For a very readable description of the binomial error model, see Crocker and Algina (1986). Feldt’s (1984)
demonstration of the relationship between the binomial error model and classical test theory is also elucidating.
In terms of software capable of deriving conditional standard error of measurement estimates,
readers could turn to Biddle’s TVAP system (Biddle, 2003), or to the Lertap system (Nelson, 2000).