Triadic Extensions of the Standard and Latent Actor-Partner Interdependence Model

To understand interpersonal processes within family systems, researchers need models that go beyond commonly investigated dyadic relationships. The current study introduces triadic (t) extensions of the standard Actor-Partner Interdependence Model for both observed variables (tAPIM) and latent variables (latent tAPIM). Using an empirical example, we illustrate the implementation of both models by presenting their formulas and providing accompanying R code. In addition, we conduct a simulation study to evaluate the performance of these models under varying levels of measurement error. The results indicate that: (1) both models are generally unaffected by convergence problems; (2) the latent tAPIM more effectively accounts for measurement error, yielding more accurate estimates; (3) the latent tAPIM produces higher standard errors compared to the tAPIM; and (4) the power and type I error rates of both models are comparable, with only minor differences. These findings offer practical guidance for researchers aiming to model interdependence in triadic data while addressing the potential bias introduced by measurement unreliability.