During the past decade, the use of polynomial regression has become increasingly prevalent in congruence research. One drawback of polynomial regression is that it relies on the assumption that variables are measured without error. This assumption is relaxed by structural equation modeling with latent variables. One application of structural equation modeling to congruence research is the latent congruence model (LCM). Although the LCM takes measurement error into account and allows tests of measurement equivalence, it is framed around the mean and algebraic difference of the components of congruence (e.g., the person and organization), which creates various interpretational problems. This article discusses problems with the LCM and shows how these problems are resolved by a linear structural equation model that uses the components of congruence as predictors and outcomes. Extensions of the linear model to quadratic equations used in polynomial regression analysis are discussed.
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