Monte Carlo EM algorithm in logistic linear models involving non-ignorable missing data

Many data sets obtained from surveys or medical trials often include missing observations. Since ignoring the missing information usually cause bias and inefficiency, an algorithm for estimating parameters is proposed based on the likelihood function of which the missing information is taken account. A binomial response and normal exploratory model for the missing data are assumed. We fit the model using the Monte Carlo EM (Expectation and Maximization) algorithm. The E-step is derived by Metropolis-Hastings algorithm to generate a sample for missing data, and the M-step is done by Newton-Raphson to maximize the likelihood function. Asymptotic variances and the standard errors of the MLE (maximum likelihood estimates) of parameters are derived using the observed Fisher information.