The Application Of Mixed Effect Regression Splines Model On Panel Data

In the study of medicine,biology,economics,finance and agricultural measures,the panel data,or longitudinal data are offten encountered.In order to solve practical problems,scholars put forward the nonparametric regression model of panel data.Developed in the 1990's,nonparametric regression model is an important statistical model.In the solution of actual problem,it can be more close to the true model,making full use of the data provided in the information.Regression splines mixed effects model is a nonparametric regression model on panel data with its high determinability and operability,and wide application.This paper consists of five chapters: the first is the introduction,which describes the background,purpose and significance of this research,as well as systematical analysis of the modeling assumptions and basic forms of panel data mixed effects model.The second one is a part of theory,in which the most widely-used mixed effects model of panel data—regression splines mixed effects model(MERS)—is introduced,including: method of MERS construction,methods for solving the model and for choosing smoothing parameters.The third is simulation comparison.A Monte Carlo simulation comparison is conducted on MERS model and polynomial method.A conclusion is made that MERS model is the optimal in estimating population function compared with polynomial method.But in terms of individual function estimation,the performance of polynomial method is better.In addition,when the relationship between corresponding variables and prediction variables is unkown or complex,MERS model is more robust,and more applicable.The forth is a part of empirical research.The first empirical research studies the relationship of urban-rural income gap and economic growth in China.This part expounds the evolution trend of income gap between urban and rural areas.Empirical analysis is conducted by the construction of the MERS model on the relationship between the income gap and the economic growth.It is proved that there is a inverted-U relationship between the urban-rural income gap and the economic growth.Then,this article estimates the year in which China and its individual provinces reached the peak point of urban-rural income gap and the per capita GDP of the peak point.At last economic and social policies are put forward to close the gap between urban and rural income.The second part is an empirical research of BMI-age relationship based on MERS model.The estimates are made,of the population mean function and its derivative,and of the individual function of the obese and overweight subjects.Base on the the analysis of population,the estimate of the age with the the fastest-growing BMI,is 13.7.And the trigger ages of overweight and obesity are made through the analysis of obese and overweight individuals,with their sample means being 20.41 and 21.17.Theanalysis of obese and overweight individuals shows that the trigger ages of overweight and obesity are mostly between the age of 15 and the age of 25,so that,there is a need for diet and exercise intervention in high school and college.The last one is a summary of full text.