Subsampling Method For Large Sample Linear Mixed Effect Model And Its Application

The rapid development of science and technology in the past decade has brought a lot of data.One of the main challenges is that the progress of computing resources is still far behind the exponential growth of the database.One normal method for dealing with large-scale data sets is subsampling.For example,It is an important sampling distribution by using the empirical statistical leveraging scores in the linear regression model in order to improve computational efficiency of least-squares estimtor.This paper considers constructing a new leverage sampling method for panel data,then applying it to the mixed effect model,and studying the excellent properties of the new method through random simulation.This paper mainly considers the subsampling of the mixed effect model in the case of large samples.In the error component regression model,there will be repeated observations for each individual.When the number of individuals is large,the repeated observations further magnify the scale of the data.Therefore,it is proposed to reduce the computational complexity by using the subsampling algorithm.Firstly,according to the nature of correlation within the group based on the panel data,this paper constructs a method for determining the leveraging weight of group data,and then uses it as the sampling probability of sub-samples.Furthermore,we conducted a random simulation comparison study between the new method and the uniform sampling method and then applied the sampling method to the multivariate normal distribution,the T distribution with a degree of freedom of 1,and the T distribution with a degree of freedom of 3 in order to verify the effectiveness of the new method.Leverage sampling is designed under the sub-sampling framework,in which a small portion of the data(subsamples)is extracted from all the data,and then the subsamples are used instead of the full sample to perform the expected calculations.Different parameter estimates for the mixed-effects model for panel data extracted using different methods,including uniform sampling estimates(UNIF),leveraged sampling estimates(LEV),and unweighted leveraged sampling estimates(LEVUW).The leverage method uses the leverage score to construct a non-uniform sampling probability,and an interpretable subsampling method can be obtained.Finally,the sampling estimation method is compared and analyzed,and the application range of different sub-sampling methods is given.