What’s the difference? A clarification of the statistical assumptions in congruence modeling

Abstract

This report translates statistical research on congruence modeling to family science. In particular, it highlights the limitations of the latent congruence model (LCM; Cheung, 2009), which was recently re-branded as the dyadic score model (Iida et al., 2018). A general model for congruence research based on polynomial response surface analysis is presented, along with unconstrained and constrained examples of first- (linear), second- (quadratic), and third-order (cubic) polynomial models. Following Edwards’ (2009) critique, the LCM coefficients are shown to be equivalent to compound coefficients of the linear polynomial model that conceal the effects of its components. The implicit constraints and limitations of the LCM are demonstrated using an exploratory empirical example of sexual desire discrepancy’s effects on sexual satisfaction for heterosexual couple therapy clients. These results are discussed, followed by key takeaways for family scientists.