Many-Facet Rasch Measurement

Both address rater and task effects, but at different levels. Generalizability theory partitions score variance into components attributable to facets (raters, tasks, occasions) and estimates how reliable scores are under various designs. MFRM goes further by estimating a parameter for each individual element — this specific rater's severity, this specific task's difficulty — and adjusting examinee measures accordingly. G-theory characterizes the facet as a whole; MFRM models the elements within it. They are complementary, not competing. See the related Generalizability Theory entry.

A fair score (or fair average) is the examinee ability estimate adjusted to what it would have been under raters and tasks of average severity and difficulty. Because examinees in realistic designs are not all judged by the same raters, raw averages are not comparable; the fair score corrects for the particular, possibly harsher or easier, raters each examinee happened to encounter, making cross-examinee comparison defensible.

To place all raters on a common severity scale, the design must link them — for example, by having overlapping raters score common performances or anchor tasks. If the data split into disconnected subsets with no shared elements, the model cannot tell whether one subset scored low because its examinees were weaker or its raters harsher. A connected design ensures every facet parameter is estimable on the same scale.