A user's guide to MLwiN Jon Rasbash William Browne Harvey Goldstein Min Yang Ian Plewis Michael Healy Geoff Woodhouse David Draper Ian Langford Toby Lewis Version 2.1d for use with MLwiN 1.10 Centre for Multilevel Modelling Institute of Education University of London A user's guide to MLwiN 2000. Jon Rasbash, William Browne, Harvey Goldstein, Min Yang, Ian Plewis, Michael Healy, Geoff Woodhouse, David Draper, Ian Langford and Toby Lewis. No part of this document may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, for any purpose other than the owner's personal use, without the prior written permission of one of the copyright holders. ISBN: 085473 6123 Printed in the United Kingdom A user's guide to MLwiN by Jon Rasbash William Browne Harvey Goldstein Min Yang Ian Plewis Michael Healy Geoff Woodhouse David Draper* Ian Langford** Toby Lewis** Centre for Multilevel Modelling Institute of Education University of London *University of Bath **University of East Anglia Version 2.1d July 2002 CONTENTS Introduction ................................................................................................................................................1 About the Centre for Multilevel Modelling.............................................................................................1 Installing the MLwiN software.................................................................................................................2 Enhancements in Version 1.1 ..................................................................................................................4 MLwiN Help........................................................................................................................................4 Compatibility with existing MLn software .........................................................................................4 Macros ................................................................................................................................................4 Prerequisites and the structure of the user's guide ...................................................................................4 Acknowledgements .................................................................................................................................5 Further information about multilevel modelling......................................................................................5 Technical Support....................................................................................................................................6 Chapter 1. Introducing multilevel models................................................................................................6 Multilevel data structures ........................................................................................................................6 Consequences of ignoring a multilevel structure.....................................................................................7 Levels of a data structure.........................................................................................................................8 An introductory description of multilevel modelling ............................................................................10 PART 1. FITTING TWO LEVEL MODELS....................................................... 15 Chapter 2: Random Intercept and Random Slope Models...................................................................15 Opening the worksheet and looking at the data .....................................................................................15 Setting up a variance components multilevel model .............................................................................20 Estimation..............................................................................................................................................27 Graphing Predictions: Variance components.........................................................................................29 A Random slopes model........................................................................................................................35 Graphing predictions : random slopes ...................................................................................................39 What you should have learnt from this chapter .....................................................................................40 Chapter 3: Residuals................................................................................................................................43 What are multilevel residuals?...............................................................................................................43 Calculating residuals in MLwiN.............................................................................................................45 What you should have learnt from this chapter .....................................................................................48 Chapter 4. Graphical procedures for exploring the model...................................................................49 Displaying graphs..................................................................................................................................49 What you should have learnt from this chapter .....................................................................................62 Chapter 5: Contextual effects..................................................................................................................63 Pupil gender and school gender effects .................................................................................................64 Contextual effects..................................................................................................................................69 What you should have learnt from this chapter .....................................................................................75 Chapter 6: Modelling the variance as a function of explanatory variables.........................................77 Complex variation at level 1..................................................................................................................80 What you should have learnt from this chapter .....................................................................................88 Chapter 7: Getting started with your data and dealing with problems...............................................89 Inputting your data set into MLwiN .......................................................................................................89 Inputting via files..............................................................................................................................89 Common problems with ASCII data input........................................................................................90 Pasting data from the clipboard .............................................................................................................91 Naming Columns...................................................................................................................................92 Category Names ....................................................................................................................................92 Missing Data..........................................................................................................................................93 Level Identification Columns ................................................................................................................94 Saving the worksheet.............................................................................................................................94 Fitting Models in MLwiN.......................................................................................................................94 What are you trying to model?..........................................................................................................94 Do you really need to fit a multilevel model?...................................................................................95 Have you sorted your dataset?...............................................................................................................95 Have you built up your model from a variance components model?.....................................................98 Have you centered your predictor variables?.........................................................................................98 What you should have learnt from this chapter .....................................................................................98 PART 2. MORE COMPLEX MODELS............................................................. 99 Chapter 8: Modelling binary and general Binomial responses ............................................................99 Binary response models.........................................................................................................................99 A dataset on political voting..................................................................................................................99 Specifying a simple binary response model.........................................................................................101 Quasilikelihood – MQL/PQL methods................................................................................................104