Calibrated spline estimation of detailed fertility schedules from abridged data¹

Child mortality estimation: An assessment of summary birth history methods using microsimulation

“…Models for the estimation of the probability of dying between birth and exact ages of early childhood. Single year age-specific fertility rates were smoothed from the WPP abridged data using the calibrated spline estimator developed by Schmertmann (2012). The abridged life tables were interpolated only for ages 2, 3, and 4, to which indirect estimates are sensitive, using the ICM application 18 of the UN's MORTPAK software package (UN 2013b).…”

Fertility progression in Germany: An analysis using flexible nonparametric cure survival models

“…In this paper, we model the transition to the next child using a flexible non-parametric model, based on Bayesian P-splines (Bremhorst and Lambert 2016). Flexible nonparametric modeling was used by demographers before: For example, Gayawan and Adebayo (2013) used Bayesian P-splines to model the baseline and the non-linear effects in an extended Cox model when studying the age at first birth in Nigeria, while calibrated splines were specified by Schmertmann (2012) to obtain a flexible estimation of the fertility schedule from abridged data. In this work, we employ post-estimation procedures to visualize the baseline intensities for the total population and the 'susceptible' women (those who had another child).…”

Bayes plus Brass: Estimating total fertility for many small areas from sparse census data

“…We propose a penalised spline interpolation procedure, described in detail in a working paper (Schmertmann 2012: Appendix), for resolving the first issues. This method uses a set of predetermined constants to construct estimated ( F 15–19… F 45–49 ) and (μ 17.5– 17.5 … μ 47.5– 47.5) values from ( f 15–19… f 45–49 ).…”

“…Our earlier article and the supplemental web site for this paper (Schmertmann et al 2012) contain the operational details of the method, so we offer only a brief overview here. Bayesian estimators of all varieties compromise between (1) fitting observed data (e.g., matching the birth/woman ratios in Figure 1), and (2) matching a prior distribution that probabilistically describes any likely features of the parameter set that are known before examining the data.…”