Experiments in Modelling Recent Danish Fertility Curves
Level 4 - case-series / case-control
Level is by design analogy (methodological curve-fitting study on aggregate demographic time-series data).
OpenAlex W1987329690 · doi:10.2307/2061095
What was done
Least-squares curve fitting was performed on annual sets of Danish age-specific fertility rates covering 1962 through 1971. Nine distinct functional forms were evaluated: a cubic spline, Hadwiger function, Coale-Trussell function, gamma density, beta density, two polynomial variants, two of Brass's relational procedures, and the Gompertz curve.
What was found
The abstract reports no numerical goodness-of-fit statistics or error values. Descriptively, the cubic spline function fit all annual fertility curves substantially better than any alternative model. The Coale-Trussell procedure and gamma density demonstrated comparable second-tier performance, followed closely by the Hadwiger function. One polynomial variant showed acceptable fit, whereas beta densities, Brass relational methods, Gompertz curves, and the other polynomial variant performed poorly.
Why it matters
This study provides an empirical comparison of mathematical and demographic functions for representing empirical age-specific fertility distributions, showing that flexible non-parametric splines capture empirical curves better than rigid classical parametric models.
Limits
The abstract provides no quantitative goodness-of-fit metrics (such as R-squared or root-mean-square error). Analysis is limited to a single country across a single decade (Denmark, 1962–1971), and the performance of these mathematical forms may not generalize to populations with differing reproductive patterns or data quality.
Cited by
- context The age distribution of motherhood across societies fits a bell curve with approximately a 98% R-squared match.