The PTOPALS buildmethod fits fertility rates by representing them relative to a standard fertility curve in terms of a linear P-Spline (see Dyrting 2018).
The user must specify the population at risk and the standard fertility using an extrainfo string of the form PTOPALS:PInfo,SInfo[,ExtraInfo]. If PInfo is a number then the population in each age interval of the fertility curve is flat at this value. If it is a string then it specifies the name of a PCURVE object. If SInfo is a number then the standard fertility rates are flat at this value. If it is a string then it specifies the name of the standard FERTILITY object. ExtraInfo is an optional comma-separated list of quoted strings of the form "Parameter=Value" which can be used to change the method's default settings.
By default PTOPALS uses linear B-Splines. The degree of splines can be changed with the extrainfo string "Degree=m".
By default PTOPALS uses a first order penalty. The order can be changed with the extrainfo string "Order=k".
There are two ways to set the B-Spline knots. The first way is to set the minimum and maximum ages using extrainfo strings "MinAge=\(\minage\)" and "MaxAge=\(\maxage\)" respectively. 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 values are \(\minage=0\) and \(\maxage=55\) and \(\knotspacing=2\). The second way is to set the knots explicitly using the extrainfo string "Knots=\(\minage\)|\(x_1\)|\(x_2\)|\(\ldots\)|\(x_\nintern\)|\(\maxage\)".
By default PTOPALS automatically calculates the penalty \(\pen\) by minimizing the Bayesean information criterion ("Penalty=BIC"). An alternative is the Akaike information criterion ("Penalty=AIC"). The penalty can also be specified explicitly using "Penalty=\(\pen\)".