Establishment Of The Network Model Based On Longitudinal Data With Its Applications

Longitudinal data are widely used in the fields of economics,medicine,psychology,sociology and so on,which is the data of repeated measurement for several experimental individuals according to the evolution of time,and has the characteristics of both time series and cross section data.At present,there are many methods to model the longitudinal data.This paper gives a study on the longitudinal data based on the ordinary differential equation(ODE)model.This paper establishes a network model,combining the characteristics of ordinary differential equation and longitudinal data and considering the interrelationship between multiple variables from two angles of time and individual.In practical applications,the parameters in models are often not directly obtained,and need to be estimated by observation data.Therefore,accurate estimation of parameters in the model is very important for building suitable models to better evaluate and predict.To avoid the problem of large amount of computation in traditional method of parameter estimation,two-step estimation method is proposed by literature.The computation of two-step estimation method is small,but there is a boundary effect,which will affect the accuracy of parameter estimation.Therefore,it is often difficult to balance computation and estimation accuracy in actual models.As for defects of the above ODE model,an effective statistical diagnosis method is proposed in this paper.On the basis of this,we come up with an adaptive two-step estimation method for ODE model.First,based on two-step estimation method,the local perturbation analysis of the ODE model in the classical Euclidean space is extended to function space in this paper.In the two cases where the redundant parameters exist and do not exist in the model,we make the local perturbation analysis of the independent variable,the dependent variable and the weight function respectively,and discussing the specific expression of the diagnostic function under the three cases.Next,aiming at the boundary effect problem in the statistical diagnosis model,on the basis of the above statistical diagnosis results,we choose the right weighting function to balance the boundary effect and parameter estimation efficiency,so that we can get the optimal parameter estimation,which is called the adaptive two step estimation method.The proposed statistical diagnosis method and the adaptive two-step estimation method in this paper are carried out in the simulation experiment and the case analysis.From the analysis of the experimental results,we can find that:(1)the local perturbation analysis method proposed in this paper can effectively detect the strong influence points in the observed values,but the sensitivity of the different regions to the disturbance is different.Moreover,the model has boundary effect;(2)the adaptive two-step estimation method is more accurate than the traditional two-step estimation method,and preserves the advantages of the two-step estimation,which well balances the computation and accuracy in the parameter estimation.