In this study, we have further extended the methodology proposed, first, by Lin et al. (2002) and, later, extended by Stevens et al. (2017, 2018), on the coverage probability/probability of agreement, by relaxing the strong parametric assumptions regarding the distribution of the latent trait and developing inference methods allowing to compute both pointwise and simultaneous confidence bands. The methodology requires repeated measurements by at least one of the two measurement methods and accommodates heteroscedastic measurement errors. It performs often very well even when one has only one measurement by one of the two measurement methods and at least five repeated measurements from the other. It circumvents some of the deficiencies of the Bland & Altman limits of agreement method and provides a more direct assessment of the agreement level.