Linear mixed-effects models using R a step-by-step approach Gałecki, Andrzej. creator Burzykowski, Tomasz. text bibliography nyu New York Springer c2013 2013 monographic eng
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xxxii, 542 p. : ill. ; 24 cm.
Preface Methods of Statistical Model Estimation has been written to develop a particular pragmatic viewpoint of statistical modelling. Our goal has been to try to demonstrate the unity that underpins statistical parameter estimation for a wide range of models. We have sought to represent the techniques and tenets of statistical modelling using executable computer code. Our choice does not preclude the use of explanatory text, equations, or occasional pseudo-code. However, we have written computer code that is motivated by pedagogic considerations first and foremost. An example is in the development of a single function to compute deviance residuals in Chapter 4. We defer the details to Section 4.7, but mention here that deviance residuals are an important model diagnostic tool for GLMs. Each distribution in the exponential family has its own deviance residual, defined by the likelihood. Many statistical books will present tables of equations for computing each of these residuals. Rather than develop a unique function for each distribution, we prefer to present a single function that calls the likelihood appropriately itself. This single function replaces five or six, and in so doing, demonstrates the unity that underpins GLM. Of course, the code is less efficient and less stable than a direct representation of the equations would be, but our goal is clarity rather than speed or stability. This book also provides guidelines to enable statisticians and researchers from across disciplines to more easily program their own statistical models using R. R, more than any other statistical application, is driven by the contributions of researchers who have developed scripts, functions, and complete packages for the use of others in the general research community-- Part I Introduction -- 1. Introduction -- 2. Case Studies -- 3. Data Exploration -- Part II Linear Models for Independent Observations 4. Linear Models with Homogeneous Variance -- 5. Fitting Linear Models with Homogeneous Variance: The lm() and gls() Functions -- 6. ARMD Trial: Linear Model with Homogeneous Variance -- 7. Linear Models with Heterogeneous Variance -- 8. Fitting Linear Models with Heterogeneous Variance: The gls() Function -- 9. ARMD Trial: Linear Model with Heterogeneous Variance -- Part III Linear Fixed-effects Models for Correlated Data -- 10. Linear Model with Fixed Effects and Correlated Errors -- 11. Fitting Linear Models with Fixed Effects and Correlated Errors: The gls() Function -- 12. ARMD Trial: Modeling Correlated Errors for Visual Acuity -- Part VI Linear Mixed-effects Models -- 13. Linear Mixed-Effects Model -- 14. Fitting Linear Mixed-Effects Models: The lme()Function -- 15. Fitting Linear Mixed-Effects Models: The lmer() Function -- 16. ARMD Trial: Modeling Visual Acuity -- 17. PRT Trial: Modeling Muscle Fiber Specific-Force -- 18. SII Project: Modeling Gains in Mathematics Achievement-Scores -- 19. FCAT Study: Modeling Attainment-Target Scores -- 20. Extensions of the RTools for Linear Mixed-Effects Models-- Acronyms-- References-- Function Index-- Subject Index. Andrzej Gałecki and Tomasz Burzykowski. Includes bibliographical references and indexes. Linear models (Statistics) R (Computer program language) G151 000SA.062 9781461438991 (alk. paper) ISI Library 120613 20150115123311.0 17344489