A general method of decomposing a difference between two rates into several components

Abstract

In her work on the components of a difference between two rates, Kitagawa (1955) was successful in dividing the difference into the rate effect and the effect of the factor, for data classified by one factor. Her formulation for data classified by two factors, however, involves an interaction term which is difficult to interpret. Retherford and Cho (1973) devised a method that does not include any interaction terms. However, their method has other limitations, such as the dependence of the results on the order in which the effects of the factors are computed. In this paper, we provide a general method capable of handling any number of factors, which is developed along the lines suggested by Kitagawa and by Retherford and Cho but without the limitations of their methods.