The analysis of longitudinal data has been a popular subject for the recent years. The growth of the Generalized Estimating Equation (GEE) Liang & Zeger, 1986) is one of the most influential recent developments in statistical practice for this practice. GEE methods are attractive both from a theoretical and a practical standpoint. In this paper, we are interested in the influence of different "working" correlation structures for modeling the longitudinal data. Furthermore, we propose a new AIC-like method for the model assessment which generalized AIC from the point of view of the data generating. By comparing the difference of the log-likelihood functions between different correlation models, we define the exact value to create an interval for our model selection. In this thesis, we combine the GEE method and a new generalized AIC Index for the longitudinal data with different correlation structures.