Abstract: The fitting condition of Linear Logistic Test Model(LLTM)and its relationship with homogeneity of problem solving strategies were discussed.In this research the subjects were asked to compare two negative whole number index powers.It was found that the data of all of the subjects could not fit Rasch model and LLTM.But after the subjects were divided into four strategy homogeneous groups, the data within each of these groups could fit Rasch model well.However,some items fit LLTM better,others did not fit LLTM so well within each group.This showed that the homogeneity of problem solving strategies was the necessary condition but not the sufficient condition for the fitting of LLTM.

Key words: item response theory, problem solving strategy, model fitting