Parameter Estimation Based On Clustering And Parallel Analysis In Panel Data Models With Grouped Factor Structure

Panel data is a kind of important data,which is generated in many fields such as economy,management and sociology.A key problem in panel data research is parameter estimation of panel data model with group factor structure for unknown groups.The commonly used estimation method in literature is:firstly,a large and rough range of group number and group-specific common factor number is given artificially,then the number of groups and the number of group-specific common factors are selected by C_p-type criteria,finally estimate the model by minimizing the sum of least squared errors.The range of group number given by this estimation method is often not accurate enough:the range of group number given may not contain the real group number,or the range range given is large,which makes the difficulty of determining the group number and the calculation intensity greatly increased.In order to overcome the above shortcomings,this paper proposes an estimation method of group number range based on clustering analysis.Based on this method,the parameters are estimated,which not only improves the estimation accuracy,but also improves the operation intensity.In addition,the group number and group-specific common factor number are selected by C_p-type criteria,which result every time calculate the model scores of group number and group factor number,we need to train the model once,there are many combinations of group number and group factor number,the calculation of model selection is large.This paper proposes a parallel analysis algorithm,which puts the estimation of number of factor into the parameter estimation process of the model.When we use the least square method to solve the factors and factor loads in the model,we add parallel analysis to select the number of factors.It reduces the complexity of solving the model parameters and improves the speed of solving the model in theory.In this paper,three kinds of numerical simulation are given,which are the same as the simulation setting in the literature,small sample sizecorrelation between explanatory variables and factors.The simulation results show that the group number range estimation effect is good,The improved parameter estimation algorithm based on parallel analysis is almost accurate.Finally,this paper makes an empirical analysis of 300shares in Shanghai and Shenzhen stock market.The results show that:The results show that 300 shares in Shanghai and Shenzhen can be divided into three groups according to the factors such as stock return rate;Among the financial indexes of 300 listed companies in Shanghai and Shenzhen,Return on equity(ROE)and Asset liability ratio(DAR)have great influence on stock return rate.At the practical application level,the results of the algorithm proposed in this paper are reasonable,and the algorithm has great practical application value.