[영문] CONTENTS
1 Introduction = 1
1.1 Clustered observations = 1
1.1.1 Subjects and variables = 4
1.2 Matrices = 4
1.2.1 Matrix operations and properties = 5
1.2.2 Matrix differentiation = 7
1.3 Normal distribution = 8
1.3.1 Conditional distributions = 9
1.4 Ordinary regression = 10
1.4.1 Analysis of variance = 11
1.5 Examples = 12
1.5.1 Commuting times = 12
1.5.2 Blood pressures = 13
1.6 Fixed versus random = 15
1.7 Shrinkage estimation of cluster means = 16
1.8 Sources of variation = 18
1.9 Maximum likelihood = 19
1.9.1 Newton-Raphson method = 20
1.10 The exponential family of distributions = 22
1.11 Bibliographical notes = 23
2 Analysis of covariance with random effects = 26
2.1 Models = 26
2.1.1 The log-likelihood = 28
2.2 Examples = 30
2.2.1 Financial ratios = 30
2.2.2 Rat weights = 32
2.2.3 Monitoring pregnancy = 34
2.2.4 House prices = 36
2.2.5 Validity of an educational test = 38
2.3 Newton-Raphson and Fisher scoring algorithms = 40
2.3.1 Some technical details = 43
2.4 Generalized least squares = 46
2.5 EM algorithm = 47
2.5.1 The E-step = 48
2.5.2 The M-step = 49
2.6 Restricted maximum likelihood = 49
2.7 Balanced design = 52
2.8 The price of ignoring clustering = 53
2.9 Cluster size and information = 56
2.10 Residuals. Model checking = 60
2.10.1 Shrinkage estimators = 61
2.11 Measures of quality of the model fit = 62
2.12 Bibliographical notes = 62
3 Examples. Random-effects models = 64
3.1 Financial ratios = 64
3.2 Rat weights = 74
3.3 Monitoring pregnancy = 78
3.4 House prices = 83
3.5 GRE validity study = 86
3.5.1 Estimation based on the within-department means = 91
4 Random regression coefficients = 94
4.1 Models = 94
4.2 Invariance and linear transformations = 97
4.2.1 Invariance in ordinary regression = 97
4.2.2 Random coefficients and invariance = 98
4.3 Patterns of variation = 100
4.3.1 Categorical variables and variation = 104
4.4 Maximum likelihood estimation = 106
4.4.1 Constrained maximization = 110
4.4.2 Confounding in the variation part = 111
4.5 Longitudinal analysis = 112
4.6 Multivariate regression = 116
4.6.1 Multivariate and longitudinal data = 118
4.7 REML estimation = 123
4.8 Model checking = 124
4.9 General patterns of dependence = 124
4.9.1 General form of elementary-level variance = 126
4.10 Bibliographical notes = 127
5 Examples using random coefficient models = 128
5.1 Financial ratios = 128
5.2 Rat weights = 136
5.3 Pregnancy monitoring = 137
5.4 House prices = 141
5.5 GRE validity study = 145
6 Multiple levels of nesting = 156
6.1 Models = 156
6.1.1 Level-wise equations = 159
6.2 Estimation = 160
6.2.1 Organizing computations = 165
6.3 Model choice = 167
6.4 Restricted maximum likelihood = 169
6.5 Model diagnostics = 170
6.6 Likelihood ratio testing = 171
6.6.1 Independent data? = 172
6.6.2 An irrelevant variable = 173
6.7 More than three levels of nesting = 173
6.8 Hearing loss data = 175
6.9 Model based estimation in surveys = 184
6.9.1 A model based alternative = 187
6.10 Bibliographical notes = 189
7 Factor analysis and structural equations = 190
7.1 Introduction = 190
7.2 Factor analysis = 190
7.3 Maximum likelihood estimation = 192
7.3.1 Exploratory mode = 194
7.4 Two-level factor analysis = 195
7.4.1 Maximum likelihood estimation = 197
7.4.2 Constrained maximization = 201
7.5 Restricted maximum likelihood = 202
7.6 Saturated model (starting solution) = 203
7.7 Inference about <TEX>$$\bar y$$</TEX> = 204
7.8 Measuremement error models = 205
7.9 A two-level measurement error model = 209
7.10 General covariance structures = 212
7.11 Example. Second International Mathematics Study = 212
7.12 Hearing loss data = 215
7.13 Bibliographical notes = 218
8 GLM with random coefficients = 219
8.1 Introduction = 219
8.2 Models for independent observations = 219
8.2.1 Generalized least squares = 223
8.3 Quasilikelihood = 223
8.3.1 Extended quasilikelihood = 224
8.4 Models for clustered observations = 225
8.5 Maximum likelihood estimation = 227
8.5.1 Direct maximization = 228
8.5.2 Approximation of the integrand = 230
8.5.3 Approximate Fisher scoring algorithm = 231
8.6 Information about variation = 235
8.7 Restricted maximum likelihood = 236
8.8 Example. Interviewer variability = 237
8.9 Death rates of Medicare patients = 244
8.10 Bibliographical notes = 248
9 Appendix. Asymptotic theory = 250
9.1 Limited variance of the scoring function = 253
9.2 Asymptotic normality of the scoring vector = 254
9.3 Consistency of MLE = 254
9.4 Asymptotic normality of MLE = 255
References = 257
Index = 266
1 Introduction = 1
1.1 Clustered observations = 1
1.1.1 Subjects and variables = 4
1.2 Matrices = 4
1.2.1 Matrix operations and properties = 5
1.2.2 Matrix differentiation = 7
1.3 Normal distribution = 8
1.3.1 Conditional distributions = 9
1.4 Ordinary regression = 10
1.4.1 Analysis of variance = 11
1.5 Examples = 12
1.5.1 Commuting times = 12
1.5.2 Blood pressures = 13
1.6 Fixed versus random = 15
1.7 Shrinkage estimation of cluster means = 16
1.8 Sources of variation = 18
1.9 Maximum likelihood = 19
1.9.1 Newton-Raphson method = 20
1.10 The exponential family of distributions = 22
1.11 Bibliographical notes = 23
2 Analysis of covariance with random effects = 26
2.1 Models = 26
2.1.1 The log-likelihood = 28
2.2 Examples = 30
2.2.1 Financial ratios = 30
2.2.2 Rat weights = 32
2.2.3 Monitoring pregnancy = 34
2.2.4 House prices = 36
2.2.5 Validity of an educational test = 38
2.3 Newton-Raphson and Fisher scoring algorithms = 40
2.3.1 Some technical details = 43
2.4 Generalized least squares = 46
2.5 EM algorithm = 47
2.5.1 The E-step = 48
2.5.2 The M-step = 49
2.6 Restricted maximum likelihood = 49
2.7 Balanced design = 52
2.8 The price of ignoring clustering = 53
2.9 Cluster size and information = 56
2.10 Residuals. Model checking = 60
2.10.1 Shrinkage estimators = 61
2.11 Measures of quality of the model fit = 62
2.12 Bibliographical notes = 62
3 Examples. Random-effects models = 64
3.1 Financial ratios = 64
3.2 Rat weights = 74
3.3 Monitoring pregnancy = 78
3.4 House prices = 83
3.5 GRE validity study = 86
3.5.1 Estimation based on the within-department means = 91
4 Random regression coefficients = 94
4.1 Models = 94
4.2 Invariance and linear transformations = 97
4.2.1 Invariance in ordinary regression = 97
4.2.2 Random coefficients and invariance = 98
4.3 Patterns of variation = 100
4.3.1 Categorical variables and variation = 104
4.4 Maximum likelihood estimation = 106
4.4.1 Constrained maximization = 110
4.4.2 Confounding in the variation part = 111
4.5 Longitudinal analysis = 112
4.6 Multivariate regression = 116
4.6.1 Multivariate and longitudinal data = 118
4.7 REML estimation = 123
4.8 Model checking = 124
4.9 General patterns of dependence = 124
4.9.1 General form of elementary-level variance = 126
4.10 Bibliographical notes = 127
5 Examples using random coefficient models = 128
5.1 Financial ratios = 128
5.2 Rat weights = 136
5.3 Pregnancy monitoring = 137
5.4 House prices = 141
5.5 GRE validity study = 145
6 Multiple levels of nesting = 156
6.1 Models = 156
6.1.1 Level-wise equations = 159
6.2 Estimation = 160
6.2.1 Organizing computations = 165
6.3 Model choice = 167
6.4 Restricted maximum likelihood = 169
6.5 Model diagnostics = 170
6.6 Likelihood ratio testing = 171
6.6.1 Independent data? = 172
6.6.2 An irrelevant variable = 173
6.7 More than three levels of nesting = 173
6.8 Hearing loss data = 175
6.9 Model based estimation in surveys = 184
6.9.1 A model based alternative = 187
6.10 Bibliographical notes = 189
7 Factor analysis and structural equations = 190
7.1 Introduction = 190
7.2 Factor analysis = 190
7.3 Maximum likelihood estimation = 192
7.3.1 Exploratory mode = 194
7.4 Two-level factor analysis = 195
7.4.1 Maximum likelihood estimation = 197
7.4.2 Constrained maximization = 201
7.5 Restricted maximum likelihood = 202
7.6 Saturated model (starting solution) = 203
7.7 Inference about <TEX>$$\bar y$$</TEX> = 204
7.8 Measuremement error models = 205
7.9 A two-level measurement error model = 209
7.10 General covariance structures = 212
7.11 Example. Second International Mathematics Study = 212
7.12 Hearing loss data = 215
7.13 Bibliographical notes = 218
8 GLM with random coefficients = 219
8.1 Introduction = 219
8.2 Models for independent observations = 219
8.2.1 Generalized least squares = 223
8.3 Quasilikelihood = 223
8.3.1 Extended quasilikelihood = 224
8.4 Models for clustered observations = 225
8.5 Maximum likelihood estimation = 227
8.5.1 Direct maximization = 228
8.5.2 Approximation of the integrand = 230
8.5.3 Approximate Fisher scoring algorithm = 231
8.6 Information about variation = 235
8.7 Restricted maximum likelihood = 236
8.8 Example. Interviewer variability = 237
8.9 Death rates of Medicare patients = 244
8.10 Bibliographical notes = 248
9 Appendix. Asymptotic theory = 250
9.1 Limited variance of the scoring function = 253
9.2 Asymptotic normality of the scoring vector = 254
9.3 Consistency of MLE = 254
9.4 Asymptotic normality of MLE = 255
References = 257
Index = 266