Three Extensions of the Random Intercept Cross-Lagged Panel Model

Figures & data

Figure 1. Graphic representations of the random intercept cross-lagged panel model (RI-CLPM) and the traditional cross-lagged panel model (CLPM). $S_{it}$ denotes the observed sleep problems and $A_{it}$ denotes the observed anxiety of unit $i$ at occasion $t$

Figure 2. Two options for including a between-level predictor: In the top left, $N_i$ influences the observed variables directly; in the top right, this occurs indirectly through the random intercepts. The model in the top right is nested under the model in the top left (fixing the regression coefficients to be identical over time results in a version that is equivalent to the model on the right). Also, two options for including a between-level outcome: In the lower-left, $L_i$ is explained by the random intercepts which includes only between variance; in the lower right, panel the distal outcome is regressed on both the random intercepts and the within components such that we use both between- and within-level variance to predict $L_i$. These two models are not nested

Figure 3. Two options for incorporating multiple indicators in a RI-CLPM. Top panel shows a model with indicator-specific random intercepts that capture trait-like differences between units, and occasion-specific factors that capture the within-unit dynamics. Bottom panel shows a model in which there is a latent variable per occasion, which contains a trait-like part that is captured by the higher-order random intercepts, and a state-like part that is used to capture the dynamics over time