Experimental Study On The Effect Of Missing Data On Parameter Estimation Of EM Algorithm

Missing data is a common phenomenon of the social survey dataeven unavoidable. There are many reasons for missing data, such as lost,and no response or answer questions failed, etc. Statistically significant,the record containing the missing data is called incomplete observations.Missing data or incomplete observation has a great influence on theresults of the survey research. The research of how to use the incompletedata to study and analyze started very early, and the EM(Expectation-Maximization) algorithm is one of such research.EM algorithm, one of the maximum likelihood estimation of theparameters of iterative algorithm, has a important applications in theprocessing of incomplete data. Its biggest advantage is simple; numericalcalculation stability; small storage; in particular, each iteration can ensurethe log-likelihood function of observation data is monotonenon-decreasing. The main idea of EM algorithm is: hypothesis the initialvalue of the missing and implicit data first, then estimate the modelparameters, and then use the model parameters to estimate the missingand implicit data value, update the values of the parameters according tothe estimated values of missing and implicit data, repeated iterations aspreviously.The EM algorithm is mainly used in the following two kindsof incomplete data to estimate parameters: first, the observed data is notcomplete, it is the result of the limitations of the observation process; second, the likelihood function is not analytic or the analytic form oflikelihood function is too complex that resulting the failure of thetraditional estimation method of maximum likelihood function. Becauseof the advantage of EM algorithm, EM algorithm is widely used in thetreatment of missing data and parameter estimation with missing databased on the EM algorithm.This paper makes several researches on the problem of estimateparameter with missing data using EM algorithm:(1)Is there any impact on the EM algorithm of the different missingrate, if there is what kind of the impact;(2) The sensitivity analysis of the initial value for EM algorithm;(3)In maximum likelihood estimation, increase the number ofobserved data can effectively improve the accuracy of parameterestimation, whether the conclusion is applied to EM algorithm, If not,what the requirements of the EM algorithm for the number of observationdata.This paper obtain some conclusions from computer simulationexperiment based on the above three points, and verified the conclusionthrough the actual case.