Spline interpolation of demographic data

Abstract

There are many problems in demography involving the smoothing or interpolation of data. Usually a solution is obtained by fitting a polynomial or a suitable model curve. Often, however, fitting a spline proves to be a simple recourse. Splines, were invented nearly 30 years ago and have been shown to have desirable properties. Although spline functions are by no means unknown to demographers, no simple and direct explanation of their application exists. We hope to remedy this deficiency with this expository piece.

Smoothing internal migration age profiles for comparative research

“…Demographers were introduced to cubic splines by Shryock andSiegel (1975), andMcNeil et al (1977) popularised their use to interpolate and smooth demographic data. Since then, cubic splines have been widely used to interpolate migration data based on five-year age groupings (Rogers and Castro 1981;Rogers et al 2010), and smooth migration data classified by single years of age (Castro and Rogers 1983).…”

The use of a new indirect method to estimate ethnic-group fertility rates for subnational projections for England

“…The literature reports various ways in which the estimates of five-year rates can be converted to rates by single year of age, by modelling age-specific fertility curves as mathematical functions (McNeil et al 1977;Hoem et al 1981;Chandola et al 1999;Schmertmann 2003;Peristera and Kostaki 2007). These methods often include the fitting of splines and the application of the Hadwiger function (Hadwiger 1940), which was used for smoothing ASFRs in London boroughs (Hay and Hollis 2005).…”

A new relational method for smoothing and projecting age-specific fertility rates: TOPALS

“…The fit of the third-degree polynomial is less accurate than that of a cubic spline, which is a piecewise cubic function (Hoem et al 1981). Cubic splines are very flexible (McNeil, Trussell, and Turner 1977;Gilks 1986). A cubic spline can be described by…”