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Parameter Estimation For The Logistic Regression Model With Errors In Covariate
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Book Synopsis Parameter Estimation for the Logistic Regression Model with Errors in Covariate by : Huyen D. Nguyen
Download or read book Parameter Estimation for the Logistic Regression Model with Errors in Covariate written by Huyen D. Nguyen and published by . This book was released on 2021 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a logistic regression model, when the covariate is measured with error, the estimators of the regression coefficient parameters can be biased. We propose a method for estimating parameters of a logistic regression with case-control data, when the covariate is subject to measurement error. The density of the covariate is estimated by using the deconvolution kernel density estimation. The parameters of the regression are estimated by the integrated squared distance based on the log ratio of the estimated density. We show the consistency and the asymptotic normality of the proposed estimators. Simulation study shows the superiority of the proposed method in different sample sizes and measurement error magnitudes scenario. The methodology is applied to estimating the relationship of systolic blood pressure and the presence of coronary heart disease.
Book Synopsis Logistic Regression with Missing Values in the Covariates by : Werner Vach
Download or read book Logistic Regression with Missing Values in the Covariates written by Werner Vach and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many areas of science a basic task is to assess the influence of several factors on a quantity of interest. If this quantity is binary logistic, regression models provide a powerful tool for this purpose. This monograph presents an account of the use of logistic regression in the case where missing values in the variables prevent the use of standard techniques. Such situations occur frequently across a wide range of statistical applications. The emphasis of this book is on methods related to the classical maximum likelihood principle. The author reviews the essentials of logistic regression and discusses the variety of mechanisms which might cause missing values while the rest of the book covers the methods which may be used to deal with missing values and their effectiveness. Researchers across a range of disciplines and graduate students in statistics and biostatistics will find this a readable account of this.
Book Synopsis Adjustment for Measurement Error by :
Download or read book Adjustment for Measurement Error written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A variety of complications arise when imperfect measurements, W, are observed in place of a true variable of interest, X. In the context of linear and non-linear regression models where X is a covariate, regression parameter estimators obtained when W is substituted for X may be substantially biased. Many strategies for correcting for measurement error depend on the specific modeling or regression context and can be intractable in highly non-linear models. In addition, previous methods often assume that the measurement error is normally distributed. In our work, we focus on re-creating the distribution of X from the observed W, either as the primary quantity of interest or as a means to improving parameter estimation. We obtain estimators of X for which the first M sample moments are unbiased for the corresponding moments of X. We investigate the benefit of substituting these estimates in density estimation, logistic regression and survival models. We compare this moment adjusted imputation (MAI) approach to existing alternatives in applications with normally distributed measurement error. We identify an important case of chi-square measurement error and propose a variety of methods to adjust for it, including a version of MAI. We find that MAI is often superior and has the advantage that once the estimates of X are obtained, they can be substituted in any model, including complicated non-linear models.
Book Synopsis Dealing with Measurement Error in Covariates with Special Reference to Logistic Regression Model: a Flexible Parametric Approach by :
Download or read book Dealing with Measurement Error in Covariates with Special Reference to Logistic Regression Model: a Flexible Parametric Approach written by and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Parameter Estimation in Nonlinear Regression with Covariate Measurement Error by : Mary Margaret Dowling
Download or read book Parameter Estimation in Nonlinear Regression with Covariate Measurement Error written by Mary Margaret Dowling and published by . This book was released on 1991 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Measurement Error by : John P. Buonaccorsi
Download or read book Measurement Error written by John P. Buonaccorsi and published by CRC Press. This book was released on 2010-03-02 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last 20 years, comprehensive strategies for treating measurement error in complex models and accounting for the use of extra data to estimate measurement error parameters have emerged. Focusing on both established and novel approaches, Measurement Error: Models, Methods, and Applications provides an overview of the main techniques and illu
Book Synopsis Covariate Measurement Error in Logistic Regression by : L. A. Stefanski
Download or read book Covariate Measurement Error in Logistic Regression written by L. A. Stefanski and published by . This book was released on 1985 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a logistic regression model when covariates are subject to measurement error the naive estimator, obtained by regressing on the observed covariates, is asymptotically biased. This document introduces a bias-adjusted estimator and two estimators appropriate for normally distributed measurement errors; a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency. The four proposals are studied asymptotically under conditions which are appropriate when the measurement error is small. A small Monte-Carlo study illustrates the superiority of the measurement-error estimators in certain situations. Additional keywords: mathematical models.
Book Synopsis Statistical Analysis of Measurement Error Models and Applications by : Philip J. Brown
Download or read book Statistical Analysis of Measurement Error Models and Applications written by Philip J. Brown and published by American Mathematical Soc.. This book was released on 1990 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measurement error models describe functional relationships among variables observed, subject to random errors of measurement. This book treats general aspects of the measurement problem and features a discussion of the history of measurement error models.
Book Synopsis Case-control Studies with Errors in Covariates by : Raymond J. Carroll
Download or read book Case-control Studies with Errors in Covariates written by Raymond J. Carroll and published by . This book was released on 1991 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: We devise methods for estimating the parameters of a prospective logistic model with dichotomous response D and arbitrary covariates X from case-control data when these covariates are measured with error. We suppose that some fraction of the cases and controls provide only the error-prone covariate measurements, W (the "incomplete" or "reduced" data), whereas some of the cases and controls provide measurements on X and W (the "complete" data). We assume a measurement error density with a finite set of parameters a, namely fwlxD(wlx, d, a), and nondifferential error is treated as a special case of this model, fwlx(wlx, a). Our algorithm estimates both the logistic parameters and a from a pseudolikelihood. Because empirical distribution functions are used in place of needed distributions in the pseudolikelihoods, the required asymptotic theory is more elaborate than for pseudolikelihoods based on substitution for a finite number of nuisance parameters. We also examine computationally simpler methods under the assumptions that the disease is rare and that errors are nondifferential. Estimates of m(W) = E(X l W) are substituted for X in the logistic model when X is not available. Such estimates of m(W) can be obtained from the complete data described above or from an independent validation study. If measurements on X are not available, m(W) can still be estimated from replicated W measurements in some circumstances. A final approach uses approximate logistic regression techniques and is appropriate when a more accurate approximation is required than obtained by simply substituting m(W) for X. Asymptotic theory is presented for each of these procedures, and examples are used to illustrate the calculations.
Book Synopsis Logistic Regression Models by : Joseph M. Hilbe
Download or read book Logistic Regression Models written by Joseph M. Hilbe and published by CRC Press. This book was released on 2009-05-11 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logistic Regression Models presents an overview of the full range of logistic models, including binary, proportional, ordered, partially ordered, and unordered categorical response regression procedures. Other topics discussed include panel, survey, skewed, penalized, and exact logistic models. The text illustrates how to apply the various models t
Book Synopsis Logistic Regression Models when Covariates are Measured with Errors by :
Download or read book Logistic Regression Models when Covariates are Measured with Errors written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dimension Reduction in Semiparametric Measurement Error Models with Errors in Covariates by : Ronald Keith Knickerbocker
Download or read book Dimension Reduction in Semiparametric Measurement Error Models with Errors in Covariates written by Ronald Keith Knickerbocker and published by . This book was released on 1993 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Semiparametric Estimation in Logistic Measurement Error Models by : Raymond J. Carroll
Download or read book Semiparametric Estimation in Logistic Measurement Error Models written by Raymond J. Carroll and published by . This book was released on 1989 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: We describe semiparametric estimation and inference in a logistic regression model with measurement error in the predictors. The particular measurement error model consists of a primary data set in which only the response Y and a fallible surrogate W of the true predictor X are observed, plus a smaller validation data set for which (Y, X, W) are observed. Except for the underlying assumption of a logistic model in the true predictor, no parametric distributional assumptions are made about the true predictor or its surrogate. We develop a semiparametric parameter estimate of the logistic regression parameter which is asymptotically normally distributed and computationally feasible. The estimate relies on kernel regression techniques. For scalar predictors, by a detailed analysis of the mean-squared error of the parameter estimate, we obtain a representation for an optimal bandwidth.
Book Synopsis Resampling Approach for Estimating Prediction Error and for Adjusting Logistic Regression Models for Covariate Measurement Error by : Wei Li
Download or read book Resampling Approach for Estimating Prediction Error and for Adjusting Logistic Regression Models for Covariate Measurement Error written by Wei Li and published by . This book was released on 2002 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Regularized Regression in Generalized Linear Measurement Error Models with Instrumental Variables -variable Selection and Parameter Estimation by : Lin Xue
Download or read book Regularized Regression in Generalized Linear Measurement Error Models with Instrumental Variables -variable Selection and Parameter Estimation written by Lin Xue and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regularization method is a commonly used technique in high dimensional data analysis. With properly chosen tuning parameter for certain penalty functions, the resulting estimator is consistent in both variable selection and parameter estimation. Most regularization methods assume that the data can be observed and precisely measured. However, it is well-known that the measurement error (ME) is ubiquitous in real-world datasets. In many situations some or all covariates cannot be observed directly or are measured with errors. For example, in cardiovascular disease related studies, the goal is to identify important risk factors such as blood pressure, cholesterol level and body mass index, which cannot be measured precisely. Instead, the corresponding proxies are employed for analysis. If the ME is ignored in regularized regression, the resulting naive estimator can have high selection and estimation bias. Accordingly, the important covariates are falsely dropped from the model and the redundant covariates are retained in the model incorrectly. We illustrate how ME affects the variable selection and parameter estimation through theoretical analysis and several numerical examples. To correct for the ME effects, we propose the instrumental variable assisted regularization method for linear and generalized linear models. We showed that the proposed estimator has the oracle property such that it is consistent in both variable selection and parameter estimation. The asymptotic distribution of the estimator is derived. In addition, we showed that the implementation of the proposed method is equivalent to the plug-in approach under linear models, and the asymptotic variance-covariance matrix has a compact form. Extensive simulation studies in linear, logistic and poisson log-linear regression showed that the proposed estimator outperforms the naive estimator in both linear and generalized linear models. Although the focus of this study is the classical ME, we also discussed the variable selection and estimation in the setting of Berkson ME. In particular, our finite sample simulation studies show that in contrast to the estimation in linear regression, the Berkson ME may cause bias in variable selection and estimation. Finally, the proposed method is applied to real datasets of diabetes and Framingham heart study.
Book Synopsis Marginal Models in Analysis of Correlated Binary Data with Time Dependent Covariates by : Jeffrey R. Wilson
Download or read book Marginal Models in Analysis of Correlated Binary Data with Time Dependent Covariates written by Jeffrey R. Wilson and published by Springer Nature. This book was released on 2020-09-28 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a concise point of research topics and reference for modeling correlated response data with time-dependent covariates, and longitudinal data for the analysis of population-averaged models, highlighting methods by a variety of pioneering scholars. While the models presented in the volume are applied to health and health-related data, they can be used to analyze any kind of data that contain covariates that change over time. The included data are analyzed with the use of both R and SAS, and the data and computing programs are provided to readers so that they can replicate and implement covered methods. It is an excellent resource for scholars of both computational and methodological statistics and biostatistics, particularly in the applied areas of health.
Book Synopsis Estimating Logistic Regression Models for Correlated Binary Outcomes by : Adolfo Navarro
Download or read book Estimating Logistic Regression Models for Correlated Binary Outcomes written by Adolfo Navarro and published by . This book was released on 1998 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
