Here, d v maps each word v into a point on the axis, and a u works as a threshold.
when P( y = 1|u, v) ≥ 0.5, we can assume learner u knows word v. Due to the logistic sigmoid function, P( y = 1|u, v) ≥ 0.5 holds true if and only if the Rasch model determines that learner u knows all words whose word difficulty d v is lower than the learners' ability a u .