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Preface | |
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Acknowledgments | |
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Acronyms | |
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Introduction | |
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Advantages of Longitudinal Studies | |
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Challenges of Longitudinal Data Analysis | |
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Some General Notation | |
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Data Layout | |
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Analysis Considerations | |
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General Approaches | |
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The Simplest Longitudinal Analysis | |
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Change Score Analysis | |
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Analysis of Covariance of Post-test Scores | |
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ANCOVA of Change Scores | |
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Example | |
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Summary | |
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ANOVA Approaches to Longitudinal Data | |
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Single-Sample Repeated Measures ANOVA | |
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Design | |
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Decomposing the Time Effect | |
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Trend Analysis-Orthogonal Polynomial Contrasts | |
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Change Relative to Baseline-Reference Cell Contrasts | |
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Consecutive Time Comparisons-Profile Contrasts | |
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Contrasting Each Timepoint to the Mean of Subsequent Timepoints-Helmert Contrasts | |
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Contrasting Each Timepoint to the Mean of Others-Deviation Contrasts | |
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Multiple Comparisons | |
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Multiple-Sample Repeated Measures ANOVA | |
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Testing for Group by Time Interaction | |
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Testing for Subject Effect | |
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Contrasts for Time Effects | |
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Orthogonal Polynomial Partition of SS | |
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Compound Symmetry and Sphericity | |
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Sphericity | |
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Illustration | |
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Summary | |
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MANOVA Approaches to Longitudinal Data | |
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Data Layout for ANOVA versus MANOVA | |
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MANOVA for Repeated Measurements | |
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Growth Curve Analysis-Polynomial Representation | |
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Extracting Univariate Repeated Measures ANOVA Results | |
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Multivariate Test of the Time Effect | |
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Tests of Specific Time Elements | |
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MANOVA of Repeated Measures- s Sample Case | |
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Extracting Univariate Repeated Measures ANOVA Results | |
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Multivariate Tests | |
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Illustration | |
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Summary | |
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Mixed-Effects Regression Models for Continuous Outcomes | |
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Introduction | |
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A Simple Linear Regression Model | |
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Random Intercept MRM | |
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Incomplete Data Across Time | |
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Compound Symmetry and Intraclass Correlation | |
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Inference | |
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Psychiatric Dataset | |
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Random Intercept Model Example | |
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Random Intercept and Trend MRM | |
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Random Intercept and Trend Example | |
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Coding of Time | |
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Example | |
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Effect of Diagnosis on Time Trends | |
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Matrix Formulation | |
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Fit of Variance-Covariance Matrix | |
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Model with Time-Varying Covariates | |
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Within and Between-Subjects Effects for Time-Varying Covariates | |
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Time Interactions with Time-Varying Covariates | |
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Estimation | |
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ML Bias in Estimation of Variance Parameters | |
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Summary | |
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Mixed-Effects Polynomial Regression Models | |
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Introduction | |
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Curvilinear Trend Model | |
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Curvilinear Trend Example | |
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Orthogonal Polynomials | |
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Model Representations | |
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Orthogonal Polynomial Trend Example | |
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Translating Parameters | |
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Higher-Order Polynomial Models | |
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Cubic Trend Example | |
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Summary | |
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Covariance Pattern Models | |
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Introduction | |
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Covariance Pattern Models | |
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Compound Symmetry Structure | |
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First-Order Autoregressive Structure | |
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Toeplitz or Banded Structure | |
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Unstructured Form | |
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Random-Effects Structure | |
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Model Selection | |
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Example | |
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Summary | |
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Mixed Regression Models with Autocorrelated Errors | |
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Introduction | |
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MRMs with AC Errors | |
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AR(1) Errors | |
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MA(1) Errors | |
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ARMA(1,1) Errors | |
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Toeplitz Errors | |
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Nonstationary AR(1) Errors | |
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Model Selection | |
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Example | |
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Summary | |
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Generalized Estimating Equations (GEE) Models | |
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Introduction | |
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Generalized Linear Models (GLMs) | |
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Generalized Estimating Equations (GEE) models | |
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Working Correlation Forms | |
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GEE Estimation | |
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Example | |
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Generalized Wald Tests for Model Comparison | |
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Model Fit of Observed Proportions | |
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Summary | |
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Mixed-Effects Regression Models for Binary Outcomes | |
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Introduction | |
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Logistic Regression Model | |
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Probit Regression Models | |
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Threshold Concept | |
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Mixed-Effects Logistic Regression Model | |
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Intraclass Correlation | |
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More General Mixed-Effects Models | |
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Heterogeneous Variance Terms | |
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Multilevel Representation | |
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Response Functions | |
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Estimation | |
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Estimation of Random Effects and Probabilities | |
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Multiple Random Effects | |
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Integration over the Random-Effects Distribution | |
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Illustration | |
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Fixed-Effects Logistic Regression Model | |
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Random Intercept Logistic Regression Model | |
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Random Intercept and Trend Logistic Regression Model | |
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Summary | |
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Mixed-Effects Regression Models for Ordinal Outcomes | |
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Introduction | |
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Mixed-Effects Proportional Odds Model | |
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Partial Proportional Odds | |
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Models with Scaling Terms | |
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Intraclass Correlation and Partitioning of Between- and Within-Cluster Variance | |
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Survival Analysis Models | |
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Intraclass Correlation | |
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Estimation | |
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Psychiatric Example | |
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Health Services Research Example | |
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Summary | |
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Mixed-Effects Regression Models for Nominal Data | |
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Mixed-Effects Multinomial Regression Model | |
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Intraclass Correlation | |
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Parameter Estimation | |
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Health Services Research Example | |
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Competing Risk Survival Models | |
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Waiting for Organ Transplantation | |
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Summary | |
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Mixed-effects Regression Models for Counts | |
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Poisson Regression Model | |
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Modified Poisson Models | |
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The ZIP Model | |
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Mixed-Effects Models for Counts | |
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Mixed-Effects Poisson Regression Model | |
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Estimation of Random Effects | |
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Mixed-Effects ZIP Regression Model | |
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Illustration | |
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Summary | |
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Mixed-Effects Regression Models for Three-Level Data | |
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Three-Level Mixed-Effects Linear Regression Model | |
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Illustration | |
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Three-Level Mixed-Effects Nonlinear Regression Models | |
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Three-Level Mixed-Effects Probit Regression | |
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Three-Level Logistic Regression Model for Dichotomous Outcomes | |
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Illustration | |
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More General Outcomes | |
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Ordinal Outcomes | |
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Nominal Outcomes | |
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Count Outcomes | |
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Summary | |
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Missing Data in Longitudinal Studies | |
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Introduction | |
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Missing Data Mechanisms | |
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Missing Completely at Random (MCAR) | |
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Missing at Random (MAR) | |
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Missing Not at Random (MNAR) | |
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Models and Missing Data Mechanisms | |
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MCAR Simulations | |
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MAR and MNAR Simulations | |
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Testing MCAR | |
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Example | |
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Models for Nonignorable Missingness | |
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Selection Models | |
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Mixed-Effects Selection Models | |
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Example | |
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Pattern-Mixture Models | |
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Example | |
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Summary | |
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Bibliography | |
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Topic Index | |