Standardization and decomposition of rates from cross-classified data

Area of Science:

• Social Sciences
• Statistics
• Demography

Background:

• Social scientists traditionally use direct standardization to control for population composition.
• Understanding rate differences requires analyzing compositional and rate factor contributions.

Purpose of the Study:

• To link standardization and decomposition techniques in social science research.
• To provide explicit expressions for standardized rates and factor effects.
• To offer a computational tool for analyzing up to six factors.

Main Methods:

• Direct standardization to adjust for compositional differences.
• Decomposition analysis to quantify contributions of factors to rate differences.
• Derivation of explicit mathematical expressions for cross-classified data.

Main Results:

• Established explicit formulas for standardized rates and factor effects.
• Demonstrated the linkage between standardization and decomposition.
• Developed a general program for analyzing data with multiple factors.

Conclusions:

• The study provides a unified framework for analyzing population rates and their determinants.
• The methods are applicable to cross-classified data with multiple influencing factors.
• The provided program facilitates the application of these techniques in research.