepted regression models for analyzing proportions; indeed, researchers most often use ordinary least squares to estimate the parameters of a linear regression model for proportional data. Such an approach, however, violates several assumptions of the Classical Linear Regression Model. This report outlines the general linear model and the problems associated with using this approach to model proportions and considers a variety of alternate approaches that researchers have taken to model proportions. These alternatives include transforming the dependent variable, a censored regression (Tobit) model, a Fractional Logit model, and Beta Regression. All of the approaches considered are implemented in a case study analyzing Rice party difference scores in the 93rd to 108th Congress. A comparison of the results from each approach confirms the findings of other researchers that Beta regression is the most preferred approach for modeling proportions. / text

In nonlinear regression statistical analysis based upon interpretation of the parameter estimates may be quite different from linear regression. An important point is that for finite samples the least squares estimator (LSE) is not unbiased. nor is it a minimum variance estimator: for nonlinear models, the LSE has these properties under some assumptions only asymptotically and many statistical conclusions are based upon this asymptotic theorie. But there are a lot of nonlinear models where the asymptotic properties are poorly approximated for finite samples. Assessing the nonlinearity can show us if statistical tests the justification of which rests on the assumption of linearity are valid. Better parameterizations and experimental design are good possibilities to reduce the non-neglible nonlinearitv of certain models. A case study shows that experimental design can reduce the nonlinearity considerably. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

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In 1963 – 1965, a large-scale health screening survey was undertaken in Sweden and this data set was linked to data from the national cause of death register. The data set involved more than 60,000 participants whose age at death less than 80 years. During the follow-up period until 2007, a total of 437 (338 males and 99 females) participants died from aortic aneurysm. The survival analysis, continuation ratio model, and logistic regression were applied in order to identify significant risk factors. The Cox regression after stratification for AGE revealed that SEX, Blood Diastolic Pressure (BDP), and Beta-lipoprotein (BLP) were the most significant risk factors, followed by Cholesterol (KOL), Sialic Acid (SIA), height, Glutamic Oxalactic Transaminase, Urinary glucose (URIN_SOC), and Blood Systolic Pressure (BSP). Moreover, SEX and BDP were found as risk factors in almost every age group. Furthermore, BDP was strongly significant in both male and female subgroup.   The data set was divided into two sets: 70 percent for the training set and 30 percent for the test set in order to find the best technique for predicting aortic aneurysm. Five techniques were implemented: the Cox regression, the continuation ratio model, the logistic regression, the back-propagated artificial neural network, and the decision tree. The performance of each technique was evaluated by using area under the receiver operating characteristic curve. In our study, the continuation ratio and the logistic regression outperformed among the other techniques.

Regression models with a scalar response and a functional predictor have been extensively studied. One approach is to approximate the functional predictor using basis function or eigenfunction expansions. In the expansion, the coefficient vector can either be fixed or random. The random coefficient vector is also known as random effects and thus the regression models are in a mixed effects framework. The random effects provide a model for the within individual covariance of the observations. But it also introduces an additional parameter into the model, the covariance matrix of the random effects. This additional parameter complicates the covariance matrix of the observations. Possibly, the covariance parameters of the model are not identifiable. We study identifiability in normal linear mixed effects models. We derive necessary and sufficient conditions of identifiability, particularly, conditions of identifiability for the regression models with a scalar response and a functional predictor using random effects. We study the regression model using the eigenfunction expansion approach with random effects. We assume the random effects have a general covariance matrix and the observed values of the predictor are contaminated with measurement error. We propose methods of inference for the regression model's functional coefficient. As an application of the model, we analyze a biological data set to investigate the dependence of a mouse's wheel running distance on its body mass trajectory.

In many fields of statistical application the fundamental task is to quantify the association between some explanatory variables or covariates and a response or outcome variable through a suitable regression model. The accuracy of such quantification depends on how precisely we measure the relevant covariates. In many instances, we can not measure some of the covariates accurately, rather we can measure noisy versions of them. In statistical terminology this is known as measurement errors or errors in variables. Regression analyses based on noisy covariate measurements lead to biased and inaccurate inference about the true underlying response-covariate associations. In this thesis we investigate some aspects of measurement error modelling in the case of binary logistic regression models. We suggest a flexible parametric approach for adjusting the measurement error bias while estimating the response-covariate relationship through logistic regression model. We investigate the performance of the proposed flexible parametric approach in comparison with the other flexible parametric and nonparametric approaches through extensive simulation studies. We also compare the proposed method with the other competitive methods with respect to a real-life data set. Though emphasis is put on the logistic regression model the proposed method is applicable to the other members of the generalized linear models, and other types of non-linear regression models too. Finally, we develop a new computational technique to approximate the large sample bias that my arise due to exposure model misspecification in the estimation of the regression parameters in a measurement error scenario.

For longitudinal data where the response and time-dependent predictors within each individual are measured at distinct time points, traditional longitudinal models such as generalized linear mixed effects models or marginal models cannot be directly applied. Instead, some preprocessing such as smoothing is required to temporally align the response and predictors. In Chapter 2, we propose a binning method, which results in equally spaced bins of time for both the response and predictor(s). Hence, after incorporating binning, traditional models can be applied. The proposed binning approach was applied on a longitudinal hemodialysis study to look for possible contemporaneous and lagged effects between occurrences of a health event (i.e., infection) and levels of a protein marker of inflammation (i.e., C-reactive protein). Both Poisson mixed effects models and zero-inflated Poisson (ZIP) mixed effects models were applied to the subsequent binned data, and some important biological findings about contemporaneous and lagged associations were uncovered. In addition, a simulation study was conducted to investigate various properties of the binning approach. In Chapter 3, asymptotic properties have been derived for the fixed effects association parameter estimates following binning, under different data scenarios. In addition, we propose some leave-one-subject-out cross-validation algorithms for bin size selection. In Chapter 4, in order to identify levels of a predictor that might be indicative of recently occurred event(s), we propose a generalized mixed effects regression tree (GMRTree) based method which estimates the tree by standard tree method such as CART and estimates the random effects by a generalized linear mixed effects model. One of the main steps in this method was to use a linearization technique to change the longitudinal count response into a continuous surrogate response. Simulations have shown that the GMRTree method can effectively detect the underlying tree structure in an applicable longitudinal dataset, and has better predictive performance than either a standard tree approach without random effects or a generalized linear mixed effects model, assuming the underlying model indeed has a tree structure. We have also applied this method to two longitudinal datasets, one from the aforementioned hemodialysis study and the other from an epilepsy study.

Cancer is a dangerous disease causing the most deaths in the world today and around 550,000 deaths in America per year (American Cancer Society). Larynx cancer data was recorded by Kardaun (1983). The data was collected at a Dutch hospital during 1970 – 1978. Ninety male adults with cancer of larynx were involved into the study. Each patient was divided into one of four groups depending on his or her illness condition. The data also recorded their age, lifetime, and year of entering the research. These are common factors as factors of other cancer data. The purpose of this thesis is to apply proportional hazard regression model, additive hazard regression model, censored quantiles regression model, and censored linear regression model to analyze the above larynx cancer data and find the best regression model of data by using each method. Comparison and suggestion for which method should be used in specific situation are also made. Some related topics are also mentioned so we can have resource for future study. Key words: right censoring, proportional risk model, additive risk model, quantiles regression model, linear regression model.

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