This article considers a new multidimensional Item Response Model called "OR Model"; it also presents the application of the model to TPI data. The TPI is a kind of personality Inventory. In the questionnaire data, the subject's response to an item is almost always under the influence of multidimensional traits. In this model, it is assumed that the response to an item occurs whenever at least one of the subject's traits is considered high enough. It means that the subject's response to an item would be explained by the disjunctive condition that exists between latent traits rather than the conjunctive condition. On the other hand, in the test data, the conjunctive condition may be preferable to the disjunctive condition, so this model is very useful in analyzing questionnaire data. In the applications of this model, the plausibility of the model and its effectiveness are confirmed.