EM Algorithm and Missing Information for Left-Inflated Mixture Models

Data with bound-inflated responses are common in many areas of application. Often the data are bounded below by a real number (e.g., zero) with a substantial portion of observations at the boundary value. One approach to analyze such data is the general class of left-inflated mixture models. As a competitive alternative to the quasi-Newton BFGS method, we implement in this article the EM algorithm and the Louis method to estimate the inflated mixture models and obtain the asymptotic standard errors based on the complete data. In addition, the generalized Louis method is formulated, which provides a consistent covariance estimator robust to mis-specification of the covariance structure for correlated data in general incomplete data problems. The methods are illustrated with an ultrasound safety study in laboratory rabbits.