Longitudinal Functional Dynamic Regression Analysis

Longitudinal data and functional data are important means to analyze social science problems such as biomedicine,meteorology,and transportation.It is of great significance to consider the characteristics of longitudinal data and functional data to establish dynamic regression.Combined with longitudinal data and functional data,this paper analyzes the meteorological data from meteorological stations in several cities in China from January 1,2015 to February 29,2016,establishes a model between temperature and wind speed,realizes the prediction of wind speed,and makes a contribution to the acquisition of wind energy.Firstly,this paper improves the existing functional regression model.Considering that the influence of functional predictors on response variables changes dynamically with time,a longitudinal dynamic regression model between functional predictors and response functions is constructed.Model does not directly to response model,but the response of function model,so as to adapt to the actual application in many itself does not meet the normal distribution but after simple transform satisfy normal distribution of data,expanding the scope of application of the model,and the connection function do not take the given method in advance,but through the actual data fitting,make full use of the data and information,improve the model fitting accuracy.The model not only considers the influence of functional predictors on the response variables,but also considers the influence of scalar predictors and random effects between individuals on the response,which reduces the fitting error and makes the model more explanable.Secondly,the marginal covariance function of functional predictors was decomacted by using principal component analysis method,and the potential functional predictors and regression coefficients were expanded by using its empirical feature basis.Then,the regression model was expanded by combining B-spline basis function.Then the kernel function method is used to estimate the connection function and the maximum likelihood method is used to estimate and solve the model parameters.Finally,through the simulation results and actual data analysis,the model proposed in this paper has better fitting effect and practical significance.