  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-specific mortality and fertility rates. Finally, the model is used (1)
to predict age-specific mortality using HIV indicators and summary measures of
age-specific mortality, 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 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.
