An ML estimation method is proposed for a recursive model of categorical variables which is too large to handle as a single model. The whole model is first split into a set of submodels which can be arranged in the form of a tree. Two conditions are suggested as an instrument for estimating the parameters of the whole model yet working within individual submodels. Theorems are proved to the effect that, when missing values are involved, the principle of EM can be generalized and applied to the tree of submodels so that the ML estimation is possible for a recursive model of any size. For illustration, the proposed method is applied successfully to real data where 28 binary variables are involved. (c) 2004 Elsevier B.V. All rights reserved.