Figure 1.

(A) CLPM: 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: 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: 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. To improve readability, the modeling of means is not shown in this figure. For complete path diagrams with means, please see Figure A1 in the Appendix A.