❞ 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




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