Decomposition of the difference between two rates with hierarchical factors

A decomposition method for the difference between two rates when data are classified by two factors, one of which may be considered as a more direct factor than the other for the event under consideration, is presented in this paper. The two factors are treated as hierarchical and thus this method is conceptually different from the decomposition methods of Kitagawa (1955) and Das Gupta (1978), in which two factors are treated as symmetrical. Our method is shown to be a balanced version of the Cho-Retherford (1973) decomposition method. Analyses of neonatal mortality rates using our method are presented as an example.