Linear mixed effects model for a factorial experiment. i = 1, ..., I is the index of a feature, j = 1, ..., J the index of a condition, k = 1, ..., K the index of a biological replicate, and l = 1, ..., L of a technical replicate. Notation S(C)k(j) is read as "biological replicate within a condition", and is the unique identifier of each biological replicate. is the variance of the measurement error and the between-subject variance in the underlying population. μ111 is the expected log-intensity of the arbitrary chosen first feature, first condition, and first biological replicate. (a) and (b) are two alternative interpretations of the term subject, which distinguish reduced and expanded scopes of biological replication. A separate such model is specified for each protein.
Clough et al. BMC Bioinformatics 2012 13(Suppl 16):S6 doi:10.1186/1471-2105-13-S16-S6