Polytomous item ordering theory based on ramsay's kernel smoothing nonparametric item response theory

Our previous work, Liu's polytomous ordering theory can be used for any testing with homogeneous or heterogeneous polytomous response. It is more useful than other well-known polytomous ordering theories. However, it can only be used to detect item ordering relationships for a group of subjects, not for any personal of subject. To overcome this drawback, in this paper, the above-mentioned theory is improved by integrating Ramsay's kernel smoothing nonparametric item response theory which can be used to estimate the joint probability of any two items, and construct \personal item ordering structures without the local independence assumption. A computer program is developed for computing and drawing item structures. A calculus test example is also provided in this paper to illustrate the advantages of the proposed methods.