A new unidimensional latent trait theory for polytomous data is developed. A unique feature of the theory is that this model explains a psychological process through which a subject reaches a certain response ; this model is an integration of two parts. One part discriminates states of knowledge, namely, it classifies them into three categories, i.e. a) full knowledge, b) partial knowledge, and c) complete ignorance. The other part of the model describes how the subject chooses a certain alternative when the state of knowledge is known. When the subject has full knowledge, he chooses the correct alternative immediately. When he holds only partial knowledge, he chooses an alternative according to the multivariate logistic model. In the case of complete ignorance, he chooses an alternative only randomly. Then a new model was applied to the vocabulary test data of high school students. The results showed a new model produced always better precision than a usual IRT model.