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详细说明：2019 Multilevel Modeling using R 2019 Multilevel Modeling using RTaylor francis Taylor Francis Group http://taylorandfrancis.com Multilevel modeling Using r Second edition W. Holmes Finch, Jocelyn E. Bolin and Ken Kelley (CRC) CRC Press Taylor Francis Group Boca Raton London New york CRC Press is an imprint of the Taylor &r Francis Group, an informa business CRC Press Taylor Francis Group 52 Vanderbilt Avenue New York, NY 10017 o 2019 by Taylor Francis Group, llc CRC Press is an imprint of Taylor Francis Group, an Informa business No claim to original U.s. Government works Printed on acid-free paper International Standard Book Number-13: 978-1-1384-8071-1(Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www copyright.com(http://www.copyright.com/)orcontacttheCopyrightClearanceCenter,Inc.(ccc), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Visit the Taylor francis Web site at http://www.taylorandfrancis.com and the crc Press web site at http://www.crcpress.com Contents Authors 1 Linear models Simple linear regression…… Estimating Regression Models with Ordinary Least Squares Distributional Assumptions Underlying Regression Coefficient of determination 22345 Inference for Regression Parameters.................5 Multiple regression Example of Simple Linear Regression by Hand Regression in r 11 Interaction Terms in Regression .14 Categorical Independent variables. .....15 Checking regression assumptions with r 18 Summary 2 An Introduction to Multilevel data Structure. ......................................23 ested Data and Cluster Sampling designs……….23 Intraclass Correlation Pitfalls of ignoring multilevel Data Structure.............29 Multilevel linear models 9 Random Intercept……… Random slopes ∴.31 Centering 34 Basics of parameter estimation with mlms..............35 Maximum likelihood estimation ...................................................36 Restricted Maximum Likelihood Estimation 36 Assumptions Underlying MLMs…… …37 Overview of Two-Level mlms 37 Overview of Three-Level MLMs. ......................................................39 Overview of Longitudinal Designs and Their relationship to MLMs.....40 Summary 41 3 Fitting two- Level models in r………… 43 Simple( Intercept-Only) Multilevel models…… 43 Interactions and Cross-Level Interactions Using R 48 Random Coefficients Models using R.…………………………50 Centering p g redactors Contents Additional Options..... 56 Parameter Estimation method Estimation Controls∴ 56 Comparing model Fit 57 Ime4 and Hypothesis Testing ∴58 Su ummar Note ….61 4 Three-Level and higher models …63 Defining Simple Three-Level Models Using the Ime4 Package...63 Defining Simple Models with More than Three Levels in the Ime4 ackage 70 Random Coefficients models with Three or more Levels in the lme4 Package……… Summary 74 74 5 Longitudinal Data Analysis Using Multilevel Models………………75 The Multilevel longitudinal framework Person Period Data Structure Fitting Longitudinal Models Using the Ime4 Package 78 Benefits of Using Multilevel Modeling for Longitudinal Analysis...82 S ummary.………… 83 Note 83 6 Graphing Data in Multilevel Contexts Plots for Linear models 90 Plotting Nested Data…… 93 Using the Lattice Package…………… ∴94 Plotting Model Results Using the Effects Package 104 ummary…………… ..114 7 Brief Introduction to Generalized Linear models 115 Logistic Regression Model for a Dichotomous Outcome Variable..116 Logistic Regression Model for an Ordinal Outcome Variable....120 Multinomial logistic regression 123 Models for Count data 126 isson Regression 126 Models for Overdispersed Count data ∴128 ummary 131 8 Multilevel Generalized Linear Models (mglms).........133 MGLMs for a Dichotomous Outcome variabl .133 Random Intercept Logistic regression 134 Random Coefficients Logistic Regression....... 137 Inclusion of additional Level-1 and Level-2 Effects in mlm... 139 Contents v11 MGLM for an ordinal outcome variable.................. 143 Random Intercept Logistic Regression 143 MGLM for Count data................................146 Random Intercept Poisson regression .147 Random Coefficient Poisson regression 148 Inclusion of additional Level-2 Effects to the multilevel poisson Regression model...........................150 Summary...........….………………………158 9 Bayesian Multilevel Modeling……………159 MCMCglmm for a Normally Distributed Response Variable 162 Including level-2 Predictors with MCMCglmm 168 User Defined priors …174 MCMCglmm for a dichotomous dependent variable………………,178 MCMCglmm for a Count-Dependent variable.............181 Summary ……187 10 Advanced Issues in Multilevel Modeling 189 Robust Statistics in the Multilevel Context Identifying Potential Outliers in Single-Level Data.......190 Identifying Potential Outliers in Multilevel Data……….19 Identifying Potential Multilevel Outliers Using R........194 Robust and rank-Based estimation for multilevel models 202 Fitting robust and rank-Based Multilevel Models in r……………205 Cauchy ……208 ash........... 208 Contaminated …………209 Multilevel lasso …210 Fitting the Multilevel lasso in r……… 211 Multivariate multilevel models …215 Multilevel generalized Additive models 217 Fitting GAMM using r………………………218 Predicting Level-2 Outcomes with level- Variables…………223 Power Analysis for multilevel models .........................................227 Summary… 231 References 233 Index 247 Taylor francis Taylor Francis Group http://taylorandfrancis.com Authors W. Holmes Finch is the george and frances Ball Distinguished Professor of educational psychology at ball state University, where he teaches courses on factor analysis, structural equation modeling, categorical data analysis regression, multivariate statistics, and measurement to graduate students in psychology and education. Dr. Finch is also an accredited professional stat- istician(PStat). He earned a PhD from the University of South Carolina His research interests include multilevel models, latent variable modeling, methods of prediction and classification and nonparametric multivariate statistics Jocelyn E. Bolin is a professor in the Department of Educational psychology at Ball state University where she teaches courses on introductory and inter mediate statistics, multiple regression analysis, and multilevel modeling to graduate students in social science disciplines. Dr. Bolin is a member of the American Psychological Association, the American Educational Research Association and the american Statistical Association and is an accredited professional statistician(PStat ) She earned a PhD in educational psychol- ogy from Indiana University Bloomington. Her research interests include statistical methods for classification and clustering and use of multilevel modeling in the social sciences Ken Kelley is the Viola D. Hank associate professor of management in the Mendoza College of Business at the University of Notre Dame. Dr. Kelley is also an accredited professional statistician(PStat) and associate editor of Psychological methods. His research involves the development, improvement and evaluation of quantitative methods, especially as they relate to statisti cal and measurement issues in applied research. He is the developer of the MBESS package for the r statistical language and environment

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