Formal Methods in Lifespan Psychology
 

Research Scientists
Aaron Peikert (Project Leader)

Andreas M. Brandmaier
Hannes Diemerling (until 01/2026)
Maximilian Ernst (MPSCog, since 09/2023)
Nicklas Jakob Hafiz
Leonie Hagitte (LIFE, since 04/2025)
Laurenz Lammer (MPSCog, since 01/2026)
Ulman Lindenberger
Ai Ye (as of 05/2025)

Improving Longitudinal Study Design in the Cognitive Neurosciences
SEM as a Tool for Theory Development
Open Research Practices

Since it was founded by the late Paul B. Baltes in 1981, the Center for Lifespan Psychology has sought to promote conceptual and methodological innovation within developmental psychology and in an interdisciplinary context. Over the years, the critical examination of relations among theory, method, and data has evolved into a distinct feature of the Center.

Based on the tenets of lifespan psychology, the Formal Methods project seeks to develop and refine statistical methods and research designs that articulate human development across different timescales, levels of analysis, and functional domains. Hence, the project is characterized by an emphasis on methodology, understood as the reciprocal interplay between concepts and methods that is at the heart of scientific progress. The mission of the project is to create a methodological foundation and an evolving set of statistical methods for high-quality research on lifespan development that encourages researchers to address their research questions with methodological rigor, including a commitment to open science practices.

During the reporting period, the project has focused on three domains of inquiry: (1) estimating the reliability of human brain imaging techniques; (2) improving tooling and theory for flexible theory driven modelling and; (3) conceptualizing the interactions among study planning, theorizing, and data analysis.

Improving Longitudinal Study Design in the Cognitive Neurosciences

To integrate evidence across different sources in longitudinal cognitive neuroscience, it is indispensable to understand the psychometric properties of the measurement instruments that are being used. Toward that end, the Formal Methods team proposed the intraclass effect decomposition (ICED) framework (Brandmaier et al., 2018) in the previous reporting period. ICED is used to attribute variability in measures to different sources, such as measurement error and true between-person differences. Using this decomposition, it is straightforward to obtain reliability estimates as the ratio of measurement error to total variance in the context of structural equation modeling (SEM).

In the meantime, the team has applied ICED to larger data sets that include additional sources of measurement error. For example, Parsons et al. (2024) applied ICED to a sample of 7,269 children aged 9 to 11 years who were measured yearly over three measurement occasions in the ABCD Study. Replicating the original results reported by Brandmaier et al. (2018), we found that the reliability of the myelin water fraction (MWF) differs significantly between brain regions. The study encompassed more than 20 measurement sites, which enabled us to also look at site differences. Sizable differences in reliability between sites were found, primarily reflecting differences in measurement error. Given that sites are often likely to differ on dimensions of interest, such as socioeconomic status, such confounds between site and measurement error, if ignored, can constitute a problematic source of bias.

The ICED approach has also directly influenced the design of intervention studies in LIP, such as the CHOROS-II study of the Plasticity project. In CHOROS-II, assessing magnetic resonance parameters twice before and after the intervention in two separate sessions each will allow researchers to better separate occasion-specific variance from true linear change.

To improve the planning of longitudinal studies, the team wrote a tutorial on how to conduct power simulations for longitudinal data using SEM (Buchberger et. al., 2024). Also, following up on earlier work, the project showed how the number of measurement occasions and the total duration of a study influence the ability to detect interindividual differences in linear change (Brandmaier et al., 2024).

Key References

SEM as a Tool for Theory Development

SEM helps to link comprehensive theories and complex study designs to testable models. The Formal Methods team has continued to develop open-source software for the application of SEM by different groups of researchers. On the one hand, it continues to support Ωnyx, which offers a user-friendly graphical user interface, and is often used by SEM novices. On the other hand, the team further developed StructuralEquationModels.jl, which features cutting-edge estimators and high-performance computing by using the programming language Julia. The massive improvement in computational efficiency achieved by StructuralEquationModels.jl facilitates the application of advanced statistical methods within SEM. One such method is regularization, where, in addition to parameters, parts of the model structure are estimated. Others have warned that convergence problems stand in the way of applying regularization to SEM. The team's findings show that the use of StructuralEquationModels.jl greatly reduces conversion problems, due to innovations in the way regularization is implemented in the software (Friemelt et al., 2023).

The team also went the complementary route, in the sense that the advancement of statistical theory enables better software. Specifically, Ernst et al. (2023) derived a statistical approach that improves computational efficiency for least-squares parameter estimation in SEM. In the meantime, this approach has been implemented in OpenMX, lavaan, and StructuralEquationModels.jl.

Another example of how theoretical innovation and practical implementation can advance in tandem is the collaboration between the project and the OpenMX team in developing the Products of Variables Models (Boker et al., 2023). This work introduces a fundamentally new and more expressive description language for structural equation models by providing a general method to decompose variance in product variables into contributions from their multiplicands. The theoretical breakthrough—showing that centered multiplicands lead to unidentified models while non-zero means ensure identification—resolves longstanding challenges in modeling interactions between latent variables, incorporating latent moderators, and handling manifest moderators with missing values. This innovation has been implemented in both OpenMx and Ωnyx, enabling researchers to apply these methods to substantive questions about moderation and nonlinear effects in psychological processes.

Key References

Open Research Practices

Open Science has focused on testing theories, but methods for specifying, sharing, and iteratively improving theories remain underdeveloped. During the reporting period, the Formal Methods project has continued its earlier work on computational reproducibility, preregistration, and theory-informed exploratory statistical modelling in two major ways. First, the R package reproducibleRchunks (Brandmaier & Peikert, 2025), which automates the testing and verification of computational reproducibility, was developed and published. Second, the project has introduced a formal analysis of the mechanisms of preregistration in Peikert et al. (in press). The authors argue that preregistration makes evidence more persuasive, not by ensuring fully confirmatory results, as is often assumed, but by the transparency with which it separates confirmation from exploration. In doing so, they seek to fully integrate exploratory statistical modelling into open science practices, thereby promoting the ideal of a transparent, cumulative science that acknowledges the reciprocal interactions between discovery and the hypothesis testing. This ideal has also motivated the project's work on Findable Accessible Interoperable Reusable Theories (FAIR Theories, Van Lissa et al., 2026). In that work, the authors propose a metadata standard for theories and a corresponding workflow, according to which principles and infrastructure that have already transformed data sharing are applied to theories as well. In their view, FAIR theories address a critical gap in open research practices and support the renewed interest in theory development in the social and behavioral sciences.

Key References