The latent congruency model is a measurement model designed for organizational research which creates two factors to represent the mean and difference of two interdependent component measures. It can estimate and control for measurement error, provide straightforward ways for examining measurement equivalence, allow for the examination of complex theoretical models, and allow the examination antecedents and consequences of congruence constructs and component measures.
Cheung, G. W. (2009). Introducing the latent congruence model for improving the assessment of similarity, agreement, and fit in organizational research. Organizational Research Methods, 12(1), 6-33. https://doi.org/10.1177/1094428107308914.