Simulation Research And Application Of Factor Analysis Model With Factor Following Gamma Distribution

As an important analysis technology of multivariate statistical analysis,factor analysis plays an important role in data dimension reduction,but the traditional factor analysis model assumes that the factors follow normal distribution,which is not appropriate in some application research fields where the data are non negative.In this paper,a more practical factor model is constructed based on the assumption that the factors obey the gamma distribution,and then the maximum likelihood estimation method based on EM algorithm is used to study the parameter estimation of the model.Step E is implemented by the Metropolis-Hastings algorithm in MCMC method.When doing empirical analysis,in order to facilitate the interpretation of the analysis results,this paper defines the true loading matrix to explain the analysis results of the model.In the analysis of the results,this paper uses the factor analysis model of gamma distribution to do empirical analysis on the real student achievement data.In order to highlight the unique advantages of the new factor analysis model,this paper compares the new model with the original model.First of all,the author compares the two models by using simulation data to explain that it is unreasonable to use the traditional factor analysis model to do factor analysis when the factors really obey the gamma distribution;then,the new model and the original model are used to do factor analysis on the real student achievement data.The results show that under the premise of the same number of factors,the new model has better information extraction ability than the original model,and the new model can extract the information in the original data more fully.Therefore,the research results show that the topic selection and research results of the factor model studied in this paper are of theoretical and practical value.