Abstract

Conventional methods of decomposing the difference between two rates, such as Kitagawa’s classic component analysis, are confined to taking the average of compositional differences. I propose a more general modeling approach involving three steps: (1) A system of equations with the various additive components of the rate difference is set up; (2) unknowns (refined rate differences) are estimated with Clogg’s purging method; (3) the components are calculated. I use an example of U.S. mortality data to compare the proposed method with the conventional ones. The method can be generalized to decompositions for multiple groups and for multiple confounding factors. Kitagawa's method is a special case of this general approach.

An erratum to this article is available at http://dx.doi.org/10.1007/BF03201476.

References

Cho, L. J., & Retherford, R. D. (
1973
).
Comparative analysis of recent fertility trends in East Asia
Proceedings of the 17th General Conference of the IUSSP, August 1973
(pp.
163
181
).
Liège, Belgium
:
International Union for the Scientific Study of Population
.
Clogg, C. C. (
1978
).
Adjustment of rates using multiplicative models
.
Demography
,
15
,
523
539
. 10.2307/2061204
Clogg, C. C, & Eliason, S. R. (
1988
).
A flexible procedure for adjusting rates and proportions, including statistical methods for group comparisons
.
American Sociological Review
,
53
,
267
283
. 10.2307/2095692
Clogg, C. C, J. W. Schockey, and S. R. Eliason. 1987. A General Statistical Framework for Adjustment of Rates. Unpublished manuscript, Pennsylvania State University, Population Issues Research Center.
Das Gupta, P. (
1978
).
A general method of decomposing a difference between two rates into several components
.
Demography
,
15
,
99
112
. 10.2307/2060493
Kim, Y. J., & Strobino, D. M. (
1984
).
Decomposition of the difference between two rates with hierarchical factors
.
Demography
,
21
,
361
372
. 10.2307/2061165
Kitagawa, E. M. (
1955
).
Components of a difference between two rates
.
Journal of the American Statistical Association
,
50
,
1168
1194
. 10.2307/2281213
Kobrin, F. E. (
1973
).
Household headship and its changes in the United States, 1940–1960, 1970
.
Journal of the American Statistical Association
,
68
,
793
800
. 10.2307/2284502
Vital Statistics of the United States, 1970 (Vol. 2): Mortality, Part B
. (
1974
).
Washington, D.C
:
U.S. Government Printing Office
.
Vital Statistics of the United States, 1985 (Vol. 2): Mortality, Part B
. (
1988
).
Washington, D.C
:
U.S. Government Printing Office
.
Estimates of the Population of the United States, by Age, Sex, and Race: 1970–75
. (
1975
).
Washington, D.C
:
U.S. Government Printing Office
.
Estimates of the Population of the United States, by Age, Sex, and Race: 1980–86
. (
1987
).
Washington, D.C
:
U.S. Government Printing Office
.