In latent trait models the standard procedure for handling the problem caused by guessing on multiple choice tests is to estimate a parameter which is intended to measure the "guessingness" inherent in an item. Birnbaum's three parameter model, which handles guessing in this manner, ignores individual differences in guessing tendency. This paper presents a model or procedure which uses the information contained in the interaction between a person and an item to remove the effects of random guessing from estimates of ability, difficulty, and discrimination. Simulated and real data are presented which support the model in terms of fit and information. (Author/RC)