Cross-lagged panel model

The cross-lagged panel model is a type of discrete time structural equation model used to analyze panel data in which two or more variables are repeatedly measured at two or more different time points. This model aims to estimate the directional effects that one variable has on another at different points in time. ^{[1] [2]} This model was first introduced in 1963 by Donald T. Campbell and refined during the 1970s by David A. Kenny. ^[3] Kenny has described it as follows: "Two variables, X and Y, are measured at two times, 1 and 2, resulting in four measures, X1, Y1, X2, and Y2. With these four measures, there are six possible relations among them – two synchronous or cross‐sectional relations (see cross‐sectional design) (between X1 and Y1 and between X2 and Y2), two stability relations (between X1 and X2 and between Y1 and Y2), and two cross‐lagged relations (between X1 and Y2 and between Y1 and X2)." ^[4] Though this approach is commonly believed to be a valid technique to identify causal relationships from panel data, its use for this purpose has been criticized, as it depends on certain assumptions, such as synchronicity and stationarity, that may not be valid. ^{[5] [6] [7]}

Random-Intercept Cross-Lagged Panel Model (RI-CLPM)

The Random-Intercept Cross-Lagged Panel Model (RI-CLPM) is a widely-used extension that directly addresses the traditional model's limitation of confounding variance. ^[8] The RI-CLPM disentangles these effects by explicitly modeling stable individual differences through random intercepts (a form of latent factor). By accounting for this stable, trait-like variance, the model's remaining cross-lagged paths represent a purer estimate of the true within-person processes. This allows researchers to more accurately test whether a change in one variable predicts a future change in another.

Cross-Lagged Panel Network (CLPN)

Another extension is the Cross-Lagged Panel Network (CLPN), which moves the analysis from the latent construct level to the individual item level. ^[9] Instead of modeling the relationships between broad variables (e.g., "depression" and "anxiety"), the CLPN estimates a network of predictive relationships between their individual components (e.g., "low mood" predicting "concentration problems," or "worry" predicting "insomnia"). This network approach allows for a more granular understanding of the dynamic system. It can be used to identify specific, nuanced pathways of influence and find "bridge nodes" (e.g., a specific symptom) that may link two different constructs over time.

References

1. Kuiper, Rebecca M.; Ryan, Oisín (2018-09-03). "Drawing Conclusions from Cross-Lagged Relationships: Re-Considering the Role of the Time-Interval". Structural Equation Modeling . 25 (5): 809–823. doi: 10.1080/10705511.2018.1431046 . ISSN   1070-5511.
2. "Cross-Lagged Panel Analysis" . The SAGE Encyclopedia of Communication Research Methods. 2455 Teller Road, Thousand Oaks, California, 91320: SAGE Publications, Inc. 2017. doi:10.4135/9781483381411.n117. ISBN   978-1-4833-8143-5.
3. Berry, Daniel; Willoughby, Michael T. (July 2017). "On the Practical Interpretability of Cross-Lagged Panel Models: Rethinking a Developmental Workhorse". Child Development . 88 (4): 1186–1206. doi:10.1111/cdev.12660. PMID   27878996.
4. Kenny, David A. (2014-09-29). "Cross-Lagged Panel Design". Wiley StatsRef: Statistics Reference Online. Chichester, UK: John Wiley & Sons, Ltd. pp. stat06464. doi:10.1002/9781118445112.stat06464. ISBN   978-1-118-44511-2.
5. Ellen, Hamaker; Rebecca, Kuiper; Raoul, Grasman (March 2015). "A Critique of the Cross-Lagged Panel Model" (PDF). Psychological Methods . 20 (1): 102–116. doi:10.1037/a0038889. PMID   25822208.
6. Mund, Marcus; Nestler, Steffen (September 2019). "Beyond the Cross-Lagged Panel Model: Next-generation statistical tools for analyzing interdependencies across the life course". Advances in Life Course Research . 41: 100249. doi:10.1016/j.alcr.2018.10.002. PMID   36738028. S2CID   150324087.
7. Kenny, David A. (1975). "Cross-lagged panel correlation: A test for spuriousness" . Psychological Bulletin . 82 (6): 887–903. doi:10.1037/0033-2909.82.6.887. ISSN   0033-2909.
8. Hamaker, Ellen L.; Kuiper, Rebecca M.; Grasman, Raoul P. P. P. (2015). "A critique of the cross-lagged panel model". Psychological Methods. 20 (1): 102–116. doi:10.1037/a0038889. ISSN   1939-1463.
9. Wysocki, Anna; McCarthy, Ian; van Bork, Riet; Cramer, Angélique O. J. (2025-06-18). "Cross-lagged panel networks". advances.in/psychology. 2: e739621. doi:10.56296/aip00037. ISSN   2976-937X.