The Method of Simulated Scores for Estimating Multinormal Regression Models with Missing Values

Given a set of continuous variables with missing data, we prove in this paper that the iterative application of a simple “least-squares estimation/multivariate normal simulation” procedure produces an efficient parameters estimator. There are two main assumptions behind our proof: (1) the missing data mechanism is ignorable; (2) the data generating process is a multivariate normal linear regression. Disentangling the iterative procedure and its convergence conditions, we show that the estimator is a “method of simulated scores” (a particular case of McFadden’s “method of simulated moments”), thus equivalent to maximum likelihood if the number of replications is conveniently large. We thus provide a non-Bayesian re-interpretation of the estimation/simulation problem. The computational procedure is obtained introducing a simple modification into existing algorithms. Its software implementation is straightforward (few simple statements in any programming language) and easily applicable to datasets with large number of variables.