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. This model was first introduced in 1963 by Donald T. Campbell and refined during the 1970s by David A. Kenny. 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, two stability relations, and two cross‐lagged relations." 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.
Random-Intercept Cross-Lagged Panel Model (RI-CLPM)
The Random-Intercept Cross-Lagged Panel Model is a widely-used extension that directly addresses the traditional model's limitation of confounding variance. The RI-CLPM disentangles these effects by explicitly modeling stable individual differences through random intercepts. 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, which moves the analysis from the latent construct level to the individual item level. Instead of modeling the relationships between broad variables, the CLPN estimates a network of predictive relationships between their individual components. 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" that may link two different constructs over time.