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      Multilevel Modeling in Plain Language

       Karen Robson

       David Pevalin

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      © Karen Robson and David Pevalin 2016

      First published 2016

      Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act, 1988, this publication may be reproduced, stored or transmitted in any form, or by any means, only with the prior permission in writing of the publishers, or in the case of reprographic reproduction, in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers.

       Library of Congress Control Number: 2015938248

       British Library Cataloguing in Publication data

      A catalogue record for this book is available from the British Library

      ISBN 978-0-85702-915-7

      ISBN 978-0-85702-916-4 (pbk)

      Editor: Mila Steele

      Assistant editor: James Piper

      Production editor: Ian Antcliff

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      Cover design: Jennifer Crisp

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      Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY

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      About the Authors

      Karen Robsonis Associate Professor of Sociology at York University. Her research areas include the barriers to postsecondary education for marginalized youth, intersectionality as a policy framework and critical race theory. She also has a strong interest in the analysis of large longitudinal data sets to examine issues around social mobility and the transition to postsecondary education. Dr Robson has also written key textbooks in the area of social research methods and the sociology of education, as well as several articles in various sociology journals.David Pevalinis Professor in the School of Health and Human Sciences and Dean of Postgraduate Research and Education at the University of Essex. His research focuses on macro and micro social inequalities in health. He co-authored (with Karen Robson) The Stata Survival Manual (Open University Press, 2009), co-edited (with David Rose) The Researcher’s Guide to the National Statistics Socio-economic Classification (SAGE, 2003), and authored research reports for the Department of Work and Pensions and the Health Development Agency. He has published papers in Journal of Health & Social Behavior, British Journal of Sociology, The Lancet, Public Health and Housing Studies.

      ONE What Is Multilevel Modeling and Why Should I Use It?

      chapter contents

       Mixing levels of analysis 4

       Theoretical reasons for multilevel modeling 6

       What are the advantages of using multilevel models? 7

       Statistical reasons for multilevel modeling 7

       Assumptions of OLS 8Dependence among observations 8Group estimates 12Varying effects across contexts 13Degrees of freedom and statistical significance 16

       Software 17

       How this book is organized 19

      You are probably reading this book because someone – a professor, a supervisor, a colleague, or even an anonymous reviewer – told you that you needed to use multilevel modeling. It sounds pretty impressive. It is perhaps even more impressive that multilevel modeling is known by several other names, including, but not limited to: hierarchical modeling, random coefficients models, mixed models, random effects models, nested models, variance component models, split-plot designs, hierarchical linear modeling, Bayesian hierarchical linear modeling, and random parameter models. It can seem confusing, but it doesn’t need to be.

      This book is for a special type of user who is far more common than experts tend to recognize, or at least acknowledge. This book is for people who want to learn about this technique but are not all that interested in learning all the statistical equations and strange notations that are typically associated with teaching materials in this area. That is not to say we are flagrantly trying to promote bad research, because we are not. We are trying to demystify these types of approaches for people who are intimidated by technical language and mathematical symbols.

      Have you ever been in a lecture or course on a statistical topic and felt you understand everything quite well until the instructor starts putting equations on the slides, and talking through them as though everyone understands them? ‘As this clearly shows … theta … gamma ….’. Have you ever been in a course where several slides of equations are used to justify and demonstrate a procedure and you just didn’t understand? Perhaps you were thinking, ‘These equations must mean something in words. Why can’t they just use the words?’ You might also just want some practical examples that are fully explained in plain language that you may be able to apply to your own research questions. If this sounds like you, then this book is for you. If you are really fond of equations, then we’re afraid that our approach in this book won’t appeal to you.

      Before we get started, we also want to emphasize that this book is not about ‘dumbing down’ complicated subject matter; it’s about making it accessible. We are not endorsing using modeling techniques without understanding them. This leads to sloppy and unscientific analyses that are painful to read. What this book does is unpack these sophisticated techniques and explain them in non-technical language. We assume that you understand the principles of hypothesis testing, sampling, research design, and statistical analysis up to and including ordinary least squares regression (OLS) with interaction terms. The techniques discussed here are just extensions of regression. Really! We do try to keep the jargon to a minimum but, as with all things new, there are some new terms and phrases to get to grips with.

      So, why might you have been told that you need to use multilevel modeling? The chances are that it is because

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