كتاب A User’s Guide to MLwiN

A User’s Guide to MLwiN Version 2.26 by Jon Rasbash, Fiona Steele, William J. Browne & Harvey Goldstein اسس تصميم مركز حرفى Contents Table of Contents viii Introduction ix About the Centre for Multilevel Modelling . . . . . . . . . . . . . . ix Installing the MLwiN software . . . . . . . . . . . . . . . . . . . . . ix MLwiN overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . x Enhancements in Version 2.26 . . . . . . . . . . . . . . . . . . . . . xi Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Exploring, importing and exporting data . . . . . . . . . . . . xi Improved ease of use . . . . . . . . . . . . . . . . . . . . . . . xii MLwiN Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii Compatibility with existing MLn software . . . . . . . . . . . . . . xii Macros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii The structure of the User’s Guide . . . . . . . . . . . . . . . . . . . xiii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Further information about multilevel modelling . . . . . . . . . . . xiv Technical Support . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv 1 Introducing Multilevel Models 1 1.1 Multilevel data structures . . . . . . . . . . . . . . . . . . . . 1 1.2 Consequences of ignoring a multilevel structure . . . . . . . . 2 1.3 Levels of a data structure . . . . . . . . . . . . . . . . . . . . 3 1.4 An introductory description of multilevel modelling . . . . . . 6 2 Introduction to Multilevel Modelling 9 2.1 The tutorial data set . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Opening the worksheet and looking at the data . . . . . . . . 10 2.3 Comparing two groups . . . . . . . . . . . . . . . . . . . . . . 13 2.4 Comparing more than two groups: Fixed effects models . . . . 20 2.5 Comparing means: Random effects or multilevel model . . . . 28 Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 35 3 Residuals 37 3.1 What are multilevel residuals? . . . . . . . . . . . . . . . . . . 37 3.2 Calculating residuals in MLwiN . . . . . . . . . . . . . . . . . 40 3.3 Normal plots . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 45 4 Random Intercept and Random Slope Models 47 v vi CONTENTS 4.1 Random intercept models . . . . . . . . . . . . . . . . . . . . 47 4.2 Graphing predicted school lines from a random intercept model 51 4.3 The effect of clustering on the standard errors of coefficients . 58 4.4 Does the coefficient of standlrt vary across schools? Intro- ducing a random slope . . . . . . . . . . . . . . . . . . . . . . 59 4.5 Graphing predicted school lines from a random slope model . 62 Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 64 5 Graphical Procedures for Exploring the Model 65 5.1 Displaying multiple graphs . . . . . . . . . . . . . . . . . . . . 65 5.2 Highlighting in graphs . . . . . . . . . . . . . . . . . . . . . . 68 Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 77 6 Contextual Effects 79 6.1 The impact of school gender on girls’ achievement . . . . . . . 80 6.2 Contextual effects of school intake ability averages . . . . . . . 83 Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 87 7 Modelling the Variance as a Function of Explanatory Vari- ables 89 7.1 A level 1 variance function for two groups . . . . . . . . . . . 89 7.2 Variance functions at level 2 . . . . . . . . . . . . . . . . . . . 95 7.3 Further elaborating the model for the student-level variance . 99 Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 106 8 Getting Started with your Data 107 8.1 Inputting your data set into MLwiN . . . . . . . . . . . . . . . 107 Reading in an ASCII text data file . . . . . . . . . . . . . . . 107 Common problems that can occur in reading ASCII data from a text file . . . . . . . . . . . . . . . . . . . . . . . . . 108 Pasting data into a worksheet from the clipboard . . . . . . . 109 Naming columns . . . . . . . . . . . . . . . . . . . . . . . . . 110 Adding category names . . . . . . . . . . . . . . . . . . . . . . 111 Missing data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Unit identification columns . . . . . . . . . . . . . . . . . . . . 112 Saving the worksheet . . . . . . . . . . . . . . . . . . . . . . . 112 Sorting your data set . . . . . . . . . . . . . . . . . . . . . . . 112 8.2 Fitting models in MLwiN . . . . . . . . . . . . . . . . . . . . 115 What are you trying to model? . . . . . . . . . . . . . . . . . 115 Do you really need to fit a multilevel model? . . . . . . . . . . 115 Have you built up your model from a variance components model? . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Have you centred your predictor variables? . . . . . . . . . . . 116 Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 116 9 Logistic Models for Binary and Binomial Responses 117 9.1 Introduction and description of the example data . . . . . . . 117 9.2 Single-level logistic regression . . . . . . . . . . . . . . . . . . 119 Link functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 CONTENTS vii Interpretation of coefficients . . . . . . . . . . . . . . . . . . . 120 Fitting a single-level logit model in MLwiN . . . . . . . . . . . 120 A probit model . . . . . . . . . . . . . . . . . . . . . . . . . . 126 9.3 A two-level random intercept model . . . . . . . . . . . . . . . 127 Model specification . . . . . . . . . . . . . . . . . . . . . . . . 127 Estimation procedures . . . . . . . . . . . . . . . . . . . . . . 128 Fitting a two-level random intercept model in MLwiN . . . . . 128 Variance partition coefficient . . . . . . . . . . . . . . . . . . . 131 Adding further explanatory variables . . . . . . . . . . . . . . 134 9.4 A two-level random coefficient model . . . . . . . . . . . . . . 135 9.5 Modelling binomial data . . . . . . . . . . . . . . . . . . . . . 139 Modelling district-level variation with district-level proportions 139 Creating a district-level data set . . . . . . . . . . . . . . . . . 140 Fitting the model . . . . . . . . . . . . . . . . . . . . . . . . . 142 Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 143 10 Multinomial Logistic Models for Unordered Categorical Re- sponses 145 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 10.2 Single-level multinomial logistic regression . . . . . . . . . . . 146 10.3 Fitting a single-level multinomial logistic model in MLwiN . . 147 10.4 A two-level random intercept multinomial logistic regression model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 10.5 Fitting a two-level random intercept model . . . . . . . . . . . 155 Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 159 11 Fitting an Ordered Category Response Model 161 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 11.2 An analysis using the traditional approach . . . . . . . . . . . 162 11.3 A single-level model with an ordered categorical response vari- able . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 11.4 A two-level model . . . . . . . . . . . . . . . . . . . . . . . . . 171 Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 181 12 Modelling Count Data 183 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 12.2 Fitting a simple Poisson model . . . . . . . . . . . . . . . . . 184 12.3 A three-level analysis . . . . . . . . . . . . . . . . . . . . . . . 186 12.4 A two-level model using separate country terms . . . . . . . . 188 12.5 Some issues and problems for discrete response models . . . . 192 Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 192 13 Fitting Models to Repeated Measures Data 193 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 13.2 A basic model . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 13.3 A linear growth curve model . . . . . . . . . . . . . . . . . . . 203 13.4 Complex level 1 variation . . . . . . . . . . . . . . . . . . . . . 206 13.5 Repeated measures modelling of non-linear polynomial growth 206 Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 210 viii CONTENTS 14 Multivariate Response Models 211 14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 14.2 Specifying a multivariate model . . . . . . . . . . . . . . . . . 212 14.3 Setting up the basic model . . . . . . . . . . . . . . . . . . . . 214 14.4 A more elaborate model . . . . . . . . . . . . . . . . . . . . . 219 14.5 Multivariate models for discrete responses . . . . . . . . . . . 222 Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 224 15 Diagnostics for Multilevel Models 227 15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 15.2 Diagnostics plotting: Deletion residuals, influence and leverage 233 15.3 A general approach to data exploration . . . . . . . . . . . . . 242 Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 242 16 An Introduction to Simulation Methods of Estimation 243 16.1 An illustration of parameter estimation with Normally dis- tributed data . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 16.2 Generating random numbers in MLwiN . . . . . . . . . . . . . 251 Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 255 17 Bootstrap Estimation 257 17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 17.2 Understanding the iterated bootstrap . . . . . . . . . . . . . . 258 17.3 An example of bootstrapping using MLwiN . . . . . . . . . . . 259 17.4 Diagnostics and confidence intervals . . . . . . . . . . . . . . . 266 17.5 Nonparametric bootstrapping . . . . . . . . . . . . . . . . . . 266 Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 272 18 Modelling Cross-classified Data 273 18.1 An introduction to cross-classification . . . . . . . . . . . . . . 273 18.2 How cross-classified models are implemented in MLwiN . . . . 275 18.3 Some computational considerations . . . . . . . . . . . . . . . 275 18.4 Modelling a two-way classification: An example . . . . . . . . 277 18.5 Other aspects of the SETX command . . . . . . . . . . . . . . 279 18.6 Reducing storage overhead by grouping . . . . . . . . . . . . . 281 18.7 Modelling a multi-way cross-classification . . . . . . . . . . . . 282 18.8 MLwiN commands for cross-classifications . . . . . . . . . . . 283 Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 284 19 Multiple Membership Models 285 19.1 A simple multiple membership model . . . . . . . . . . . . . . 285 19.2 MLwiN commands for multiple membership models . . . . . . 288 Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 288 Bibliography 289 Index 292 Design Center Harfy pdf
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من الهندسة المدنية - مكتبة كتب الهندسة والتكنولوجيا.