Research On Estimation Method Of Logistic Model With Missing Covariates

In today’s big data era of information digitization,various research fields have the problem of missing data,and missing values often have a great negative impact on data inference conclusions.Therefore,in the process of data analysis,missing values need to be handled correctly and appropriately to make the research more meaningful.Logistic regression is a common classification method in supervised learning.The model has the advantages of simple structure and convenient use.It is widely used in biology,medicine,engineering and other disciplines,but there is very little research on the modeling scheme of Logistic model in the problem of missing data;SAEM(Stochastic Approximation EM)algorithm replaces the expectation step of the EM algorithm by one iteration of a stochastic approximation procedure.It has high timeliness and good effect in dealing with missing data,therefore,for the Logistic model with missing covariates,this paper uses the improved SAEM algorithm to model it parametrically.Firstly,NI-missing mechanism is introduced to improve the performance of SAEM algorithm.Secondly,SAEM algorithm is further improved by pseudo continuous method,and a new PC(Pseudo Continuous)-SAEM algorithm is proposed.Through a large number of simulation experiments,the performance of PC-SAEM algorithm is tested under different missing rates,and compared with semiparametric method.The main content of this paper has two aspects.1.Firstly,the performance of NI-missing mechanism is analyzed through comparative experiments.Then,NI-missing mechanism is introduced to improve SAEM algorithm.Through simulation experiments,the improved SAEM algorithm is compared with the semiparametric method in the missing data with the missing rates of 10%,20%,30% and 40%.The experimental results show that the performance of the improved SAEM algorithm is better than that of the semiparametric method when dealing with data with low missing rate,and the running time is much shorter than that of semiparametric method,which is more than 600 times.In addition to the traditional criterion,a new criterion for evaluating the performance of the algorithm,the back judgment accuracy,is proposed and applied to numerical simulation research.2.In order to apply SAEM algorithm to discrete data,firstly,pseudo continuous the missing discrete data,and then use SAEM algorithm to estimate the parameters of missing data.Therefore,a new PC-SAEM algorithm is proposed.Through simulation experiments,in the missing data with missing rates of 5%,10%,20%,30% and 35%,the absolute error,standard error and the back judgment accuracy of dependent variables of parameter estimation results are taken as the criteria to evaluate the performance of PC-SAEM algorithm,through the above criteria,it is compared with the semiparametric method.Finally,the algorithm is applied to two groups of medical data: endometrial cancer and hip fracture.