Alastair H. Leyland Peter P. Groenewegen Multilevel Modelling for Public Health and Health Services Research Health in Context Multilevel Modelling for Public Health and Health Services Research Alastair H. Leyland • Peter P. Groenewegen Multilevel Modelling for Public Health and Health Services Research Health in Context Alastair H. Leyland MRC/CSO Social and Public Health Sciences Unit University of Glasgow Glasgow, UK Peter P. Groenewegen Netherlands Institute for Health Services Research (NIVEL) Utrecht, The Netherlands ISBN 978-3-030-34799-4 ISBN 978-3-030-34801-4 (eBook) https://doi.org/10.1007/978-3-030-34801-4 © The Author(s) 2020. This book is an open access publication. Open Access This book is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this book are included in the book's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the book's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a speci fi c statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional af fi liations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Endorsements “ Leyland and Groenewegen have a long international experience in teaching together multilevel modelling to public health and health services researchers. Their experience makes the structure of this book and accompanying tutorials especially worthwhile for those aiming to gain a practical introduction to multilevel analysis. ” — Juan Merlo , Professor of Social Epidemiology, Lund University “ Comprehensive and insightful. A must for anyone interested in applications of multilevel modelling to population health. ” — S. (Subu) V. Subramanian , Professor of Population Health and Geography, Harvard University Preface This book is designed as a practical introduction to multilevel analysis (MLA). It is borne out of a course that we have taught over the past 20 years for an international audience of public health and health services researchers of varied statistical ability. The practical side of the book is in the use of the data sets that are supplied with the book. The book contains full guidance for the analysis of these real-life data sets. The level of statistical sophistication that we expect from the readership is what we usually found among early stage PhD researchers in the health and healthcare fi eld: a basic understanding of ordinary least squares and logistic regression. This is not to say that our target audience is restricted to PhD researchers; anyone who has discovered the need for MLA in health research with these basic statistical skills should be able to bene fi t from this book. The contents of the book are divided into four parts. The fi rst part introduces the theoretical, conceptual and methodological background to MLA (Chaps. 1 – 4). The second part is devoted to the statistical background (Chaps. 5 and 6). Part III takes the fi nal step towards application as we discuss aspects of the modelling process and pay attention to the presentation of research that uses MLA (Chaps. 7 – 10). With Part IV, we move to practical applications using example data sets. This part also introduces and discusses the use of MLwiN, the statistical package that is used with the example data sets. We work through three example data sets and introduce readers to the use of the software and the application of the ideas discussed in the previous chapters (Chaps. 11 – 13). Our suggested use of this book is as part of the learning process for health researchers, whether this is through formal teaching (Chaps. 1 – 10 can be thought of as a series of lectures with Chaps. 11 – 13 forming the basis of practical work) or through self-training. Either way we would urge the user to work through all chapters sequentially. Throughout the book we refer to further sources of informa- tion, whether these relate to the methodology introduced or to substantive examples or applications. This should further assist the users in the contextualisation of their own research. We advise readers to download and read articles that relate to examples that they fi nd interesting. With this book you will be able to download vii training material comprising not just the datasets analysed in Chaps. 11 – 13 but also a free training version of the multilevel modelling software MLwiN that can be used with these datasets. (The restriction of the software is in terms of the datasets that can be analysed and not in the analytic capabilities of the software; users are not restricted to the analyses presented in this book but may analyse these datasets in other ways.) The MLwiN website is at https://www.bristol.ac.uk/cmm/software/ mlwin/. The teaching version of the software is available from https://www.bristol. ac.uk/cmm/software/mlwin/download/. On completion of this textbook Multilevel Modelling for Public Health and Health Services Research: Health in Context , the user will have an understanding of the most important concepts of multilevel analysis — the relevance of different contexts, different hierarchical data structures, the difference between variables and levels and so on. We take the user through the formulation of hypotheses for multilevel models to the modelling process and the presentation of results and encourage the reader to start applying these ideas to their own data straight away. Readers who want to explore the background of multilevel analysis in greater depth or want to read more about more complicated models than those detailed in this book are referred to the following books among others: – de Leeuw J, Meijer E (eds) (2008) Handbook of multilevel analysis. Springer, New York – Gelman A, Hill J (2007) Data analysis using regression and multilevel/hierarchi- cal models. Cambridge University Press, Cambridge – Goldstein H (2010) Multilevel statistical models, 4th edn Wiley, Chichester – Hox JJ (2002) Multilevel analysis: techniques and applications. Lawrence Erlbaum Associates – Leyland AH, Goldstein H (2001) Multilevel modelling of health statistics. Wiley, Chichester – Snijders TAB, Bosker RJ (2012) Multilevel analysis, 2nd edn. Sage, Los Angeles Glasgow, UK Alastair H. Leyland Utrecht, The Netherlands Peter P. Groenewegen viii Preface Acknowledgements The Social and Public Health Sciences Unit is core funded by the Medical Research Council (MC_UU_12017/13) and the Scottish Government Chief Scientist Of fi ce (SPHSU13). NIVEL (the Netherlands Institute for Health Services Research) is core funded by the Ministry of Health, Welfare and Sports. ix Contents Part I Theoretical, Conceptual and Methodological Background 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Importance of MLA for Research in Health and Care . . . . . . . . . . . . . 4 The Scope of Public Health and Health Services Research . . . . . . . . . . 4 Research and Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2 Health in Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Relationships Between the Macro and Micro Levels . . . . . . . . . . . . . . 14 Micro Level: Behaviour of Patients and Providers . . . . . . . . . . . . . . . . 18 The Behaviour of Healthcare Providers . . . . . . . . . . . . . . . . . . . . . 19 The Behaviour of Patients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Patient – Provider Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 From Macro to Micro Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 What Contexts Are Relevant? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 From Micro to Macro Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 The Use of “ League Tables ” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3 What Is Multilevel Modelling? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Methodological Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Why Use Multilevel Modelling? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Aggregate Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Individual Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Separate Individual Analyses Within Each Higher Level Unit . . . . . 33 Individual-Level Analysis with Dummy Variables . . . . . . . . . . . . . 33 xi What Is a Multilevel Model? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 What Is a Level? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 How Many Units Do We Need at Each Level? . . . . . . . . . . . . . . . . . . 38 Hypotheses That Can Be Tested with Multilevel Analysis . . . . . . . . . . 39 Hypotheses About Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Individual-Level Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Context Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Cross-Level Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4 Multilevel Data Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Strict Hierarchies: The Basic Model . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Multistage Sampling Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Evaluating Community Interventions and Cluster Randomised Trials . . 52 Designs Including Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Multiple Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Non-hierarchical Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Cross-Classi fi ed Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Multiple Membership Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Correlated Cross-Classi fi ed Model . . . . . . . . . . . . . . . . . . . . . . . . . 58 Other Multilevel Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Pseudo-levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Incomplete Hierarchies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Part II Statistical Background 5 Graphs and Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Ordinary Least Squares (Single-Level) Regression . . . . . . . . . . . . . . . 72 Random Intercept Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Random Slope Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Three-Level Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Heteroscedasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Fixed Effects Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Rankings and Institutional Performance . . . . . . . . . . . . . . . . . . . . . . . 85 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 6 Apportioning Variation in Multilevel Models . . . . . . . . . . . . . . . . . 89 Variance Partitioning for Continuous Responses . . . . . . . . . . . . . . . . . 90 Variance Partitioning for Multilevel Logistic Regression . . . . . . . . . . . 90 Variance Partitioning for Models with Three or More Levels . . . . . . . . 91 xii Contents Interpretation of Variances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Zero Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Multilevel Power Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Software for Multilevel Power Calculations . . . . . . . . . . . . . . . . . . . . 99 Population Average and Cluster-Speci fi c Estimates . . . . . . . . . . . . . . . 100 Omitting a Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Part III The Modelling Process and Presentation of Research 7 Context, Composition and How Their In fl uences Vary . . . . . . . . . . 107 Context or Composition? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 Using Multilevel Modelling to Investigate Compositional and Contextual Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Model M0: Null Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Model M1: Individual Social Capital . . . . . . . . . . . . . . . . . . . . . . . 111 Model M2: Neighbourhood Social Capital . . . . . . . . . . . . . . . . . . . 112 Model M3: Individual and Neighbourhood Social Capital . . . . . . . . 113 Model M4: Individual and Neighbourhood Social Capital and Their Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Random Slopes and Cross-Level Interactions . . . . . . . . . . . . . . . . . . . 115 Impact of Compositional and Contextual Variables on the Variances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Model Speci fi cation and Model Interpretation . . . . . . . . . . . . . . . . . . . 118 Sources of Error Affecting the Estimation of Contextual Effects . . . . . . 119 Lack of Variation in the Contextual Variable . . . . . . . . . . . . . . . . . 119 Precision of Estimates and Study Design . . . . . . . . . . . . . . . . . . . . 120 Selection Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 Confounding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 Information Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Model Speci fi cation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 8 Ecometrics: Using MLA to Construct Contextual Variables from Individual Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Problems with Simple Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . 124 Single Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Composite Variables: The Traditional Method . . . . . . . . . . . . . . . . . . 126 Composite Variables: A Simple Multilevel Model . . . . . . . . . . . . . . . . 127 Ecometric Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Application of the Ecometric Approach . . . . . . . . . . . . . . . . . . . . . . . 132 Comparison of the Traditional and Ecometric Approach . . . . . . . . . . . 134 Contents xiii Further Ecometric Properties of the Scale . . . . . . . . . . . . . . . . . . . . . . 135 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 9 Modelling Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 De fi ne the Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Measurement Level and Distribution of the Dependent Variable . . . . . . 142 The Baseline Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Exploratory Research and Hypothesis Testing . . . . . . . . . . . . . . . . . . . 143 Context and Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Modelling the Effects of Higher Level Characteristics . . . . . . . . . . . . . 145 Random Effects at Higher Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 Interpreting the Results in the Light of Common Assumptions . . . . . . . 147 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 10 Reading and Writing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Critical Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 What Is the Research Question? . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Which Levels Can Be Distinguished Theoretically? . . . . . . . . . . . . 154 What Is the Structure of the Actual Data Used? . . . . . . . . . . . . . . . 155 What Statistical Model Was Used? . . . . . . . . . . . . . . . . . . . . . . . . 157 What Was the Modelling Strategy? . . . . . . . . . . . . . . . . . . . . . . . . 158 Does the Paper Report the Intercept Variation at Different Levels? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Cross-Level Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 What Are the Shortcomings and Strong Points of the Article? . . . . . 161 Writing Up Your Own Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 The Introduction or Background Section . . . . . . . . . . . . . . . . . . . . 161 The Methods Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 The Results Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 The Conclusion and Discussion Section . . . . . . . . . . . . . . . . . . . . . 165 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Part IV Tutorials with Example Datasets 11 Multilevel Linear Regression Using MLwiN: Mortality in England and Wales, 1979 – 1992 . . . . . . . . . . . . . . . . . . . . . . . . . . 173 Introduction to the Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 Introduction to MLwiN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 Opening a Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 Names Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 xiv Contents Data Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 Graph Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Closing Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Model Speci fi cation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 Creating New Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 Equations Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Fitting the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Variance Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 A 2-Level Variance Components Model . . . . . . . . . . . . . . . . . . . . . 187 Sorting the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 The Hierarchy Viewer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 Adding a Further Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Interpreting the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 Residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 Predictions Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 Model Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 Adding More Fixed Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 Intervals and Tests Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Random Coef fi cients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Random Slopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Variance Function Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 Higher-Level Residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 Complex Level 1 Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 A Poisson Model: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Setting Up a Generalised Linear Model in MLwiN . . . . . . . . . . . . . . . 236 The Offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 Non-linear Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 Model Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 Predictions and Con fi dence Envelopes . . . . . . . . . . . . . . . . . . . . . . . . 248 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 12 Multilevel Logistic Regression Using MLwiN: Referrals to Physiotherapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 Multilevel Logistic Regression Model . . . . . . . . . . . . . . . . . . . . . . . . 256 Example: Variation in the GP Referral Rate to Physiotherapy . . . . . . . 256 The Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Model Set-Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 Non-linear Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 Model Interpretation and Model Building . . . . . . . . . . . . . . . . . . . . . . 263 A Note on Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 Further Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 Contents xv 13 Untangling Context and Composition . . . . . . . . . . . . . . . . . . . . . . . 271 The Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 Structure of the Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 Estimating the Null Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 Fixed Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 Additional Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 xvi Contents About the Authors Alastair H. Leyland, PhD , is professor of Population Health Statistics and associate director of the MRC/CSO Social and Public Health Sciences Unit at the University of Glasgow in Scotland, UK. He has been working in public health for over 30 years and is currently the advisor to the Research Pillar of the European Public Health Association. His research interests are in the measurement and analysis of inequalities in health, particularly using administrative data, and in the evaluation of the effects of social policies on health. Peter P. Groenewegen, PhD , is a senior researcher and former director at NIVEL, Netherlands Institute for Health Services Research, in Utrecht. He is emeritus professor at Utrecht University in the departments of Sociology and of Human Geography. Peter was trained as a sociologist and wrote his PhD on the spatial distribution of general practitioners in the Netherlands. His research interests are in the area of international comparisons of health systems with a focus on primary health care, medical practice variations, and environment and health. xvii Part I Theoretical, Conceptual and Methodological Background Chapter 1 Introduction Abstract In this chapter we describe in general terms what we mean by the equivalent terms multilevel analysis (MLA) or multilevel modelling. We place MLA in the context of public health and health services research. Most of our readers will be working in this fi eld, and this book is speci fi cally written for them. As public health and health services research is an applied research, it is strongly oriented towards solving practical problems in health, healthcare and health policy. Therefore we will also discuss the relationships between research on the one hand and policy and practice on the other. We end with some conclusions on the relevance of MLA for public health and health services research. Keywords Multilevel analysis · Public health research · Health services research · Health policy · Health system organisation · Inequalities in health The fact that we are willing to consider ‘ Health in context ’ means that people ’ s health depends on the context in which they live. This is a basic credo of social medicine and public health (Rosen 1993). Not only health and well-being but also health behaviour and healthcare utilisation depend partly on people ’ s personal resources and partly on shared resources and circumstances — in other words, their context. People ’ s personal resources can be their personal stock of health — their health capital in other words — as well as other more tangible resources. So if we talk about health, we are implicitly talking about two distinct levels: people and their context. MLA makes it possible to handle this reality of health operating at different levels. Although MLA is a statistical method, it would be too narrow to restrict the teaching of multilevel modelling to statistical methods courses. Statistics is a tool to solve problems, so the methods should not be seen to be isolated from the problems themselves. In other words, if we want to understand MLA, we should also pay attention to the substantive fi elds of public health and health services research and to the origins of their research problems. Moreover, in sociology, a lot of attention has been paid to the relationships between different levels, from the micro level of individual people, via intermediate levels of families, schools and work © The Author(s) 2020 A. H. Leyland, P. P. Groenewegen, Multilevel Modelling for Public Health and Health Services Research , https://doi.org/10.1007/978-3-030-34801-4_1 3 organisations, to the macro social levels of cities or countries. Social science helps us to conceptualise these different levels and to decide which levels are relevant for certain research problems. Therefore, it is not only statistics that we will be dealing with in this book; theoretical considerations about levels and about human behaviour in context are equally important. We should add a third pillar to this book: study design and methodology. Between theory and statistics stand the study design and method- ology — the way we design our research and collect data to test our theoretical ideas. Importance of MLA for Research in Health and Care MLA is important for research in the fi elds of public health and healthcare for two reasons. The fi rst is substantive: many of the problems studied involve different levels or contexts. To analyse such problems with state-of-the-art methods, MLA is the most appropriate statistical tool. Secondly, research in the fi elds of public health and healthcare increasingly uses MLA. It is therefore important that even if you do not apply MLA yourself, you are able to understand research that uses MLA. Nowadays it is nearly impossible to understand, appreciate and critically appraise published articles in our fi eld of research if you are not acquainted with MLA. The pioneering development of MLA methodology has been in education where researchers have been interested in studies examining how pupil outcomes (such as examination scores) are related to both the characteristics of the pupils themselves and those of the schools (Aitken and Longford 1986; Snijders and Bosker 2012). The use of MLA has since been widespread in the overlapping fi elds of health services research, epidemiology and public health (Diez-Roux 2000; Leyland and Groenewegen 2003; Merlo et al. 2005a, b, c, 2006; Rice and Leyland 1996; Subramanian et al. 2003), assisted by the development of specialist multilevel software and the addition of multilevel capabilities to common statistical packages (de Leeuw and Kreft 2001). The educational example may be transferred to a public health context in several ways. For example, when studying outcomes in hospitalised patients, interest focuses on the roles played by both hospitals and patients. The individual and the workplace may both in fl uence absence from work due to sickness. Regional differences in incidence of heart disease may re fl ect differences in the composition of populations and in the success of local health promotion programmes. The Scope of Public Health and Health Services Research The intended readership of this book consists of researchers with an interest in public health and health services research. We will now brie fl y discuss the scope of these two areas of research and will show that they are often related. Public health research studies the conditions in which populations can be healthy. Health at group or population level is the focal point of interest. According to the Lalonde model 4 1 Introduction (1974), the health of the population is in fl uenced by social, psychological, biological and healthcare determinants (see Fig. 1.1). In some form, this model has been at the root of public health policy in numerous countries. Health and health inequality at a group or population level are based on some aggregation or transformation of the health status of the people who form the group or population. The determinants of health can be both individual level and group or population level. Psychological determinants of health are typically individual characteristics. However, in the form of shared ideas and common psychological traits, they could build a collective characteristic, such as a group mentality. Biological characteristics can be individual, but they can also be shared characteristics of larger populations of genetically related individuals or those exposed to the same environmental hazard. Healthcare deter- minants are typically group or population-level characteristics determined by the administration or government, whether this is at the local (e.g. municipality) or national level. Social in fl uences will also often operate through various higher (population) levels such as family, peer group or neighbourhood. Compared to public health research, the scope of health services research places more emphasis on healthcare and healthcare utilisation than on health per se (Fig. 1.2). Health services research focuses on the relationships between demand for care and supply of care, as in fl uenced by the structure and institutions of the healthcare system. It is a multidisciplinary fi eld of scienti fi c investigation that studies social influences health service utilisation Health (healthy population) biological/ genetic influences psychological/ behavioural influences Fig. 1.1 In fl uences on population health Supply of health care Structure Institutions Health care utilisation Health Demand for health care Fig. 1.2 In fl uences on healthcare utilisation (and health) The Scope of Public Health and Health Services Research 5 how social factors, fi nancing systems, organisational structures and processes, health technologies and personal behaviours affect access to healthcare, the quality and cost of healthcare and ultimately our health and well-being. Its research domains are individuals, families, organisations, institutions, communities and populations (AcademyHealth 2005). Quality of care is an important research area, and this can be de fi ned in relation to structures, processes and outcomes in the provision of health services (Donabedian 2003). Healthcare utilisation is traditionally the centre of attention in health services research. It is in fl uenced by the demand for healthcare. The demand for healthcare is partly based on health — people with health problems tend to use health services — but not completely. There are also social and psychological in fl uences on healthcare utilisation. People differ individually in the way they cope with ill health, and the threshold at which they will visit a healthcare professional also differs. There are also social in fl uences, such as family or group norms as to when to invoke the help of others. The supply of healthcare also in fl uences healthcare utilisation. The availabil- ity of hospital facilities, for example, in fl uences their utilisation. And the organisa- tion of healthcare facilities also affects utilisation; supply of and demand for healthcare exert their in fl uence within an institutional context. This is the way in which the system is organised and funded. Whether or not general practitioners (GPs) have a gatekeeping role in fl uences the utilisation, not only of the services that GPs provide but also of specialist services. Financial accessibility, in terms of organisation in systems of insurance or other funding of healthcare, also in fl uences utilisation. Again we can say that these in fl uences can be individual characteristics but often they are group- or population-level characteristics. Countries differ regard- ing the structure of their healthcare system, regions differ in the supply and mix of services, and social groups differ in how quickly they invoke healthcare. Figures 1.1 and 1.2 also show the relationship between public health research and health services research. In public health research, the utilisation of health services is one of the determinants of health whilst in health services research one of the in fl uences on healthcare utilisation is ill-health, and one of the outcomes of health service utilisation is the creation of health. Both public health research that does not take healthcare into account as an input and health services research that does not take health into account as an outcome can exist. This brief discussion of the scope of public health and health services research has drawn our attention to different in fl uences. Researchers with different educa- tional backgrounds can study each of these in fl uences on their own. Public health and health services research is populated by researchers who studied medicine, health sciences, epidemiology, psychology, sociology, statistics, human geography, economics, political science, etc. (and we must still have forgotten some). This diversity is the reason why we discuss rather broad substantive and theoretical issues in the fi rst two chapters of this book. This ensures that we have a common understanding of the kind of research we are doing before proceeding to the statistical approach. 6 1 Introduction