Logistic Regression with Missing Values in the Covariates - Werner Vach

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Résumé :
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.

Sommaire:
1. Introduction.- I: Logistic Regression with Two Categorical Covariates.- 2. The complete data case.- 3. Missing value mechanisms.- 4. Estimation methods.- 5. Quantitative comparisons: Asymptotic results.- 6. Quantitative comparisons: Results from finite sample size simulation studies.- 7. Examples.- 8. Sensitivity analysis.- II: Generalizations.- 9. General regression models with missing values in one of two covariates.- 10. Generalizations for more than two covariates.- 11. Missing values and subsampling.- 12. Further Examples.- 13. Discussion.- Appendices.- A. 1 ML Estimation in the presence of missing values A.2 The EM algorithm.- B. 1 Explicit representation of the score function of ML Estimation and the information matrix in the complete data case.- B. 2 Explicit representation of the score function of ML Estimation and the information matrix.- B. 3 Explicit representation of the quantities used for the asymptotic variance of the PML estimates.- B. 4 Explicit representation of the quantities used for the asymptotic variance of the estimates of the Filling method.- References.- Notation Index.