The chapter "Random Effects Models for Longitudinal Data" by Verbeke, Molenberghs, and Rizopoulos provides an overview of methods for analyzing longitudinal data, which are outcomes measured repeatedly over time within the same subjects. The authors highlight the challenges posed by the correlation between repeated measurements from the same subject and discuss the importance of accounting for this correlation in statistical analyses. The chapter begins with an introduction to repeated measures and their applications in various fields, such as biometrics and social sciences. It emphasizes the use of random effects models to capture hierarchical data structures, where random coefficients are constant within a given level but vary across levels. Examples include longitudinal studies where data are hierarchical due to repeated measurements over time, and multilevel settings like school children nested within classes and schools. The authors then discuss the analysis of multivariate longitudinal data, where multiple repeated measures sequences are recorded simultaneously, and the computational challenges that arise, especially in high-dimensional settings. They also address the integration of longitudinal data with time-to-event outcomes, such as in clinical trials where survival outcomes are evaluated alongside longitudinal markers. Key modeling tools for Gaussian and non-Gaussian longitudinal data are presented, including linear mixed models and generalized linear mixed models (GLMMs). The chapter explains how these models can handle correlated outcomes and how they can be extended to handle multivariate outcomes. It also discusses the use of generalized estimating equations (GEE) for inference in non-Gaussian settings. The chapter includes case studies to illustrate the application of these models, such as the analysis of toenail infection data, hearing threshold data, liver cirrhosis data, orthodontic growth data, and age-related macular degeneration trial data. These examples demonstrate the practical use of random effects models in various research contexts. Finally, the chapter explores the analysis of multivariate longitudinal data, including the development of a flexible joint model that can handle any number of outcomes measured longitudinally. It introduces a pairwise model-fitting approach for high-dimensional applications, which involves fitting bivariate models for each pair of outcomes and combining the results to estimate the parameters of the full multivariate model.The chapter "Random Effects Models for Longitudinal Data" by Verbeke, Molenberghs, and Rizopoulos provides an overview of methods for analyzing longitudinal data, which are outcomes measured repeatedly over time within the same subjects. The authors highlight the challenges posed by the correlation between repeated measurements from the same subject and discuss the importance of accounting for this correlation in statistical analyses. The chapter begins with an introduction to repeated measures and their applications in various fields, such as biometrics and social sciences. It emphasizes the use of random effects models to capture hierarchical data structures, where random coefficients are constant within a given level but vary across levels. Examples include longitudinal studies where data are hierarchical due to repeated measurements over time, and multilevel settings like school children nested within classes and schools. The authors then discuss the analysis of multivariate longitudinal data, where multiple repeated measures sequences are recorded simultaneously, and the computational challenges that arise, especially in high-dimensional settings. They also address the integration of longitudinal data with time-to-event outcomes, such as in clinical trials where survival outcomes are evaluated alongside longitudinal markers. Key modeling tools for Gaussian and non-Gaussian longitudinal data are presented, including linear mixed models and generalized linear mixed models (GLMMs). The chapter explains how these models can handle correlated outcomes and how they can be extended to handle multivariate outcomes. It also discusses the use of generalized estimating equations (GEE) for inference in non-Gaussian settings. The chapter includes case studies to illustrate the application of these models, such as the analysis of toenail infection data, hearing threshold data, liver cirrhosis data, orthodontic growth data, and age-related macular degeneration trial data. These examples demonstrate the practical use of random effects models in various research contexts. Finally, the chapter explores the analysis of multivariate longitudinal data, including the development of a flexible joint model that can handle any number of outcomes measured longitudinally. It introduces a pairwise model-fitting approach for high-dimensional applications, which involves fitting bivariate models for each pair of outcomes and combining the results to estimate the parameters of the full multivariate model.