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arXiv · 2603.28656

Statistical Models for the Inference of Within-person Relations: A Random Intercept Cross-Lagged Panel Model and Its Interpretation

Satoshi Usami
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Abstract

The cross-lagged panel model (CLPM) has been widely used, particularly in psychology, to infer longitudinal relations among variables. At the same time, controlling for between-person heterogeneity and capturing within-person relations as processes of within-person change are regarded as key components to causal inference based on longitudinal data. Since Hamaker, Kuiper, and Grasman (2015) criticized the CLPM for its limitations in inferring within-person relations, the random intercept cross-lagged panel model (RI-CLPM), which incorporates stable trait factors representing stable individual differences, has rapidly spread, especially in psychology. At the same time, although many statistical models are available for inferring within-person relations, the distinctions among them have not been clearly delineated, and discussions over the interpretation and selection of statistical models remain active. In this paper, I position the RI-CLPM as one useful method for inferring within-person relations, explain its practical issues, and organize its mathematical and conceptual relationships with other statistical models, as well as potential problems that may arise in their application. In particular, I point out that a distinctive feature of the stable trait factors in the RI-CLPM, in representing between-person heterogeneity, is the assumption that they are uncorrelated with within-person variability, and that this point serves as an important link to the mathematical relationship with the dynamic panel model, another promising alternative.

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Satoshi Usami. 2026-03-30. Statistical Models for the Inference of Within-person Relations: A Random Intercept Cross-Lagged Panel Model and Its Interpretation. https://doi.org/10.11201/jjdp.33.267

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