\( \newcommand{\pen}{\lambda} \newcommand{\minage}{\alpha} \newcommand{\maxage}{\beta} \newcommand{\knotspacing}{\Delta x} \newcommand{\nintern}{n} \newcommand{\ceil}[1]{\left\lceil #1\right\rceil} \)

Smoothed ASFR

Smooths a fertility curve by fitting fertility rates using cubic P-Splines. The penalty is chosen to minimize the Bayesian Information Criterion.

ExtraInfo

Degree

By default SMOOTHED_ASFR uses cubic B-Splines. The degree of splines can be changed with the extrainfo string "Degree=m".

Order

By default SMOOTHED uses a third order penalty. The order can be changed with the extrainfo string "Order=k".

Knots

There are two ways to set the B-Spline knots. In the first way minimum age \(\minage\) and maximum age \(\maxage\) are taken from the Age column of the fertility object being smoothed. The internal points are then equally spaced upwards from \(\minage\) as follows \begin{eqnarray} x_i&=&\minage+\knotspacing\times i,\quad i=1,\ldots,\nintern\\ \end{eqnarray} where \begin{equation} \nintern=\ceil{\frac{\maxage-\minage}{\knotspacing}}-1 \end{equation} and the spacing \(\knotspacing\) is specified by the extrainfo string "KnotSpacing=\(\knotspacing\)". The default value is \(\knotspacing=2\). The second way is to set the knots explicitly using the extrainfo string "Knots=\(\minage\)|\(x_1\)|\(x_2\)|\(\ldots\)|\(x_\nintern\)|\(\maxage\)".