Browsing by Subject "Regression analysis."
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Item Bayesian and maximum likelihood methods for some two-segment generalized linear models.(2008-10-14T20:38:46Z) Miyamoto, Kazutoshi.; Seaman, John Weldon, 1956-; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.The change-point (CP) problem, wherein parameters of a model change abruptly at an unknown covariate value, is common in many fields, such as process control, epidemiology, and ecology. CP problems using two-segment regression models, such as those based on generalized linear models, are very flexible and widely used. For two-segment Poisson and logistic regression models, misclassification in the response is well known to cause attenuation of key parameters and other difficulties. How misclassification effects estimation of a CP in such models has not been studied. In this research, we consider the effect of misclassification on CP problems in Poisson and logistic regression. We focus on maximum likelihood and Bayesian methods.Item Bayesian approach to inference and variable selection for misclassified and under-reported response models.(2009-07-01T17:02:34Z) Powers, Stephanie L.; Stamey, James D.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.Response partial missingness is a problem in studies conducted in a variety of disciplines. We investigate the impact ignoring response partial missingness has on determining a subset of significant covariates in non-linear regression. In particular, we consider non-differential misclassification in logistic regression and non-differential under-reporting in Poisson regression. Differential misclassification and differential under-reporting are also addressed but in less detail. We then develop a Bayesian approach to select significant covariates while accounting for the partial missingness. Examples of response partial missingness in which the variable selection method is applied include determining the factors that contribute to whether or not an individual will stop smoking and how many days an individual is absent from work.Item Logistic regression with misclassified response and covariate measurement error: a Bayesian approach.(2007-12-04T19:56:26Z) McGlothlin, Anna E.; Stamey, James D.; Seaman, John Weldon, 1956-; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.In a variety of regression applications, measurement problems are unavoidable because infallible measurement tools may be expensive or unavailable. When modeling the relationship between a response variable and covariates, we must account for the uncertainty that is inherently introduced when one or both of these variables are measured with error. In this dissertation, we explore the consequences of and remedies for imperfect measurements. We consider a Bayesian analysis for modeling a binary outcome that is subject to misclassification. We investigate the use of informative conditional means priors for the regression coefficients. Additionally, we incorporate random effects into the model to accommodate correlated responses. Markov chain Monte Carlo methods are utilized to perform the necessary computations. We use the deviance information criterion to aid in model selection. Next, we consider data where measurements are flawed for both the response and explanatory variables. Our interest is in the case of a misclassified dichotomous response and a continuous covariate that is unobservable, but where measurements are available on its surrogate. A logistic regression model is developed to incorporate the measurement error in the covariate as well as the misclassification in the response. The methods developed are illustrated through an example. Results from a simulation experiment are provided illustrating advantages of the approach. Finally, we expand this model to incorporate random effects, resulting in a generalized linear mixed model for a misclassified response and covariate measurement error. We demonstrate the use of this model using a simulated data set.Item Maximum-likelihood-based confidence regions and hypothesis tests for selected statistical models.(2007-02-07T18:56:44Z) Riggs, Kent Edward.; Young, Dean M.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.We apply maximum likelihood methods for statistical inference on parameters of interest for three different types of statistical models. The models are a seemingly unrelated regression model, a bivariate Poisson regression model, and a model of two inversely-related Poisson rate parameters with misclassified data. The seemingly unrelated regression (SUR) model promotes more efficient estimation as opposed to an ordinary least squares approach (OLS). However, the exact distribution of the SUR estimator is complex and does not yield easily-formed confidence regions of a coefficient parameter. Therefore, one can apply maximum likelihood (ML) asymptotic-based methods to construct a confidence region. Here, we invert a Wald statistic with a size-corrected critical value to construct a confidence region for a coefficient parameter vector. We compare the coverage and ellipsoidal volume properties of three SUR ML-related confidence regions and two SUR two-stage confidence region methods in a Monte Carlo simulation study, and demonstrated how they yield smaller confidence regions as compared to the OLS approach. The bivariate Poisson regression model allows for joint estimation of two Poisson counts as a function of possibly-different covariates. We derive the Wald, score, and likelihood ratio test statistics for testing a single coefficient parameter vector. Also, we derive a Wald statistic for testing the equality of two coefficient parameter vectors. In addition, we derive a confidence interval for the covariance parameter. We then study the size and power of the test statistics and the coverage properties of the confidence interval in a Monte Carlo simulation. Lastly, we consider confidence interval estimation for parameters in a Poisson count model where the rate parameters are inversely related and the data is subject to misclassification. We derive confidence intervals for a Poisson rate parameter by inverting the appropriate Wald, score, and likelihood ratio statistics. We also derive confidence intervals for a misclassification parameter by inverting the appropriate Wald, score, and likelihood ratio statistics. Another interesting parameter is the difference of the two complementary Poisson rate parameters, for which we derive a Wald-type confidence interval. We then examine the coverage and length properties of these confidence intervals via a Monte Carlo simulation study.Item A novel spectropolarimeter for determiation of sucrose and other optically active samples.(2006-07-25T15:34:19Z) Calleja-Amador, Carlos Enrique.; Busch, Kenneth W.; Busch, Marianna A.; Chemistry and Biochemistry.; Baylor University. Dept. of Chemistry and Biochemistry.Polarimetry and spectropolarimetry are important tools in the sugar industry and pharmaceutical research. Polarimetric measurements cannot be performed on colored samples because the presence of color interferes with the final reading. To avoid the effect of color in sugar samples, lead subacetate is added. Its use to decolorize sugar is problematic because lead is a pollutant. In this work, a novel spectropolarimeter based on an ordinary spectrophotometer is described for determination of sucrose and other optically active samples. The instrument has no moving parts, and optical rotation is encoded as apparent absorbance which makes it suitable for colored samples. Background correction before apparent absorbance measurements, combined with multivariate statistical analysis over a wide spectral range, proved efficient to avoid chemical pretreatment of the samples. The instrument showed good performance for sucrose predictions and multivariate enantiomeric discrimination.Item Studies on new approaches of chiral discrimination for chiral analysis by regression modeling of spectral data.(2009-07-01T17:00:13Z) Modzabi, Selorm Kwame.; Busch, Kenneth W.; Busch, Marianna A.; Chemistry and Biochemistry.; Baylor University. Dept. of Chemistry and Biochemistry.Two new approaches of chiral discrimination for enantiomeric composition analysis using isotropic spectroscopic techniques and multivariate regression modeling were investigated. This is in view of the urgent need for rapid and improved strategies for chiral analysis due to the rising preference and demand for chiral drugs. In the first approach, (S)-(+)-1,2-propanediol or the racemic mixture of 2-butanol was reacted with the enantiomers of amino acids or chiral pharmaceutical compounds to form covalent derivatives (diastereomers). To circumvent usually long and cumbersome separation processes required by some chiral analysis techniques, the isotropic UV or fluorescence spectra of solutions of the reaction matrix containing the derivatized enantiomers were subjected to partial least squares regression (PLSR) modeling. PLSR was used as a means of extracting latent or structured information from the spectral data, which might contain interference and/or redundant information from the reaction matrix. Evaluation of the above approach using a test set of samples gave results with root-mean-square errors (RMSEs) of 0.0012-0.042. In the second approach, PLS-1 regression analysis were performed on the UV spectral data of samples containing different compositions of enantiomeric pairs, which were non-covalently discriminated in situ using a multi-functional chiral selected, (S)-(-)-1-phenylethylamine. Enantiomeric compositions of test samples of three amino acids and a carbohydrate determined using the second approach gave RMSEs of 0.006-0.025. In view of the need for micro-scale techniques in analyses such as this, a capillary tube, with a total volume of 95 µL, was custom-designed in the cause of this research for the measurement of fluorescence emission spectra of micro volumes of samples. The custom-designed capillary tube, which has an internal diameter of 1 mm and requires not more than 25 µL of sample solution for spectral measurement, was found to result in higher fluorescence emission intensities than measured using a commercial 10-mm pathlength fluorometer cell. Results of quantitative studies performed using the custom-designed capillary micro cell for spectral measurement were significantly identical to the results of studies conducted using the commercial cell.Item Studies on regression modeling of spectral data as a means of chiral analysis.(2006-10-13T16:32:15Z) Ingle, Jemima Rose.; Busch, Kenneth W.; Busch, Marianna A.; Chemistry and Biochemistry.; Baylor University. Dept. of Chemistry and Biochemistry.The enantiomeric composition of samples was determined using spectroscopy and multivariate regression modeling. Partial least-squares (PLS-1) regression models were developed from the spectral data of solutions containing both enantiomers in varying ratios. The developed regression models were used to predict the enantiomeric composition of unknown validation samples. The predictive ability of the models was evaluated in terms of the root mean square absolute error and the root mean square percent relative error. To address the issue of enantiomeric compositions higher than 0.9, a study was conducted using a large number of samples of phenylalanine and [beta]-cyclodextrin in the upper percentile range, varying from 90-100%. Validation studies with these samples gave absolute errors of 0.0217. In order to study the effects of varying the analyte concentration, two compounds were studied at five concentration levels. Three analyses were performed for each compound. One analysis used only the raw spectral data, one analysis included the concentration as a variable, and one analysis utilized the normalized spectra. Solutions of phenylalanine and [beta]-cyclodextrin resulted in a best absolute error of 0.0316 for the normalized spectral data. Solutions of norephedrine and [beta]-cyclodextrin resulted in a best absolute error of 0.0367 for the raw data. Finally, the spectral data can be used to predict the concentration, the predicted concentration used to normalize the data, and the new normalized data used to predict the enantiomeric composition with an absolute error of less than 0.06 for both compounds. Two simple sugars were tested for their use as chiral auxiliaries. Validation studies with fructose gave absolute errors of 0.0211 (2-octanol) and 0.0308 (phenylalanine); validation studies with glucose gave an absolute error of 0.0184. A comparison study between NIR and UV-visible spectral ranges yielded much poorer results in the NIR (absolute error 0.298) than in the UV-visible (absolute error 0.0308). Finally, a comparison study of 2-octanol and [alpha]-methylbenzylamine with and without a chiral auxiliary was completed. These results varied widely based on solvent and concentration. Modeling studies with impurities did not resemble the spectral behavior of real samples.