Some Discussions On Generalized Linear Models With Missing Data

Research on Missing Data is the topical issues in statistics, while the missing data often occurs in practice. The commonly-used statistical methods can not be applied directly due to the missing data. Then we should explore new methods to process these data.Generalized liner model is the extension of the linear regression model. The corresponding probability distributions belong to the exponential family distribution. Most researches focused on the conditions that the missing data is negligible both domestically and internationally. Then statistical theories on the generalized liner model should be re-established to deal with these data. However, the missing data in most cases cannot be neglected in practice, the estimated result will be biased if the previous method is still adopted. Therefore, it has profound practical significance to research on the generalized liner model with non-neglectful data.This dissertation introduces the reason, the modes and the classification mechanisms of the missing data. Our dissertation lists several common methods which can be applied to solve the missing data. One example is given to illustrate the weighted adjustment group method.This dissertation illustrates a new graphic method of expression which is to explain the data missing mechanism using the graph theory method. Firstly, the dissertation introduces three independent conditional statements under the data missing mechanism respectively. Secondly, the concrete definitions of m-map and d-separation criteria are given. Finally, it explains these three types of data missing mechanisms by using different graphs.On the theory of the generalized liner models, we list the maximum likelihood estimation and EM algorithm under the condition of missing data. The data missing mechanism and the procedures of missing data are introduced to the generalized liner model. We can get the logistic regression model:(1)If φ1=…=φp+q=0, then MCAR holds.(2)If φmI=0, then MAR holds.(3)If not all φml=0, then NMAR holds.At last, two real examples are given to illustrate the EM algorithm method of dealing with the missing data, the results are excellent by MATLAB software.