Incomplete Data Parameters Logistic Regression Models

Logistic regression model is a model of binary dependent variable (namely y=1or y=0) to do regression analysis which is widely used. In recent years, Statisticalwork which is related to the Logistic regression model is a research direction ofconcern in statistical regression theory, including its parameter estimation、return tothe independent variable selection、random effect、statistical inference and so on.According to this frontier research field, to choose the Logistic regression modelparameter estimation as the research content of this master’s degree thesis.For many problems in reality, however, we often miss or can’t get some part ofdata, such as some of the individual reluctant to provide information investigatorsneeded in sampling investigation, researchers can’t pick up the complete information,abandon or lost data by human error, etc. All in all, missing data in the data analysis,data mining, etc, often appears in the sample survey, social and economic research inareas such as image processing, is also universal. In order to solve the situation, theLogistic regression model parameter estimation problem in the situation of missingdata discussed in this master’s degree thesis.Paper first introduces the data missing problem, the logistic regression model andits property, model parameter estimation method, the solution to the problem requiredby EM algorithm theory also has made the brief statement. Secondly, based on EMalgorithm, in view of the data loss situation, model of maximum likelihood estimationwas deduced in detail the EM algorithm. Lastly, related to the actual data, theapplication of stochastic simulation method, has carried on the empirical research forthis article. Experimental results show that in the absence of data, using the EMalgorithm for maximum likelihood estimate logistic regression model, the estimationprecision is higher, and the algorithm is feasible.