The Variable Selection Based On Quasi Likelihood Criterion Of The Growth Curve Model

Growth curve model, which was first set up by Pottoff R. F and Roy S. N, has been emphasized heavily for almost half a century. Furthermore, the direction of research based on the growth curve model is attached more important to. In addition, in various fields, such as biostatistics, environmental science, economic science etc., the most important work is selecting the useful variables which have the weight of a large proportion in the model, at the same time, reject the variables which give smaller influence for the model as well.The research focused on variable selection method for growth curve model, our study was based the Quasi-Likelihood function, transform the form of the model from one to another. Furthermore, we combined with Quasi-penalty function, improved the method. Analysis from three aspects as the following:Firstly, the paper introduced the model’s setting and application, then analysis the Quasi-Likelihood Estimation principle, adopted the quasi-logarithmic function and quasi-score function, got the estimation as well. Furthermore, the paper discussed the traditional method of the selection, for their disadvantage.Secondly, according to the principle of Quasi-Likelihood Estimator, combined with penalty function and its properties, the paper proposed quasi-penalty function on growth curve model, and give the definition of punishment to the logarithmic function. Get the penalty quasi-likelihood estimation at last. The paper also gave the algorithm of the penalty quasi-likelihood estimation.Thirdly, the paper final proof the penalty quasi-likelihood estimation has these two outstanding characters:the estimation with consistency and non asymptotic normality of parameter estimation during the variables selection process of the model. The character also called large sample character, we proofed it.All research of above can solve the problem about the stability of the model which impacted by variable selection. At the end of the paper, we give some suggestions.