Adjusting the EM algorithm for design of experiments with missing data

The analysis of designed experiment with missing observation has been dealt by the use of the EM algorithm even before the fundamental paper by Dempster, Laird and Rubin (1977). The direct application of the EM algorithm to a data set following designed experiments such as randomized. block designs, or factorial experiments, with missing observations may lead to the estimation of parametric functions that are not estimable. In this paper we present an adjustment of the EM algorithm for additive classification models that prevents the user from obtaining results which are not reliable. The adjustment consists in applying the R-process introduced by Birkes, Dodge and Seely (1976), that determines which are the estimable parametric functions. The observations and the parameters are then partitioned in a suitable way, and the maximum likelihood estimates for the estimable parametric functions are derived applying EM to each partition. The proposed algorithm is called REM; several numerical examples and one application are presented.