Figure A1.

(A) CLPM (with means): The cross-lagged panel model (CLPM) is used to estimate bidirectional lagged effects between X and Y ($b_{Y2X1}$ and $b_{X2Y1}$). This model was used as the reference model for integrating instrumental variables. (B) IV Regression (with means): The instrumental variables regression (IVR) model fitted in a Structural Equation Modeling framework. The model uses the instrumental variable for X, IVx, to estimate the causal effect of X on Y ($b_{YX}$). (C) IV-CLPM (with means): The proposed IV-CLPM model combines the CLPM with bidirectional IVR applied cross-sectionally at each wave. In addition to the lagged (i.e., “distal”) effects $b_{Y2X1}$ and $b_{X2Y1},$ the model utilizes IVR to estimate cross-sectional (i.e., “proximal”) effects at each wave: $b_{Y1X1}$ and $b_{X1Y1}$ at wave 1, and $b_{Y2X2}$ and $b_{X2Y2}$ at wave 2. In all three path diagrams, squares/rectangles represent the observed variables, and circles represent latent variables. Triangles represent constants used to model the variables’ mean levels.