Agreement between methods for quantitative measurements are typically assessed by computing limits of agreement between pairs of methods and/or by illustration through Bland-Altman plots. We consider the situation where the observed measurement methods are considered a random sample from a population of possible methods, and discuss how the underlying linear mixed effects model can be extended to this situation. This is relevant when, for example, the methods represent raters/judges that are used to score specific individuals or items. In the case of random methods, we are not interested in estimates pertaining to the specific methods, but are instead interested in quantifying the variation between the methods actually involved making measurements, and accommodating this as an extra source of variation when generalizing to the clinical performance of a method. In the model we allow raters to have individual precision/skill and permit linked replicates (i.e., when the numbering, labeling or ordering of the replicates within items is important). Applications involving estimation of the limits of agreement for two datasets are shown: A dataset of spatial perception among a group of students as well as a dataset on consumer preference of French chocolate. The models are implemented in the MethComp package for R [Carstensen B, Gurrin L, Ekstrøm CT, Figurski M. MethComp: functions for analysis of agreement in method comparison studies; 2013. R package version 1.22, R Core Team. R: a language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing; 2012].