"How does one translate a logit value back to a raw score?"
A motivation for constructing measures is to obtain units, e.g., logits, as independent as possible of the original raw score system. But logit-to-raw-score conversion is usually straightforward. If every person is observed on every item, then a conversion table is easy to construct. Compute the measure for every possible raw score using a method such as "Estimating measures..." in RMT 12:2. If different people are observed on different items, such as with adaptive testing, then you must specify which items are to be included in the raw score computation.
Logit to score conversion. 2001. Linacre J.M. 15:3 p. 837
Logit to score conversion Linacre J.M. Rasch Measurement Transactions, 2001, 15:3 p. 837
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