General Procedure

Abstract

How do I select the right parametric form for an age function? There is no " right " parametric form to add at any stage of the model. Fitting an exploratory non-parametric term gives you an idea about what the shape of a suitable age function should be (given the existing age/period terms in your model), but there may be several candidate functions available to you from your " toolkit " of age functions. Selecting the most appropriate of these is usually a matter of trying them, seeing which gives the best fit to the data, whether they are robust to changes made to other age/period terms in the model, and whether they, in turn, influence other age/period terms. Expert judgement is required to balance these competing factors. Do I fix the parameters for the age and period functions found at previous stages or re-estimate them at each stage? All parameters should be re-estimated at each stage as a check on the robustness of the model. One technique may be to re-estimate all the parameters at each stage, but use the values found previously as the starting point for your maximisation procedure. However, this may lead to a final fitted set of parameters which is not robust to different initial parameter estimates. It also may lead to an inefficient fitting algorithm as the final model can only be estimated by sequentially estimating all of the preceding models in order to provide initial parameter estimates. Therefore, we suggest that this approach should be avoided in the final model. Please see the question below for our approach to setting the initial parameter estimates for the fitting algorithm. The only exception to this is when a new non-parametric age function is added to the model. Mixed models, with non-parametric and parametric age functions (with freely varying parameters) are often unstable and the fitting algorithms may not converge. We therefore fixed the values of the age function parameters to be those estimated previously to avoid this. As the non-parametric terms are added purely to explore the data and will be replaced with parametric functions later (when everything will be re-estimated) we believe this procedure is justifiable.