Hypotheses about change over time are central to informing our understanding of development. Developmental neuroscience is at critical juncture: although the majority of longitudinal imaging studies have observations with two time points, researchers are increasingly obtaining three or more observations of the same individuals. The goals of the proposed manuscript are to draw upon the long history of methodological and applied literature on longitudinal statistical models to summarize common problems and issues that arise in their use. We also provide suggestions and solutions to improve the design, analysis and interpretation of longitudinal data, and discuss the importance of matching the theory of change with the appropriate statistical model used to test the theory. Researchers should articulate a clear theory of change and to design studies to capture that change and use appropriately sensitive measures to assess that change during development. Simulated data are used to demonstrate several common analytic approaches to longitudinal analyses. We provide the code for our simulations and figures in an online supplement to aid researchers in exploring and plotting their data. We provide brief examples of best practices for reporting such models. Finally, we clarify common misunderstandings in the application and interpretation of these analytic approaches.

The human brain is remarkably plastic. The brain changes dramatically across development, with ongoing functional development continuing well into the third decade of life and substantial changes occurring again in older age. Dynamic changes in brain function are thought to underlie the innumerable changes in cognition, emotion, and behavior that occur across development. The brain also changes in response to experience, which raises important questions about how the environment influences the developing brain. Longitudinal functional magnetic resonance imaging (fMRI) studies are an essential means of understanding these developmental changes and their cognitive, emotional, and behavioral correlates. This paper provides an overview of common statistical models of longitudinal change applicable to developmental cognitive neuroscience, and a review of the functionality provided by major software packages for longitudinal fMRI analysis. We demonstrate that there are important developmental questions that cannot be answered using available software. We propose alternative approaches for addressing problems that are commonly faced in modeling developmental change with fMRI data.

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The analysis of longitudinal neuroimaging data within the massively univariate framework provides the opportunity to study empirical questions about neurodevelopment. Missing outcome data are an all-to-common feature of any longitudinal study, a feature that, if handled improperly, can reduce statistical power and lead to biased parameter estimates. The goal of this paper is to provide conceptual clarity of the issues and non-issues that arise from analyzing incomplete data in longitudinal studies with particular focus on neuroimaging data. This paper begins with a review of the hierarchy of missing data mechanisms and their relationship to likelihood-based methods, a review that is necessary not just for likelihood-based methods, but also for multiple-imputation methods. Next, the paper provides a series of simulation studies with designs common in longitudinal neuroimaging studies to help illustrate missing data concepts regardless of interpretation. Finally, two applied examples are used to demonstrate the sensitivity of inferences under different missing data assumptions and how this may change the substantive interpretation. The paper concludes with a set of guidelines for analyzing incomplete longitudinal data that can improve the validity of research findings in developmental neuroimaging research.