Longitudinal Data Analysis And Its Applications Based On Mixed Effects Model

In many fields such as clinical and biomedical applications,it is often necessary to perform repeated measurements on different sources and different types of research objects.For the modeling and analysis of such longitudinal data,the mixed-effects model provides a useful and flexible framework,such as Two-step estimation,generalized estimating equation(GEE)estimator,standard partial multinomial estimator,etc.However,none of the above-mentioned traditional nonparametric regression modeling methods takes into account the estimation of the random effect curve.At the same time,in the actual application of longitudinal data,there are often situations in which multiple variables have significant effects on the observed individuals.When the number of variables is large,the multiple correlations between the variables may cause serious estimation errors;and some of the response variables There is no significant impact,and even variables with no correlation may increase the computational complexity of the model,thereby affecting the estimation efficiency.If we can simplify the most complex variables into a few variables that contain most of the effective information,and then combine the non-parametric mixed effect model for modeling and analysis,it will have a profound reality in optimizing the overall estimation effect and improving the calculation efficiency.significance.At present,there are relatively few researches in this area.This article will focus on the mixed effect model modeling method under factor analysis,and apply the method proposed in this article to the study of the development status of free trade pilot zones in the economic field.This article introduces the basic concepts of mixed effects models,local polynomial estimation,generalized cross-validation criteria,factor analysis and other methods,as well as the current research status at home and abroad.Based on the existing theoretical foundation,focusing on the two aspects of model construction and parameter estimation,expanding on the traditional model,and proposing a non-parametric mixed effects model based on factor analysis.Through factor analysis,the original variable is compressed,the data dimension is reduced,and the common factor containing most of the information is extracted as the new variable.Then through Taylor expansion,the estimator is calculated and solved under the assumption of model normality.At the same time,when determining the model parameters,a generalized cross-validation criterion is introduced to select the optimal bandwidth,and finally the local polynomial estimator(FAC＿LLME)under factor analysis is obtained.Secondly,in a large number of simulation studies,the local polynomial estimator(FAC＿LLME)under factor analysis was compared with the existing mixed-effects model estimator(LLME): On the one hand,from the perspective of the accuracy of the estimation,it is estimated after multiple simulations The average mean square error between the actual value and the true value verifies the superiority of the new method’s estimation performance;on the other hand,through different values of the simulated parameters(the number of observed individuals and the data missing rate),compare the FAC＿LLME estimator and the The LLME estimator estimates the difference in performance.The results prove that compared with LLME,the FAC＿LLME method studied in this paper performs better than the existing methods in terms of fitting effect and mean square error,especially when the internal correlation of the observed individuals is small.In the empirical analysis part,the focus is on the Chongqing Free Trade Zone as the research object.The establishment of the Chongqing Pilot Free Trade Zone(Chongqing Free Trade Zone for short)is an important strategy for the Party Central Committee and the State Council to comprehensively deepen reforms,expand opening up,and further promote the construction of the “Belt and Road”,the development of the Yangtze River Economic Belt,and the Western Development Strategy under the new situation.Initiatives.Enterprises in the free trade zone(including listed companies)are important "cells" for the growth of the free trade zone.The quality of their development directly affects the reputation and image of the free trade zone and its attractiveness to other domestic and foreign companies,even related to The level and status of China’s economic development in the international arena.In-depth study of the development of enterprises in the free trade zone,analysis of future economic trends through model modeling,helping enterprises to identify weak links,further seek advantages and avoid disadvantages,deepen internal management,improve the quality of enterprise development,and enable the Each "cell" is more dynamic,which is of great practical significance for promoting local reform and development and economic construction.This paper collects the main economic indicator data of all 16 listed companies in the Chongqing Free Trade Zone.Through factor analysis,the 7 original variables are reduced according to the principle of cumulative variance contribution rate,and the compressed 2 common factors are obtained,combined with the mixed effect.The model performs modeling estimation,and finally obtains the estimated curve of the total asset changes of listed companies.According to the results of the empirical analysis,it will provide a certain theoretical basis for the construction and development of listed companies in the free trade zone and even the entire Chongqing free trade zone.