On statistical Computing via EM Algorithm in Logistic Linear Models Involving Non-ignorable Missing data

Many data sets obtained from surveys or medical trials often include missing observations. When these data sets are analyzed, it is general to use only complete cases. However, it is possible to have big biases or involve inefficiency. In this paper, we consider a method for estimating parameters in logistic linear models involving non-ignorable missing data mechanism. A binomial response and normal exploratory model for the missing data are used. We fit the model using the EM algorithm. The E-step is derived by Metropolis-hastings algorithm to generate a sample for missing data and Monte-carlo technique, and the M-step is by Newton-Raphson to maximize likelihood function. Asymptotic variances of the MLE's are derived and the standard error and estimates of parameters are compared.