Statistical analysis with missing data

Title page ......Page 1
Preface ......Page 2
Contents ......Page 4
1.1. Missing Data ......Page 14
1.2. A Broad Taxonomy of Methods with Partially Missing Data ......Page 17
1.3. Missing-Data Patterns ......Page 18
1.4. Mechanisms That Lead to Missing Data ......Page 19
1.5. Univariate Samples with Missing Values ......Page 20
1.6. More Than One Variable, but Only One Subject to Nonresponse ......Page 24
1.7. Multivariate Missing Data ......Page 28
References ......Page 29
Problems ......Page 30
2.1. Introduction ......Page 32
2.2. The Exact Least Squares Solution with Complete Data ......Page 33
2.3. The Correct Least Squares Analysis with Missing Data ......Page 35
2.4.1. Yates's Method ......Page 36
2.4.3. Iterating to Find the Missing Values ......Page 37
2.5.1. Useful Properties of Bartlett's Method ......Page 38
2.5.3. The ANCOVA Estimates of Parameters and Missing $Y$ Values ......Page 39
2.5.4. ANCOVA Estimates of the Residual Sums of Squares and the Variance Covariance Matrix of $\hat{\beta}$ ......Page 40
2.6. Least Squares Estimates of Missing Values by ANCOVA Using Only Complete-Data Methods ......Page 41
2.7. Correct Least Squares Estimates of Standard Errors and One Degree of Freedom Sums of Squares ......Page 43
2.8. Correct Least Squares Sums of Squares with More Than One Degree of Freedom ......Page 45
References ......Page 47
Problems ......Page 48
3.1. Introduction ......Page 50
3.2. Complete-Case Analysis ......Page 51
3.3. Available-Case Methods ......Page 52
3.4.1. Introduction ......Page 54
3.4.3. Imputing Conditional Means: Buck's Method ......Page 55
3.4.4. Other Approaches ......Page 58
Problems ......Page 59
4.2. Randomization Inference with Complete Data ......Page 61
4.3. Quasi-Randomization Inference for Data with Missing Values ......Page 64
4.4.1. Weighting Cell Estimators ......Page 66
4.4.2. Choice of Adjustment Cells ......Page 67
4.4.3. Other Weighting Adjustments ......Page 69
4.5.1. Introduction ......Page 71
4.5.2. Mean Imputation ......Page 72
4.5.3. Hot Deck Imputation ......Page 73
4.6. Estimation of Sampling Variance in the Presence of Nonresponse ......Page 78
References ......Page 82
Problems ......Page 83
5.1. The Complete-Data Case ......Page 90
5.2.1. Interval Estimation ......Page 95
5.2.2. Significance Levels for Null Values of $\theta$ ......Page 98
5.3. Likelihood-Based Estimation for Incomplete Data ......Page 99
5.4.1. The Method ......Page 103
5.4.3. Examples ......Page 104
Problems ......Page 106
6.1. Introduction ......Page 108
6.2. Bivariate Normal Data with One Variable Subject to Nonresponse: ML Estimation ......Page 109
6.3.1. Large-Sample Covariance Matrix ......Page 113
6.3.2. Small-Sample Inference for the Parameters ......Page 115
6.3.3. Numerical Illustration ......Page 116
6.4. Monotone Data with More Than Two Variables ......Page 118
6.5. Computation for Monotone Normal Data via the Sweep Operator ......Page 123
6.6. Factorizations for Special Nonmonotone Patterns ......Page 130
References ......Page 135
Problems ......Page 136
7.1. Alternative Computational Strategies ......Page 138
7.2. The EM Algorithm: Background Material ......Page 140
7.3. The E Step and the M Step of EM ......Page 141
7.4. Theory of the EM Algorithm ......Page 145
7.5. The Missing Information ......Page 148
7.6. EM Theory for Exponential Families ......Page 149
References ......Page 150
Problems ......Page 151
8.2.1. The EM Algorithm for Incomplete Multivariate Normal Samples ......Page 153
8.2.2. Estimated Asymptotic Covariance Matrix of $(\theta,\hat{\theta})$. Based on the Information Matrix ......Page 156
8.3. Estimation with a Restricted Covariance Matrix ......Page 157
8.4.1. Linear Regression with Missing Values Confined to the Dependent Variable ......Page 163
8.4.2. Linear Regression with Missing Values in the Predictor Variables ......Page 164
8.5. A General Repeated Measures Model with Missing Data ......Page 168
8.6.2. Autoregressive Models for Univariate Time Series with Missing Values ......Page 173
8.6.3. Kalman Filter Models ......Page 176
References ......Page 179
Problems ......Page 180
9.1. Introduction ......Page 182
9.2.1. Introduction ......Page 183
9.2.2. ML Estimation for Monotone Patterns ......Page 184
9.2.3. Estimating the Precision of the ML Estimates ......Page 181
9.3. ML Estimation for Multinomial Samples with General Patterns of M issing Data ......Page 192
9.4.1. The Complete-Data Case ......Page 196
9.4.2. Loglinear Models for Partially Classified Tables ......Page 198
9.4.3. Goodness-of-Fit Tests for Partially Classified Data ......Page 203
Problems ......Page 204
10.1. Introduction ......Page 206
10.2.1. The Complete-Data Model and Parameter Estimates ......Page 207
10.2.2. ML Estimation with Missing Values ......Page 208
10.2.3. Details of the E-Step Calculations ......Page 211
10.3.3. Loglinear Models for the Cell Probabilities ......Page 214
10.3.4. Modifications to the Algorithm of Section 10.2.2 ......Page 215
10.3.5. Restricted Models for the St. Louis Data ......Page 216
10.4. Relationships with Other EM Algorithms for Special Missing-Data Patterns ......Page 217
10.5.2. Robust Estimation from a Univariate Sample ......Page 220
10.5.3. Robust Estimation of the Mean and Covariance Matrix: Complete Data ......Page 222
10.5.4. Robust Estimation of the Mean and Covariancc Matrix from Data with Missing Values ......Page 223
10.5.5. Extensions of the Model ......Page 226
Problems ......Page 227
11.1. Introduction ......Page 229
11.2. Likelihood Theory for Nonignorable Models ......Page 231
11.3. Models with Known Nonignorable Missing-Data Mechanisms: Grouped and Rounded Data ......Page 232
11.4.1. Maximum Likelihood Estimation for Stochastic Censoring Models ......Page 234
11.4.2. Sensitivity of ML Estimation to Normality ......Page 236
11.4.3. Heckman's Two-Step Fitting Method ......Page 240
11.5. A Predictive Bayesian Approach to Nonresponse Bias ......Page 241
11.6. Nonignorable Models for Categorical Data ......Page 246
References ......Page 252
Problems ......Page 253
12.1. Bayesian Theory with Complete Response ......Page 255
12.2. Bayesian Models for Survey Data with Nonresponse ......Page 258
12.3. Methods Based on Ignorable Nonresponse Models ......Page 261
12.4. Multiple Imputation ......Page 266
12.5. Nonignorable Nonresponse ......Page 270
12.6. Nonignorable Nonresponse with Follow-ups ......Page 273
References ......Page 275
Problems ......Page 276
Author Index ......Page 278
Subject Index ......Page 282