A Singular Value Decomposition-based Factorization and Parsimonious Component Model of Demographic Quantities Correlated by Age: Predicting Complete Demographic Age Schedules with Few Parameters
May 2014 CSSS Working Paper #143
Background. Formal demography has a long history of building simple models of age schedules of demographic quantities, e.g. mortality and fertility rates. These are widely used in demographic methods to manipulate whole age schedules using few parameters.
Objective. The Singular Value Decomposition (SVD) factorizes a matrix into three matrices with useful properties including the ability to reconstruct the original matrix using many fewer, simple matrices. This work demonstrates how these properties can be exploited to build parsimonious models of whole age schedules of demographic quantities that can be further parameterized in terms of arbitrary covariates.
Methods. The SVD is presented and explained in detail with attention to developing an intuitive understanding. The SVD is used to construct a general, component model of demographic age schedules, and that model is demonstrated with age-specificmortality and fertility rates. Finally, the model is used (1) to predict age-specific mortality using HIV indicators and summary measures of age-specificmortality, and (2) to predict age-specific fertility using the total fertility rate (TFR).
Results. The component model of age-specific mortality and fertility rates succeeds in reproducing the data with two inputs, and acting through those two inputs, various covariates are able to accurately predict full age schedules.
Conclusions. The SVD is a potentially useful as a way to summarize, smooth and model age-specific demographic quantities. The component model is a general method of relating covariates to whole age schedules.
Comments. The focus of this work is the SVD and the component model. The applications are for illustrative purposes only.
Keywords: Singular Value Decomposition, SVD, Age-specific Model, Component Model, Mortality, Fertility, Predicting demographic age schedules