Pairwise Modeling Method For The Polytomous Longitudinal Response Data

In recent years, Item Response Theory (IRT) is a very active area of research in the education and psychological measurement, IRT overcomes limitations of the classi-cal measurement theory. In the early stage, IRT is the unidimensional model, and now with the continuous development of Item Response Theory, the multidimensional item response model is developed, and applied in more fields. Longitudinal item response data can be used to investigate the changes of latent traits for a group of subjects over time, in the research, we found that as the number of dimensions increases, computational d-ifficulty also rises, when the dimension reaches a certain value, the computer can not be able to calculate the results of multiple integrals. Pairwise modeling approach based on the pseudo-likelihood effectively solves this computation problem. In this paper, pairwise modeling approach is applied to study the longitudinal item response data in General-ized Partial Credit Model (GPCM), showing the superiority of the pairwise modeling approach. Finally, we further study the impact of the same items number between two consecutive instants on the stability of the estimates, which would provide a valid basis for the more reasonable project layout used to test.