Some Discussions On Model Selection Criteria

Model selection has become a hot topic in statistic analysis, which usually contains the selections of model types and the independent variables. Since the 20th century, statistical scholars have got a lot of results on model selection, such as criterion based on information theory and Bayesian methods. However, these formulas aren’t suitable for high-dimensional models completely. The model selection methods for the high-dimensional data are the hot topics in statistics.Firstly, this dissertation introduces the basic concepts of linear regression model, as well as the Bayesian statistical inference of multiple linear regression. Meanwhile, the Deviation Information Criterion (DIC) is introduced, and we use it to the linear regression model selection. The results show that the use of DIC and MCMC sampling can lead to "best" model. Compared with the existing criteria to select the optimal model, DIC criterion is almost consistency.Secondly, the dissertation introduces the Poisson model with random effects (REP) and fixed effects (FEP), and the relationships between them are also discussed. The cross-validation log score (LScv) and full-sample log score (LSFS) are defined. We analyze the relationships between DIC and Log score function by using the data generation mechanism. Simulation results illustrate that, they have a significant negative correlation in FEP model. However, they don’t have a significant correlation in the REF model. In the end, we research the advantages and disadvantages between of Log scores and DIC with the small sample size data. The results show that DIC is slightly better than LScv, the advantages is gradually decreasing as n is increasing. But in the REP model, LSFS is more accurate than LScv and DIC.