Format:
Online-Ressource
,
v.: digital
Edition:
Online-Ausg. Springer eBook Collection. Mathematics and Statistics Electronic reproduction; Available via World Wide Web
ISBN:
1280391391
,
9781441971708
,
9781280391392
Series Statement:
Statistics for Biology and Health
Content:
This text provides, in a non-technical language, a unified treatment of regression models for different outcome types, such as linear regression, logistic regression, and Cox regression. This is done by focusing on the many common aspects of these models, in particular the linear predictor, which combines the effects of all explanatory variables into a function which is linear in the unknown parameters. Specification and interpretation of various choices of parametrization of the effects of the covariates (categorical as well as quantitative) and interaction among these are elaborated upon. The merits and drawbacks of different link functions relating the linear predictor to the outcome are discussed with an emphasis on interpretational issues, and the fact that different research questions arise from adding or deleting covariates from the model is emphasized in both theory and practice. Regression models with a linear predictor are commonly used in fields such as clinical medicine, epidemiology, and public health, and the book, including its many worked examples, builds on the authors' more than thirty years of experience as teachers, researchers and consultants at a biostatistical department. The book is well-suited for readers without a solid mathematical background and is accompanied by Web pages documenting in R, SAS, and STATA, the analyses presented throughout the text. The authors are since 1978 affiliated with the Department of Biostatistics, University of Copenhagen. Per Kragh Andersen is professor; he is a co-author of the Springer book 'Statistical Models Based on Counting Processes,' and has served on editorial boards on several statistical journals. Lene Theil Skovgaard is associate professor; she has considerable experience as teacher and consultant, and has served on the editorial board of Biometrics.
Note:
Includes bibliographical references (p. [483]-486) and index
,
""Preface""; ""Contents""; ""1 Introduction""; ""1.1 Introductory examples and types of outcome""; ""1.1.1 Introductory examples Example 1.1. Body mass index and vitamin D status""; ""1.1.2 Types of outcome""; ""1.2 Covariates""; ""1.2.1 Categorical covariates""; ""1.2.2 Quantitative covariates""; ""1.3 Link functions""; ""1.4 Building a regression model""; ""1.4.1 The linear predictor and the link function""; ""1.4.2 Regression models and their interpretation""; ""1.5 Further examples""; ""1.6 The scope of this book and how to read it""; ""2 Statistical models""
,
""2.1 Random variables and probability""""2.1.1 The Bernoulli distribution""; ""2.1.2 The Binomial distribution""; ""2.1.3 The Poisson distribution""; ""2.1.4 The Normal distribution""; ""2.1.5 Other common distributions""; ""2.1.6 Conditional probability""; ""2.2 Descriptive statistics""; ""2.2.1 Binary outcome""; ""2.2.2 Quantitative outcome""; ""2.2.3 Survival time outcome""; ""2.3 Statistical inference""; ""2.3.1 Estimation""; ""2.3.2 Model checking""; ""2.3.3 Hypothesis testing""; ""2.3.4 The likelihood function""; ""2.4 Exercises""; ""3 One categorical covariate""
,
""3.1 Binary covariate""""3.1.1 Quantitative outcome:""; ""3.1.2 Binary outcome: (2Ã?2)-tables and the chi-square test""; ""3.1.3 Survival time outcome: the 2-sample logrank test""; ""3.2 Categorical covariate with more than two levels""; ""3.2.1 Quantitative outcome: One-way analysis of variance""; ""3.2.2 Binary outcome: The 2""; ""3.2.3 Survival time outcome: The (k + 1)-sample logrank test""; ""3.3 Exercises""; ""4 One quantitative covariate""; ""4.1 Linear effect""; ""4.1.1 Quantitative outcome: Simple linear regression""; ""4.1.2 Binary outcome: Simple logistic regression""
,
""4.1.3 Survival time outcome: Simple Cox regression""""4.2 Nonlinear effect""; ""4.2.1 Dividing the covariate range into intervals Models with piecewise constant effects""; ""4.2.2 Polynomials""; ""4.2.3 Other nonlinear models with a linear predictor""; ""4.3 Exercises""; ""5 Multiple regression, the linear predictor""; ""5.1 Two covariates: Models without interaction""; ""5.1.1 Two categorical covariates""; ""5.1.2 One categorical and one quantitative covariate""; ""5.1.3 Two quantitative covariates""; ""5.2 Two covariates: Models with interaction""; ""5.2.1 Two categorical covariates""
,
""5.2.2 One categorical and one quantitative covariate Linear effect of the quantitative covariate: The vitamin D study""""5.2.3 Two quantitative covariates Two linear effects""; ""5.2.4 Saving degrees-of-freedom""; ""5.3 Several covariates""; ""5.3.1 Models without higher-order interactions""; ""5.3.2 Models with higher-order interactions""; ""5.4 Matched studies""; ""5.5 Exercises""; ""6 Model building: From purpose to conclusion""; ""6.1 General principles for model selection""; ""6.1.1 Identification of covariates""; ""6.1.2 Model diagrams""; ""6.1.3 Initial model building""
,
""6.1.4 Strategy of analysis""
,
Electronic reproduction; Available via World Wide Web
Additional Edition:
ISBN 1280390956
Additional Edition:
ISBN 9781441971692
Language:
English
Keywords:
Lineare Regression
DOI:
10.1007/978-1-4419-7170-8
URL:
Volltext
(lizenzpflichtig)
Bookmarklink
