  Age-period-cohort (APC) models are frequently used in a variety of health and
demographic related outcomes. Fitting and interpreting APC models to data in
equal intervals (equal age and period widths) is non-trivial due to the
structural link between the three temporal effects (given two, the third can
always be found) causing the well-known identification problem. The usual
method for resolving the structural link identification problem is to base a
model off identifiable quantities. It is common to find health and demographic
data in unequal intervals, this encounters further identification problems on
top of the structural link. We highlight the new issues by showing quantities
that were identifiable for equal intervals are no longer identifiable for
unequal data. Furthermore, through extensive simulation studies, we show how
previous methods for unequal APC models are not always appropriate due to their
sensitivity to the choice of functions used to approximate the true temporal
functions. We propose a new method for modelling unequal APC data using
penalised smoothing splines. Our proposal effectively resolves any additional
issues that arise and is robust to the choice of the approximating function. To
demonstrate the effectiveness of our proposal, we conclude with an application
to UK all-cause mortality data from the Human mortality database (HMD).
